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Journal articles on the topic 'String tree amplitude theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

MARUI, MIHO, ICHIRO ODA, and AKIO SUGAMOTO. "A NOTE ON STRING AMPLITUDES AT HIGH ENERGY LIMIT." Modern Physics Letters A 04, no. 22 (October 30, 1989): 2177–83. http://dx.doi.org/10.1142/s0217732389002446.

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2

LI, MIAO. "SOME REMARKS ON TACHYON ACTION IN 2D STRING THEORY." Modern Physics Letters A 08, no. 26 (August 30, 1993): 2481–89. http://dx.doi.org/10.1142/s0217732393002804.

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We discuss the effective action of tachyon in the two-dimensional string theory at tree level. We show that even starting from the cubic terms the action is nonlocal and the usually assumed simplest cubic term does not give the correct amplitude. Four-point 1PI terms are also discussed.

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3

SATHIAPALAN, B. "LOOP VARIABLES AND GAUGE INVARIANCE IN CLOSED BOSONIC STRING THEORY." Modern Physics Letters A 19, no. 38 (December 14, 2004): 2857–70. http://dx.doi.org/10.1142/s0217732304015713.

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We extend an earlier proposal for a gauge-invariant description of off-shell open strings (at tree level), using loop variables, to off-shell closed strings (at tree level). The basic idea is to describe the closed string amplitudes as a product of two open string amplitudes (using the technique of Kawai, Lewellen and Tye). The loop variable techniques that were used earlier for open strings can be applied here mutatis mutandis. It is a proposal for a theory whose on-shell amplitudes coincide with those of the closed bosonic string in 26 dimensions. It is also gauge-invariant off-shell. As was the case with the open string, the interacting closed string looks like a free closed string thickened to a band.

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4

Dolan, Louise, and Peter Goddard. "Gluon tree amplitudes in open twistor string theory." Journal of High Energy Physics 2009, no. 12 (December 9, 2009): 032. http://dx.doi.org/10.1088/1126-6708/2009/12/032.

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5

NATSUUME, MAKOTO. "ZERO MODE DIVERGENCE PROBLEM IN STRING THEORY." Modern Physics Letters A 09, no. 23 (July 30, 1994): 2113–22. http://dx.doi.org/10.1142/s0217732394001970.

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For 2D string theory, the perturbative S-matrices are not well-defined due to a zero mode divergence. Although there exist formal procedures to make the integral convergent, their physical meanings are not clear. We describe a method to obtain finite S-matrices physically to justify the formal schemes. The scheme uses asymptotic states by wave packets which fall faster than exponentials. It is shown that the scheme gives well-defined S-matrices and justifies the formal shifted Virasoro-Shapiro amplitude for simple processes. The tree-level unitarity for these processes is also shown. We point out a problem in this scheme.

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6

Dolan, Louise, and Peter Goddard. "Tree and loop amplitudes in open twistor string theory." Journal of High Energy Physics 2007, no. 06 (June 4, 2007): 005. http://dx.doi.org/10.1088/1126-6708/2007/06/005.

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7

Dolan, Louise, and Jay N. Ihry. "Conformal supergravity tree amplitudes from open twistor string theory." Nuclear Physics B 819, no. 3 (October 2009): 375–99. http://dx.doi.org/10.1016/j.nuclphysb.2009.04.003.

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8

HADASZ, LESZEK, and ZBIGNIEW JASKÓLSKI. "NONCRITICAL STRING LIOUVILLE THEORY AND GEOMETRIC BOOTSTRAP HYPOTHESIS." International Journal of Modern Physics A 19, no. 13 (May 20, 2004): 2079–93. http://dx.doi.org/10.1142/s0217751x04018427.

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The applications of the existing Liouville theories for the description of the longitudinal dynamics of noncritical Nambu–Goto string are analyzed. We show that the recently developed DOZZ solution to the Liouville theory leads to the cut singularities in tree string amplitudes. We propose a new version of the Polyakov geometric approach to Liouville theory and formulate its basic consistency condition — the geometric bootstrap equation. Also in this approach the tree amplitudes develop cut singularities.

