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Автор: Grafiati

Опубліковано: 14 березня 2023

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1

Tsai, Ya-Wen, Yao-Ting Wang, Pi-Gang Luan, and Ta-Jen Yen. "Topological Phase Transition in a One-Dimensional Elastic String System." Crystals 9, no. 6 (June 18, 2019): 313. http://dx.doi.org/10.3390/cryst9060313.

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Анотація:

We show that topological interface mode can emerge in a one-dimensional elastic string system which consists of two periodic strings with different band topologies. To verify their topological features, Zak-phase of each band is calculated and reveals the condition of topological phase transition accordingly. Apart from that, the transmittance spectrum illustrates that topological interface mode arises when two topologically distinct structures are connected. The vibration profile further exhibits the non-trivial interface mode in the domain wall between two periodic string composites.

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2

Montano, David, and Jacob Sonnenschein. "Topological strings." Nuclear Physics B 313, no. 2 (February 1989): 258–68. http://dx.doi.org/10.1016/0550-3213(89)90318-0.

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3

BALACHANDRAN, A. P., W. D. McGLINN, L. O’RAIFEARTAIGH, S. SEN, R. D. SORKIN, and A. M. SRIVASTAVA. "TOPOLOGICAL SPIN-STATISTICS THEOREMS FOR STRINGS." Modern Physics Letters A 07, no. 16 (May 30, 1992): 1427–42. http://dx.doi.org/10.1142/s0217732392001105.

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Recently, a topological proof of the spin-statistics theorem has been proposed for a system of point particles. It does not require relativity or field theory, but assumes the existence of antiparticles. We extend this proof to a system of string loops in three space dimensions and show that by assuming the existence of antistring loops, one can prove a spin-statistics theorem for these string loops. According to this theorem, all unparametrized strings (such as flux tubes in superconductors and cosmic strings) should be quantized as bosons. Also, as in the point particle case, we find that the theorem excludes non-Abelian statistics.

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4

Liu, Zhengwei, Alex Wozniakowski, and Arthur M. Jaffe. "Quon 3D language for quantum information." Proceedings of the National Academy of Sciences 114, no. 10 (February 6, 2017): 2497–502. http://dx.doi.org/10.1073/pnas.1621345114.

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We present a 3D topological picture-language for quantum information. Our approach combines charged excitations carried by strings, with topological properties that arise from embedding the strings in the interior of a 3D manifold with boundary. A quon is a composite that acts as a particle. Specifically, a quon is a hemisphere containing a neutral pair of open strings with opposite charge. We interpret multiquons and their transformations in a natural way. We obtain a type of relation, a string–genus “joint relation,” involving both a string and the 3D manifold. We use the joint relation to obtain a topological interpretation of theC∗-Hopf algebra relations, which are widely used in tensor networks. We obtain a 3D representation of the controlled NOT (CNOT) gate that is considerably simpler than earlier work, and a 3D topological protocol for teleportation.

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5

WERESZCZYŃSKI, A. "KNOTS, BRAIDS AND HEDGEHOGS FROM THE EIKONAL EQUATION." Modern Physics Letters A 20, no. 15 (May 20, 2005): 1135–46. http://dx.doi.org/10.1142/s0217732305017330.

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The complex eikonal equation in the three space dimensions is considered. We show that apart from the recently found torus knots, this equation can also generate other topological configurations with a nontrivial value of the π2(S2) index: braided open strings as well as hedgehogs. In particular, cylindric strings, i.e. string solutions located on a cylinder with a constant radius are found. Moreover, solutions describing strings lying on an arbitrary surface topologically equivalent to cylinder are presented. We discuss them in the context of the eikonal knots. The physical importance of the results originates in the fact that the eikonal knots have been recently used to approximate the Faddeev–Niemi hopfions.

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6

Li, Xinfei, Xin Liu, and Yong-Chang Huang. "Tackling tangledness of cosmic strings by knot polynomial topological invariants." International Journal of Modern Physics A 32, no. 27 (September 30, 2017): 1750164. http://dx.doi.org/10.1142/s0217751x17501640.

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Cosmic strings in the early universe have received revived interest in recent years. In this paper, we derive these structures as topological defects from singular distributions of the quintessence field of dark energy. Our emphasis is placed on the topological charge of tangled cosmic strings, which originates from the Hopf mapping and is a Chern–Simons action possessing strong inherent tie to knot topology. It is shown that the Kauffman bracket knot polynomial can be constructed in terms of this charge for unoriented knotted strings, serving as a topological invariant much stronger than the traditional Gauss linking numbers in characterizing string topology. Especially, we introduce a mathematical approach of breaking-reconnection which provides a promising candidate for studying physical reconnection processes within the complexity-reducing cascades of tangled cosmic strings.

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7

Achúcarro, A., A. Avgoustidis, A. López-Eiguren, C. J. A. P. Martins, and J. Urrestilla. "Cosmological evolution of semilocal string networks." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2161 (November 11, 2019): 20190004. http://dx.doi.org/10.1098/rsta.2019.0004.

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Semilocal strings—a particular limit of electroweak strings—are an interesting example of a stable non-topological defect whose properties resemble those of their topological cousins, the Abrikosov–Nielsen–Olesen vortices. There is, however, one important difference: a network of semilocal strings will contain segments. These are ‘dumbbells’ whose ends behave almost like global monopoles that are strongly attracted to one another. While closed loops of string will eventually shrink and disappear, the segments can either shrink or grow, and a cosmological network of semilocal strings will reach a scaling regime. We discuss attempts to find a ‘thermodynamic’ description of the cosmological evolution and scaling of a network of semilocal strings, by analogy with well-known descriptions for cosmic strings and for monopoles. We propose a model for the time evolution of an overall length scale and typical velocity for the network as well as for its segments, and some supporting (preliminary) numerical evidence. This article is part of a discussion meeting issue ‘Topological avatars of new physics’.

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8

KAPUSTIN, ANTON. "TOPOLOGICAL STRINGS ON NONCOMMUTATIVE MANIFOLDS." International Journal of Geometric Methods in Modern Physics 01, no. 01n02 (April 2004): 49–81. http://dx.doi.org/10.1142/s0219887804000034.

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We identify a deformation of the N=2 supersymmetric sigma model on a Calabi–Yau manifold X which has the same effect on B-branes as a noncommutative deformation of X. We show that for hyperkähler X such deformations allow one to interpolate continuously between the A-model and the B-model. For generic values of the noncommutativity and the B-field, properties of the topologically twisted sigma-models can be described in terms of generalized complex structures introduced by N. Hitchin. For example, we show that the path integral for the deformed sigma-model is localized on generalized holomorphic maps, whereas for the A-model and the B-model it is localized on holomorphic and constant maps, respectively. The geometry of topological D-branes is also best described using generalized complex structures. We also derive a constraint on the Chern character of topological D-branes, which includes A-branes and B-branes as special cases.

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9

NITTA, MUNETO. "KNOTTED INSTANTONS FROM ANNIHILATIONS OF MONOPOLE–INSTANTON COMPLEX." International Journal of Modern Physics A 28, no. 32 (December 30, 2013): 1350172. http://dx.doi.org/10.1142/s0217751x13501728.

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Monopoles and instantons are sheets (membranes) and strings in d = 5+1 dimension, respectively, and instanton strings can terminate on monopole sheets. We consider a pair of monopole and antimonopole sheets which is unstable to decay and results in a creation of closed instanton strings. We show that when an instanton string is stretched between the monopole sheets, there remains a new topological soliton of codimension five after the pair annihilation, i.e. a twisted closed instanton string or a knotted instanton.

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10

DUAN, YI-SHI, LI-DA ZHANG, and YU-XIAO LIU. "A NEW DESCRIPTION OF COSMIC STRINGS IN BRANE WORLD SCENARIO." Modern Physics Letters A 23, no. 24 (August 10, 2008): 2023–30. http://dx.doi.org/10.1142/s021773230802611x.