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9

SATHIAPALAN, B. "HOLOMORPHIC FACTORIZATION AND RENORMALIZATION GROUP IN CLOSED STRING THEORY." Modern Physics Letters A 20, no. 15 (May 20, 2005): 1161–76. http://dx.doi.org/10.1142/s0217732305017226.

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The prescription of Kawai, Lewellen and Tye for writing closed string tree amplitudes as sums of products of open string tree amplitudes, is applied to the worldsheet renormalization group equation. The main point is that regularization of the Minkowski (rather than Euclidean) worldsheet theory allows factorization into left-moving and right-moving sectors to be maintained. Explicit calculations are done for the tachyon and the (gauge fixed) graviton.

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10

UKEGAWA, AKINOBU. "OFF-SHELL TREE AMPLITUDES IN HIKKO’S CLOSED STRING FIELD THEORY." International Journal of Modern Physics A 07, no. 20 (August 10, 1992): 5019–26. http://dx.doi.org/10.1142/s0217751x92002283.

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11

BURIKHAM, PIYABUT. "UNIVERSAL OPEN-STRING SINGLET INTERACTION." International Journal of Modern Physics A 22, no. 01 (January 10, 2007): 29–39. http://dx.doi.org/10.1142/s0217751x07035264.

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We argue the existence of a universal open-string interaction induced by open-string singlet exchange from the universality of gravity diagram involving open strings. At the tree level, the interaction is induced by stringy massive excitations of spin-1 and spin-2 at the leading order. The origin of this interaction is purely stringy in nature with the massless contributions canceling each other at the tree level and therefore has no field theory correspondence. The effective dimension-8 interactions at low energies for both spin-1 and spin-2 are given for the four-fermion processes. The spin-2 piece of the interaction to a pair of vector bosons is twice as strong as when it couples to a pair of fermions as a result of the SUSY constraint on the amplitudes and angular momentum decomposition. The massive spin-2 piece of the interaction is separately universal for fermions and vector bosons, in contrast to conventional massive gravity.

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12

DEMETERFI, KRESIMIR, ANTAL JEVICKI, and JOĀO P. RODRIGUES. "PERTURBATIVE RESULTS OF COLLECTIVE STRING FIELD THEORY." Modern Physics Letters A 06, no. 35 (November 20, 1991): 3199–212. http://dx.doi.org/10.1142/s0217732391003699.

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We present a summary of perturbative results obtained in the framework of collective string field theory. We discuss computations of tree-level scattering amplitudes, loop corrections to tachyon self-energy, ground state energy and finite temperature free energy. A comparison with results obtained in different approaches is given. We also discuss the physical implications of our results.

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13

MARSHAKOV, A. V., and A. V. ZABRODIN. "NEW P-ADIC STRING AMPLITUDES." Modern Physics Letters A 05, no. 04 (February 10, 1990): 265–74. http://dx.doi.org/10.1142/s0217732390000317.

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It is shown that the branching multiplicative characters (corresponding to certain quadratic extensions) of the p-adic number fields can be used to construct the tree amplitudes in the p-adic string theory. In particular, the p-adic analogues of the tachyon amplitudes in the Neveu-Schwarz sector of the superstring and the p-adic amplitudes of the emission of the massless vector particles for the bosonic non-archimedean string are obtained.

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14

SATHIAPALAN, B. "LOOP VARIABLES IN STRING THEORY." International Journal of Modern Physics A 18, no. 05 (February 20, 2003): 767–809. http://dx.doi.org/10.1142/s0217751x03012126.

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The loop variable approach is a proposal for a gauge-invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space–time gauge invariance rather than world sheet properties. In essence it is a version of Wilson's exact renormalization group equation for the world sheet theory. It involves all the massive modes and is defined with a finite world sheet cutoff, which allows one to go off the mass-shell. On shell the tree amplitudes of string theory are reproduced. The equations are gauge-invariant off shell also. This paper is a self-contained discussion of the loop variable approach as well as its connection with the Wilsonian RG.