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In the light of ϕ-mapping topological current theory, the structure of cosmic strings are obtained from the Abelian Higgs model, which is an effective description to the brane world cosmic string system. In this topological description of the cosmic string, combining the result of decomposition of U(1) gauge potential, we analytically reach the familiar conclusions that in the brane world scenario the magnetic flux of the cosmic string is quantized and the RR charge of it is screened.

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11

Rocek, Martin, Cumrun Vafa, and Stefan Vandoren. "Hypermultiplets and topological strings." Journal of High Energy Physics 2006, no. 02 (February 23, 2006): 062. http://dx.doi.org/10.1088/1126-6708/2006/02/062.

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12

Berkovits, Nathan, and Cumrun Vafa. "N = 4 topological strings." Nuclear Physics B 433, no. 1 (January 1995): 123–80. http://dx.doi.org/10.1016/0550-3213(94)00419-f.

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13

Li, Xinfei, and Xin Liu. "Topological invariants for superconducting cosmic strings." International Journal of Modern Physics A 33, no. 27 (September 27, 2018): 1850156. http://dx.doi.org/10.1142/s0217751x18501567.

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Анотація:

Superconducting cosmic strings (SCSs) have received revived interests recently. In this paper we treat closed SCSs as oriented knotted line defects, and concentrate on their topology by studying the Hopf topological invariant. This invariant is an Abelian Chern–Simons action, from which the HOMFLYPT knot polynomial can be constructed. It is shown that the two independent parameters of the polynomial correspond to the writhe and twist contributions, separately. This new method is topologically stronger than the traditional (self-)linking number method, which fails to detect essential topology of knots sometimes, shedding new light upon the study of physical intercommunications of superconducting cosmic strings as a complex system.

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14

FIORE, R., D. GALEAZZI, L. MASPERI, and A. MEGEVAND. "STRINGS AND NON-TOPOLOGICAL SOLITONS." Modern Physics Letters A 09, no. 06 (February 28, 1994): 557–68. http://dx.doi.org/10.1142/s0217732394003798.

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We have numerically calculated topological and non-topological solitons in two spatial dimensions with Chern-Simons term. Their quantum stability, as well as that of the Maxwell vortex, is analyzed by means of bounce instantons which involve three-dimensional strings and non-topological solitons.

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15

BALACHANDRAN, A. P., and S. DIGAL. "TOPOLOGICAL STRING DEFECT FORMATION DURING THE CHIRAL PHASE TRANSITION." International Journal of Modern Physics A 17, no. 08 (March 30, 2002): 1149–58. http://dx.doi.org/10.1142/s0217751x02005864.

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We extend and generalize the seminal work of Brandenberger, Huang and Zhang on the formation of strings during chiral phase transitions1 and discuss the formation of Abelian and non-Abelian topological strings during such transitions in the early universe and in the high energy heavy-ion collisions. Chiral symmetry as well as deconfinement are restored in the core of these defects. Formation of a dense network of string defects is likely to play an important role in the dynamics following the chiral phase transition. We speculate that such a network can give rise to non-azimuthal distribution of transverse energy in heavy-ion collisions.

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16

DUAN, YI-SHI, and ZHEN-BIN CAO. "TOPOLOGICAL ZERO-THICKNESS COSMIC STRINGS." Modern Physics Letters A 22, no. 32 (October 20, 2007): 2471–78. http://dx.doi.org/10.1142/s0217732307022529.

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Анотація:

In this paper, based on the gauge potential decomposition and the ϕ-mapping theories, we study the topological structures and properties of the cosmic strings that arise in the Abelian–Higgs gauge theory in the zero-thickness limit. After a detailed discussion, we conclude that the topological tensor current introduced in our model is a better and more basic starting point than the generally used Nambu–Goto effective action for studying cosmic strings.

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17

Hayashi, Hirotaka, Patrick Jefferson, Hee-Cheol Kim, Kantaro Ohmori, and Cumrun Vafa. "SCFTs, holography, and topological strings." Surveys in Differential Geometry 23, no. 1 (2018): 105–211. http://dx.doi.org/10.4310/sdg.2018.v23.n1.a4.

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18

Nekrasov, N., H. Ooguri, and C. Vafa. "S-duality and Topological Strings." Journal of High Energy Physics 2004, no. 10 (October 7, 2004): 009. http://dx.doi.org/10.1088/1126-6708/2004/10/009.

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19

Hofman, Christiaan, and Whee Ky Ma. "Deformations of topological open strings." Journal of High Energy Physics 2001, no. 01 (January 24, 2001): 035. http://dx.doi.org/10.1088/1126-6708/2001/01/035.

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20

Eguchi, Tohru, and Hiroaki Kanno. "Topological strings and Nekrasov's formulas." Journal of High Energy Physics 2003, no. 12 (December 3, 2003): 006. http://dx.doi.org/10.1088/1126-6708/2003/12/006.

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21

Iqbal, Amer, Cumrun Vafa, Nikita Nekrasov, and Andrei Okounkov. "Quantum foam and topological strings." Journal of High Energy Physics 2008, no. 04 (April 2, 2008): 011. http://dx.doi.org/10.1088/1126-6708/2008/04/011.

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22

Diamantini, M. C., F. Quevedo, and C. A. Trugenberger. "Confining strings with topological term." Physics Letters B 396, no. 1-4 (March 1997): 115–21. http://dx.doi.org/10.1016/s0370-2693(97)00132-9.

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23

Ooguri, Hirosi, and Cumrun Vafa. "Knot invariants and topological strings." Nuclear Physics B 577, no. 3 (June 2000): 419–38. http://dx.doi.org/10.1016/s0550-3213(00)00118-8.

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24

Aganagic, Mina, Robbert Dijkgraaf, Albrecht Klemm, Marcos Mariño, and Cumrun Vafa. "Topological Strings and Integrable Hierarchies." Communications in Mathematical Physics 261, no. 2 (October 19, 2005): 451–516. http://dx.doi.org/10.1007/s00220-005-1448-9.

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25

Landsteiner, K., W. Lerche, and A. Sevrin. "Topological strings from WZW models." Physics Letters B 352, no. 3-4 (June 1995): 286–97. http://dx.doi.org/10.1016/0370-2693(95)00518-p.

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26

Bouchard, Vincent, Albrecht Klemm, Marcos Mariño, and Sara Pasquetti. "Topological Open Strings on Orbifolds." Communications in Mathematical Physics 296, no. 3 (March 7, 2010): 589–623. http://dx.doi.org/10.1007/s00220-010-1020-0.

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27

Ishibashi, N., and M. Li. "Topological strings from Liouville gravity." Physics Letters B 262, no. 4 (June 1991): 398–404. http://dx.doi.org/10.1016/0370-2693(91)90612-t.

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28

Alim, Murad, and Emanuel Scheidegger. "Topological strings on elliptic fibrations." Communications in Number Theory and Physics 8, no. 4 (2014): 729–800. http://dx.doi.org/10.4310/cntp.2014.v8.n4.a4.

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29

Grassi, Alba, Yasuyuki Hatsuda, and Marcos Mariño. "Topological Strings from Quantum Mechanics." Annales Henri Poincaré 17, no. 11 (April 9, 2016): 3177–235. http://dx.doi.org/10.1007/s00023-016-0479-4.

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30

Nekrasov, Nikita A. "Two-Dimensional Topological Strings Revisited." Letters in Mathematical Physics 88, no. 1-3 (March 28, 2009): 207–53. http://dx.doi.org/10.1007/s11005-009-0312-9.

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31

Arvanitakis, Alex S. "Chiral strings, topological branes, and a generalised Weyl-invariance." International Journal of Modern Physics A 34, no. 06n07 (March 10, 2019): 1950031. http://dx.doi.org/10.1142/s0217751x19500313.

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Анотація:

We introduce a sigma model Lagrangian generalising a number of new and old models which can be thought of as chiral, including the Schild string, ambitwistor strings, and the recently introduced tensionless AdS twistor strings. This “chiral sigma model” describes maps from a [Formula: see text]-brane worldvolume into a symplectic space and is manifestly invariant under diffeomorphisms as well as under a “generalised Weyl invariance” acting on space–time coordinates and worldvolume fields simultaneously. Construction of the Batalin–Vilkovisky master action leads to a BRST operator under which the gauge-fixed action is BRST-exact; we discuss whether this implies that the chiral brane sigma model defines a topological field theory.