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15

SPRADLIN, MARCUS. "YANG-MILLS AMPLITUDES FROM STRING THEORY IN TWISTOR SPACE." International Journal of Modern Physics A 20, no. 15 (June 20, 2005): 3416–19. http://dx.doi.org/10.1142/s0217751x05026698.

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Tree-level gluon scattering amplitudes in Yang-Mills theory frequently display simple mathematical structure which is completely obscure in the calculation of Feynman diagrams. We describe a novel way of calculating these amplitudes, motivated by a conjectured relation to twistor space, in which the problem of summing Feynman diagrams is replaced by the problem of solving a certain set of algebraic equations.

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16

AREF’EVA, I. YA, and A. P. ZUBAREV. "DIVERGENCES OF DISCRETE STATES AMPLITUDES AND EFFECTIVE LAGRANGIAN IN 2D STRING THEORY." Modern Physics Letters A 08, no. 16 (May 30, 1993): 1469–76. http://dx.doi.org/10.1142/s0217732393001197.

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Scattering amplitudes for discrete states in 2D string theory are considered. Pole divergences of tree-level amplitudes are observed and residues are interpreted as renormalized amplitudes for discrete states. An effective Lagrangian generating renormalized amplitudes for open string is obtained and the corresponding Ward identities are presented. A relation of this Lagrangian with homotopy Lie algebra is discussed.

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17

CHEKHOV, L. O., A. D. MIRONOV, and A. V. ZABRODIN. "MULTILOOP CALCULUS IN P-ADIC STRING THEORY AND BRUHAT-TITS TREES." Modern Physics Letters A 04, no. 13 (July 10, 1989): 1227–35. http://dx.doi.org/10.1142/s0217732389001428.

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We treat the open p-adic string world sheet as a coset space F=T/Γ, where T is the Bruhat-Tits tree for the p-adic linear group GL (2, ℚp) and Γ⊂ PGL (2, ℚp) is some Schottky group. The boundary of this world sheet corresponds to p-adic Mumford curve of finite genus. The string dynamics is governed by the local gaussian action on the tree T. We find the amplitudes for emission processes of the tachyon states from the boundary.

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18

ZABRODIN, A. "NON-ARCHIMEDEAN STRING ACTION AND BRUHAT-TITS TREES." Modern Physics Letters A 04, no. 04 (February 1989): 367–74. http://dx.doi.org/10.1142/s0217732389000447.

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It is shown that the Bruhat-Tits tree for p-adic linear group GL(2) is a natural non-archimedean analog of the open string world sheet. A boundary of the tree can be identified with the field of p-adic numbers. We construct a lattice quantum field theory on the Bruhat-Tits tree with a simple local Lagrangian and show that it leads to Freund-Olson amplitudes for emission processes of the particle states from the boundary.

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19

Bocardo-Gaspar, Miriam, Hugo García-Compeán, Edgar Y. López, and Wilson A. Zúñiga-Galindo. "Local Zeta Functions and Koba–Nielsen String Amplitudes." Symmetry 13, no. 6 (May 29, 2021): 967. http://dx.doi.org/10.3390/sym13060967.

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This article is a survey of our recent work on the connections between Koba–Nielsen amplitudes and local zeta functions (in the sense of Gel’fand, Weil, Igusa, Sato, Bernstein, Denef, Loeser, etc.). Our research program is motivated by the fact that the p-adic strings seem to be related in some interesting ways with ordinary strings. p-Adic string amplitudes share desired characteristics with their Archimedean counterparts, such as crossing symmetry and invariance under Möbius transformations. A direct connection between p-adic amplitudes and the Archimedean ones is through the limit p→1. Gerasimov and Shatashvili studied the limit p→1 of the p-adic effective action introduced by Brekke, Freund, Olson and Witten. They showed that this limit gives rise to a boundary string field theory, which was previously proposed by Witten in the context of background independent string theory. Explicit computations in the cases of 4 and 5 points show that the Feynman amplitudes at the tree level of the Gerasimov–Shatashvili Lagrangian are related to the limit p→1 of the p-adic Koba–Nielsen amplitudes. At a mathematical level, this phenomenon is deeply connected with the topological zeta functions introduced by Denef and Loeser. A Koba–Nielsen amplitude is just a new type of local zeta function, which can be studied using embedded resolution of singularities. In this way, one shows the existence of a meromorphic continuations for the Koba–Nielsen amplitudes as functions of the kinematic parameters. The Koba–Nielsen local zeta functions are algebraic-geometric integrals that can be defined over arbitrary local fields (for instance R, C, Qp, Fp((T))), and it is completely natural to expect connections between these objects. The limit p tends to one of the Koba–Nielsen amplitudes give rise to new amplitudes which we have called Denef–Loeser amplitudes. Throughout the article, we have emphasized the explicit calculations in the cases of 4 and 5 points.