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32

Nietzke, Andrew, and Cumrun Vafa. "Topological strings and their physical applications." Surveys in Differential Geometry 10, no. 1 (2005): 147–219. http://dx.doi.org/10.4310/sdg.2005.v10.n1.a6.

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33

Mariño, Marcos. "Chern-Simons theory and topological strings." Reviews of Modern Physics 77, no. 2 (August 4, 2005): 675–720. http://dx.doi.org/10.1103/revmodphys.77.675.

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34

Vafa, Cumrun. "Superstrings and topological strings at largeN." Journal of Mathematical Physics 42, no. 7 (July 2001): 2798–817. http://dx.doi.org/10.1063/1.1376161.

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35

Hollands, Lotte. "Topological strings on compact Calabi-Yau's." Nuclear Physics B - Proceedings Supplements 171 (September 2007): 281–83. http://dx.doi.org/10.1016/j.nuclphysbps.2007.06.026.

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36

Borhade, Pravina, and P. Ramadevi. "reformulated link invariants from topological strings." Nuclear Physics B 727, no. 3 (November 2005): 471–98. http://dx.doi.org/10.1016/j.nuclphysb.2005.08.027.

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37

Aganagic, Mina, Vincent Bouchard, and Albrecht Klemm. "Topological Strings and (Almost) Modular Forms." Communications in Mathematical Physics 277, no. 3 (November 22, 2007): 771–819. http://dx.doi.org/10.1007/s00220-007-0383-3.

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38

Dijkgraaf, Robbert, Herman Verlinde, and Erik Verlinde. "Topological strings in d < 1." Nuclear Physics B 352, no. 1 (March 1991): 59–86. http://dx.doi.org/10.1016/0550-3213(91)90129-l.

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39

Elitzur, S., A. Forge, and E. Rabinovici. "On effective theories of topological strings." Nuclear Physics B 388, no. 1 (December 1992): 131–55. http://dx.doi.org/10.1016/0550-3213(92)90548-p.

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40

Sato, Masatoshi, and Shigeaki Yahikozawa. "“Topological” formulation of effective vortex strings." Nuclear Physics B 436, no. 1-2 (February 1995): 100–128. http://dx.doi.org/10.1016/0550-3213(94)00531-i.

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41

Pestun, Vasily. "Topological strings in generalized complex space." Advances in Theoretical and Mathematical Physics 11, no. 3 (2007): 399–450. http://dx.doi.org/10.4310/atmp.2007.v11.n3.a3.

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42

CAO, ZHEN-BIN. "TOPOLOGICAL CONSERVATION CURRENT OF COSMIC STRINGS." Modern Physics Letters A 26, no. 37 (December 7, 2011): 2803–11. http://dx.doi.org/10.1142/s0217732311037200.

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Анотація:

In our previous research, we have constructed a second rank antisymmetric topological current to study various topological properties of cosmic strings in the early universe. In this paper, starting from the conservation equation of the current, we give a detailed discussion of the structure of the current itself, and finally obtain a new constrained equation for the motion of cosmic strings and a conserved, antisymmetric world sheet tensor which may have a deep relation with the structure of the spacetime.

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43

Szabo, Richard J. "Instantons, Topological Strings, and Enumerative Geometry." Advances in Mathematical Physics 2010 (2010): 1–70. http://dx.doi.org/10.1155/2010/107857.

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We review and elaborate on certain aspects of the connections between instanton counting in maximally supersymmetric gauge theories and the computation of enumerative invariants of smooth varieties. We study in detail three instances of gauge theories in six, four, and two dimensions which naturally arise in the context of topological string theory on certain noncompact threefolds. We describe how the instanton counting in these gauge theories is related to the computation of the entropy of supersymmetric black holes and how these results are related to wall-crossing properties of enumerative invariants such as Donaldson-Thomas and Gromov-Witten invariants. Some features of moduli spaces of torsion-free sheaves and the computation of their Euler characteristics are also elucidated.

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44

Becchi, Carlo, Stefano Giusto, and Camillo Imbimbo. "The Holomorphic Anomaly of Topological Strings." Fortschritte der Physik 47, no. 1-3 (January 1999): 195–200. http://dx.doi.org/10.1002/(sici)1521-3978(199901)47:1/3<195::aid-prop195>3.0.co;2-8.

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45

Gukov, Sergei, Albert Schwarz, and Cumrun Vafa. "Khovanov-Rozansky Homology and Topological Strings." Letters in Mathematical Physics 74, no. 1 (October 2005): 53–74. http://dx.doi.org/10.1007/s11005-005-0008-8.

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46

Oz, Y. "Topological B-model and fermionic strings." Fortschritte der Physik 53, no. 5-6 (May 13, 2005): 542–47. http://dx.doi.org/10.1002/prop.200410216.

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47

Dijkgraaf, R., and H. Fuji. "The volume conjecture and topological strings." Fortschritte der Physik 57, no. 9 (May 5, 2009): 825–56. http://dx.doi.org/10.1002/prop.200900067.

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48

RUDAZ, SERGE, AJIT M. SRIVASTAVA, and SHIKHA VARMA. "PROBING GAUGE STRING FORMATION IN A SUPERCONDUCTING PHASE TRANSITION." International Journal of Modern Physics A 14, no. 10 (April 20, 1999): 1591–604. http://dx.doi.org/10.1142/s0217751x99000804.

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Анотація:

Superconductors are the only experimentally accessible systems with spontaneously broken gauge symmetries which support topologically nontrivial defects, namely string defects. We propose two experiments whose aim is the observation of the dense network of these strings thought to arise, via the Kibble mechanism, in the course of a spontaneous symmetry breaking phase transition. We suggest ways to estimate the order of magnitude of the density of flux tubes produced in the phase transition. This may provide an experimental check for the theories of the production of topological defects in a spontaneously broken gauge theory, such as those employed in the context of the early Universe.

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ZAIKOV, R. P. "BOSONIC STRING WITH TOPOLOGICAL TERM." Modern Physics Letters A 06, no. 16 (May 30, 1991): 1453–57. http://dx.doi.org/10.1142/s0217732391001561.

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Анотація:

It is shown that in D = 3 space-time dimensions there exist a topological term for the bosonic strings. The corresponding constraints satisfy the same Virasoro algebra as the ordinary bosonic strings. These results are generalized for an arbitrary dimensional space-time if we have SO (1, 2) ⊗ O (D − 3) or SO (3) ⊗ O (1, D − 4) symmetry instead of SO (1, D − 1) space-time symmetry. A gauge-dependent correction to the Casimir energy corresponding to this topological term is derived.

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50

Stebbins, A., S. Veeraraghavan, R. Brandenberger, J. Silk, and N. Turok. "Cosmic String Wakes and Large-Scale Structure." Symposium - International Astronomical Union 130 (1988): 562. http://dx.doi.org/10.1017/s0074180900136903.

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Cosmic Strings are one-dimensional topological defects that may be formed in the early universe during a phase transition, and which may be the source of all inhomogeneities in our universe. Their mass per unit length, μ, gives us a dimensionless parameter, μ6 ≡ 106Gμ/c2, which must be of order unity for strings to seed galaxy formation. Results to date from the ongoing CfA redshift survey suggest that galaxies are distributed on two-dimensional surfaces, whose typical separation is about 50h50−1 Mpc. The loop distribution is unlikely to imprint such large-scale patterns in the galaxy positions so we have examined whether this structure could be caused by infinite strings. Because an infinite string typically moves at a substantial fraction of the speed of light, it will leave behind a very large accretion wake in the ambient medium. Gravitational instablity causes these wakes to continue to accrete matter long after the string has moved elsewhere. These wakes form around the two-dimensional surfaces swept out by the long strings.

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