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20

AREF’EVA, I. YA, P. B. MEDVEDEV, and A. P. ZUBAREV. "INTERACTION OF d=2, c=1 DISCRETE STATES FROM STRING FIELD THEORY." Modern Physics Letters A 08, no. 23 (July 30, 1993): 2167–76. http://dx.doi.org/10.1142/s0217732393001896.

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Starting from string field theory for 2D gravity coupled to c=1 matter we analyze the off-shell tree amplitudes of discrete states. The amplitudes exhibit the pole structure and we use the off-shell calculus to extract the residues and prove that only the residues are constrained by the Ward identities. The residues generate a simple effective action.

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21

Brown, Francis, and Clément Dupont. "Single-Valued Integration and Superstring Amplitudes in Genus Zero." Communications in Mathematical Physics 382, no. 2 (February 24, 2021): 815–74. http://dx.doi.org/10.1007/s00220-021-03969-4.

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AbstractWe study open and closed string amplitudes at tree-level in string perturbation theory using the methods of single-valued integration which were developed in the prequel to this paper (Brown and Dupont in Single-valued integration and double copy, 2020). Using dihedral coordinates on the moduli spaces of curves of genus zero with marked points, we define a canonical regularisation of both open and closed string perturbation amplitudes at tree level, and deduce that they admit a Laurent expansion in Mandelstam variables whose coefficients are multiple zeta values (resp. single-valued multiple zeta values). Furthermore, we prove the existence of a motivic Laurent expansion whose image under the period map is the open string expansion, and whose image under the single-valued period map is the closed string expansion. This proves the recent conjecture of Stieberger that closed string amplitudes are the single-valued projections of (motivic lifts of) open string amplitudes. Finally, applying a variant of the single-valued formalism for cohomology with coefficients yields the KLT formula expressing closed string amplitudes as quadratic expressions in open string amplitudes.

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22

AREF’EVA, I. YA, A. P. ZUBAREV, and P. B. MEDVEDEV. "N-POINT AMPLITUDES FOR d=2, c=1 DISCRETE STATES FROM STRING FIELD THEORY." Modern Physics Letters A 10, no. 30 (September 28, 1995): 2225–37. http://dx.doi.org/10.1142/s0217732395002386.

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Starting from string field theory for 2-D gravity coupled to c=1 matter we analyze N-point off-shell tree amplitudes of discrete states. The amplitudes exhibit the pole structure and we use the oscillator representation to extract the residues. The residues are generated by a simple effective action. We show that the effective action can be directly deduced from a string field action in a special transversal-like gauge.

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23

HADASZ, LESZEK, and ZBIGNIEW JASKÓLSKI. "JOINING-SPLITTING INTERACTION OF NONCRITICAL STRING." International Journal of Modern Physics A 18, no. 15 (June 20, 2003): 2609–46. http://dx.doi.org/10.1142/s0217751x0301423x.

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The joining-splitting interaction of noncritical bosonic string is analyzed in the light-cone formulation. The Mandelstam method of constructing tree string amplitudes is extended to the bosonic massive string models of the discrete series. The general properties of the Liouville longitudinal excitations which are necessary and sufficient for the Lorentz covariance of the light-cone amplitudes are derived. The results suggest that the covariant and the light-cone approach are equivalent also in the noncritical dimensions. Some aspects of unitarity of interacting noncritical massive string theory are discussed.

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24

SANCHEZ, NORMA G. "CLASSICAL AND QUANTUM STRINGS IN PLANE WAVES, SHOCK WAVES AND SPACE–TIME SINGULARITIES: SYNTHESIS AND NEW RESULTS." International Journal of Modern Physics A 18, no. 26 (October 20, 2003): 4797–809. http://dx.doi.org/10.1142/s0217751x03015787.

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Key issues and essential features of classical and quantum strings in gravitational plane waves, shock waves and space–time singularities are synthetically understood. This includes the string mass and mode number excitations, energy–momentum tensor, scattering amplitudes, vacuum polarization and wave-string polarization effect. The role of the real pole singularities characteristic of the tree level string spectrum (real mass resonances) and that of the space–time singularities is clearly exhibited. This throws light on the issue of singularities in string theory which can be thus classified and fully physically characterized in two different sets: strong singularities (poles of order ≥ 2, and black holes) where the string motion is collective and nonoscillating in time, outgoing states and scattering sector do not appear, the string does not cross the singularities; and weak singularities (poles of order < 2, (Dirac δ belongs to this class) and conic/orbifold singularities) where the whole string motion is oscillatory in time, outgoing and scattering states exist, and the string crosses the singularities. Common features of strings in singular wave backgrounds and in inflationary backgrounds are explicitly exhibited. The string dynamics and the scattering/excitation through the singularities (whatever their kind: strong or weak) is fully physically consistent and meaningful.

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25

CUOMO, FRANCESCO, FRANCESCO NICODEMI, ROBERTO PETTORINO, FRANCO PEZZELLA, GIANLUCA SABELLA, and RAFFAELE MAROTTA. "OFF-SHELL TACHYON AMPLITUDES: ANALYTICITY AND PROJECTIVE INVARIANCE." Modern Physics Letters A 16, no. 16 (May 30, 2001): 1035–47. http://dx.doi.org/10.1142/s0217732301004212.

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We compute off-shell three- and four-tachyon amplitudes at tree level by using a prescription based on the requirement of projective invariance. In particular we show that the off-shell four-tachyon amplitude can be put in the same form as the corresponding on-shell one, exhibiting therefore the same analyticity properties. This is shown both for the bosonic and for the fermionic strings. The result obtained in the latter case can be extended to the off-shell four-tachyon amplitude in type 0 theory.

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26

LOWE, DAVID A. "UNITARITY RELATIONS IN c=1 LIOUVILLE THEORY." Modern Physics Letters A 07, no. 28 (September 14, 1992): 2647–57. http://dx.doi.org/10.1142/s0217732392004122.

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We consider the S-matrix of c=1 Liouville theory with vanishing cosmological constant. We examine some of the constraints imposed by unitarity. These completely determine (N,2) amplitudes at tree level in terms of the (N,1) amplitudes when the "plus" tachyon momenta take generic values. A surprising feature of the matrix model results is the lack of particle creation branch cuts in the higher genus amplitudes. In fact, we show that the naive field theory limit of Liouville theory would predict such branch cuts. However, unitarity in the full string theory ensures that such cuts do not appear in genus one (N,1) amplitudes. We conclude with some comments about the genus one (N,2) amplitudes.

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27

Kitazawa, Noriaki. "Toward the stabilization of extra dimensions by brane dynamics." International Journal of Modern Physics A 30, no. 11 (April 16, 2015): 1550055. http://dx.doi.org/10.1142/s0217751x15500554.

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All the models of elementary particles and their interactions derived from String Theory involve a compact six-dimensional internal space. Its volume and shape should be fixed or stabilized, since otherwise massless scalar fields (moduli) reflecting their deformations appear in our four-dimensional space–time, with sizable effects on known particles and fields. We propose a strategy toward stabilizing the compact space without fluxes of three-form fields from closed strings. Our main motivation and goal is to proceed insofar as possible within conventional string worldsheet theory. As we shall see, D-branes with magnetic flux ("magnetized D-branes") and the forces between them can be used to this end. We investigate here some necessary ingredients: open string one-loop vacuum amplitudes between magnetized D-branes, magnetized D-branes fixed at orbifold singularities, and potential energies among such D-branes in the compact space that result from tree-level closed string exchanges.

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28

Brandt, F., F. Machado, and R. Medina. "Open and Closed Superstring Five-Point Amplitudes at Tree-Level." International Journal of Modern Physics A 18, no. 12 (May 10, 2003): 2127–33. http://dx.doi.org/10.1142/s0217751x0301557x.

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In this contribution the tree-level effective actions for gluons and gravitons, as derived from Open and Closed Superstring theories, are reviewed respectively. As known for a long time, at zero order in α′ (the string fundamental constant) the first action is pure Yang-Mills while the second one is pure Einstein-Hilbert. The first Superstring Theory corrections turn up to appear at [Formula: see text] order in the first case while they appear at [Formula: see text] in the second one, as known from the three and four-point scattering amplitudes for gluons and gravitons, respectively. Recent work involving the [Formula: see text] order contributions to the Yang-Mills action is reviewed with some detail, including the authors' present line of research. Also, the uncharted territory of five graviton scattering is commented, looking forward to derive the [Formula: see text] Superstring Theory corrections to the Einstein-Hilbert action.

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29

Ivanov, A. N., R. Höllwieser, N. I. Troitskaya, M. Wellenzohn, and Ya A. Berdnikov. "Gauge properties of hadronic structure of nucleon in neutron radiative beta decay to order O(α/π) in standard V − A effective theory with QED and linear sigma model of strong low-energy interactions." International Journal of Modern Physics A 33, no. 33 (November 30, 2018): 1850199. http://dx.doi.org/10.1142/s0217751x18501993.

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Within the standard [Formula: see text] theory of weak interactions, Quantum electrodynamics (QED) and the linear [Formula: see text]-model (L[Formula: see text]M) of strong low-energy hadronic interactions, we analyze gauge properties of hadronic structure of the neutron and proton in the neutron radiative [Formula: see text]-decay. We show that the Feynman diagrams, describing contributions of hadronic structure to the amplitude of the neutron radiative [Formula: see text]-decay in the tree-approximation for strong low-energy interactions in the L[Formula: see text]M, are gauge invariant. In turn, the complete set of Feynman diagrams, describing the contributions of hadron–photon interactions in the one-hadron-loop approximation, is not gauge invariant. In the infinite limit of the scalar [Formula: see text]-meson, reproducing the current algebra results (S. Weinberg, Phys. Rev. Lett. 18, 188 (1967)), and to leading order in the large nucleon mass expansion the Feynman diagrams, violating gauge invariance, do not contribute to the amplitude of the neutron radiative [Formula: see text]-decay in agreement with Sirlin’s analysis of strong low-energy interactions in neutron [Formula: see text] decays. We assert that the problem of appearance of gauge noninvariant Feynman diagrams of hadronic structure of the neutron and proton is related to the following. The vertex of the effective [Formula: see text] weak interactions does not belong to the combined quantum field theory including the L[Formula: see text]M and QED. We argue that gauge invariant set of Feynman diagrams of hadrons, coupled to real and virtual photons in neutron [Formula: see text] decays, can be obtained within the combined quantum field theory including the Standard Electroweak Model (SEM) and the L[Formula: see text]M, where the effective [Formula: see text] vertex of weak interactions is a result of the [Formula: see text]-electroweak boson exchange.

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30

Fisk, Mark D. "Five-point tree amplitude for the heterotic string." Nuclear Physics B 320, no. 2 (July 1989): 377–400. http://dx.doi.org/10.1016/0550-3213(89)90255-1.

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31

LICCARDO, ANTONELLA, FRANCO PEZZELLA, and RAFFAELE MAROTTA. "CONSISTENT OFF-SHELL TREE STRING AMPLITUDES." Modern Physics Letters A 14, no. 12 (April 20, 1999): 799–808. http://dx.doi.org/10.1142/s0217732399000845.

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We construct off-shell tree bosonic string amplitudes, based on the operatorial formalism of the N-string vertex, with three external massless states both for open and closed strings by requiring them to be projective invariant. In particular our prescription leads, in the low-energy limit, to the three-gluon amplitude in the usual covariant gauge.

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32

Hua, Long, and Michio Kaku. "Shapiro-Virasoro amplitude and string field theory." Physical Review D 41, no. 12 (June 15, 1990): 3748–67. http://dx.doi.org/10.1103/physrevd.41.3748.

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33

Ketov, S. V. "Graviton scattering amplitude in Bose string theory." Soviet Physics Journal 31, no. 12 (December 1988): 966–68. http://dx.doi.org/10.1007/bf01101162.

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34

MELLOR, BLAKE. "TREE DIAGRAMS FOR STRING LINKS." Journal of Knot Theory and Its Ramifications 15, no. 10 (December 2006): 1303–18. http://dx.doi.org/10.1142/s0218216506005159.

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In previous work, the author defined the intersection graph of a chord diagram associated with a string link (as in the theory of finite type invariants). In this paper, we classify the trees which can be obtained as intersection graphs of string link diagrams.

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35

Giddings, Steven B. "The Veneziano amplitude from interacting string field theory." Nuclear Physics B 278, no. 2 (December 1986): 242–55. http://dx.doi.org/10.1016/0550-3213(86)90211-7.

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36

VAISBURD, I. D. "P-LOOP VACUUM AMPLITUDE IN THE OPEN BOSONIC STRING THEORY." Modern Physics Letters A 03, no. 05 (April 1988): 511–16. http://dx.doi.org/10.1142/s0217732388000611.

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37

TSEYTLIN, A. A. "SIGMA MODEL APPROACH TO STRING THEORY." International Journal of Modern Physics A 04, no. 06 (April 10, 1989): 1257–318. http://dx.doi.org/10.1142/s0217751x8900056x.

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A review of the σ-model approach to derivation of effective string equations of motion for the massless fields is presented. We limit our consideration to the case of the tree approximation in the closed Bose string theory.

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38

Sakai, K. "Off-Shell Amplitude in Witten's Bosonic String Field Theory." Progress of Theoretical Physics 80, no. 2 (August 1, 1988): 294–310. http://dx.doi.org/10.1143/ptp.80.294.

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39

Siopsis, George. "Closed string field theory and the Shapiro-Virasoro amplitude." Nuclear Physics B - Proceedings Supplements 11 (October 1989): 406–13. http://dx.doi.org/10.1016/0920-5632(89)90027-3.

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40

PERIWAL, VIPUL. "RENORMALIZATION AND STRING AMPLITUDES." Modern Physics Letters A 04, no. 01 (January 1989): 33–37. http://dx.doi.org/10.1142/s0217732389000058.

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41

PAL, SHESANSU SEKHAR. "A NOTE ON NONCOMMUTATIVE STRING THEORY AND ITS LOW ENERGY LIMIT." International Journal of Modern Physics A 18, no. 10 (April 20, 2003): 1733–47. http://dx.doi.org/10.1142/s0217751x03014162.

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The noncommutative string theory is described by embedding open string theory in a constant second rank antisymmetric Bμν field and the noncommutative gauge theory is defined by a deformed ⋆ product. As a check, the study of various scattering amplitudes in both noncommutative string and noncommutative gauge theory confirms that in the α′ → 0 limit, the noncommutative string theoretic amplitude goes over to the noncommutative gauge theoretic amplitude and the couplings are related as [Formula: see text]. Furthermore, we show that in this limit there will not be any correction to the gauge theoretic action because of the absence of massive modes. We get sin/cos factors in the scattering amplitudes depending on the odd/even number of external photons.

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42

Graehl, Jonathan, Kevin Knight, and Jonathan May. "Training Tree Transducers." Computational Linguistics 34, no. 3 (September 2008): 391–427. http://dx.doi.org/10.1162/coli.2008.07-051-r2-03-57.

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Many probabilistic models for natural language are now written in terms of hierarchical tree structure. Tree-based modeling still lacks many of the standard tools taken for granted in (finite-state) string-based modeling. The theory of tree transducer automata provides a possible framework to draw on, as it has been worked out in an extensive literature. We motivate the use of tree transducers for natural language and address the training problem for probabilistic tree-to-tree and tree-to-string transducers.

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43

Hatefi, Ehsan. "Three Point Tree Level Amplitude in Superstring Theory." Nuclear Physics B - Proceedings Supplements 216, no. 1 (July 2011): 234–38. http://dx.doi.org/10.1016/j.nuclphysbps.2011.04.166.

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Freedman, Daniel Z., Steven B. Giddings, Joel A. Shapiro, and Charles B. Thorn. "The nonplanar one-loop amplitude in Witten's string field theory." Nuclear Physics B 298, no. 2 (March 1988): 253–322. http://dx.doi.org/10.1016/0550-3213(88)90268-4.

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Yahikozawa, Shigeaki. "Evaluation of the one-loop amplitude in heterotic string theory." Physics Letters B 166, no. 2 (January 1986): 135–40. http://dx.doi.org/10.1016/0370-2693(86)91364-x.

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Dayi, Ömer F. "Four-photon scattering amplitude in bosonic open string field theory." Physics Letters B 200, no. 4 (January 1988): 471–77. http://dx.doi.org/10.1016/0370-2693(88)90154-2.

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47

NAKAZAWA, NAOHITO, KENJI SAKAI, and JIRO SODA. "RENORMALIZATION GROUP FLOW AND OPEN STRING DYNAMICS." Modern Physics Letters A 03, no. 18 (December 1988): 1797–805. http://dx.doi.org/10.1142/s0217732388002166.

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The renormalization group flow in the nonlinear sigma model approach is explicitly solved to the fourth order in the case of an open string propagating in the tachyon background. Using a regularization different from the original one used by Klebanov and Susskind (K-S), we show that its fixed point solution produces the tree-level 5-point tachyon amplitude. Furthermore we prove K-S’s conjecture, i.e., the equivalence between the vanishing β-function defined by our regularization and the equation of motion arising from the effective action, up to all orders.

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48

Guellouma, Younes, Hadda Cherroun, Djelloul Ziadi, and Bruce W. Watson. "From Tree Automata to String Automata Minimization." Theory of Computing Systems 62, no. 5 (September 27, 2017): 1203–22. http://dx.doi.org/10.1007/s00224-017-9815-4.

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49

PASQUINUCCI, ANDREA, and MICHELA PETRINI. "ON THE EVALUATION OF COMPTON SCATTERING AMPLITUDES IN STRING THEORY." International Journal of Modern Physics A 13, no. 27 (October 30, 1998): 4717–57. http://dx.doi.org/10.1142/s0217751x98002237.

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We consider the Compton amplitude for the scattering of a photon and an (massless) "electron/positron" at one loop (i.e. genus 1) in a four-dimensional fermionic heterotic string model. Starting from the bosonization of the world sheet fermions needed to explicitly construct the spin fields representing the space–time fermions, we present all the steps of the computation which leads to the explicit form of the amplitude as an integral of modular forms over the moduli space.

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IOFA, MIKHAIL Z. "DYONIC BLACK HOLES WITH STRING-LOOP CORRECTIONS." International Journal of Modern Physics A 18, no. 11 (April 30, 2003): 1903–33. http://dx.doi.org/10.1142/s0217751x03013740.

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In heterotic string theory compactified to four dimensions with N = 2 supersymmetry, string-loop corrections to the universal sector of the low-energy effective action are studied. Within the framework of N = 2 supersymmetric formulation of the theory, in the first order in string coupling constant, we solve the system of the loop-corrected Maxwell and Killing spinor equations. Taking as the input the tree-level dyonic black hole solution, we calculate string-loop corrections to the string tree-level metric and moduli of dyonic black hole.

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