Academic literature on the topic 'String theory, supersymmetry, supergravity, topological field theories'

This survey is devoted to possible manifestations of remarkable topological duality between real scalar and spinor fields (TDSS) existing on a great number of manifolds important in physical applications. The given manifestations are demonstrated to occur within the framework of miscellaneous branches in ordinary and supersymmetric quantum field theories, supergravity, Kaluza-Klein type theories, cosmology, strings, membranes and p-branes. All this allows one to draw the condusion that the above duality will seem to be an essential ingredient in many questions of present and future investigations.

Abdus Salam was a true master of 20th Century Theoretical Physics. Not only was he a pioneer of the Standard Model (for which he shared the Nobel Prize with S. Glashow and S. Weinberg), but he also (co)authored many other outstanding contributions to the field of Fundamental Interactions and their unification. In particular, he was a major contributor to the development of supersymmetric theories, where he also coined the word “Supersymmetry” (replacing the earlier “Supergauges” drawn from String Theory). He also introduced the basic concept of “Superspace” and the notion of “Goldstone Fermion” (Goldstino). These concepts proved instrumental for the exploration of the ultraviolet properties and for the study of spontaneously broken phases of super Yang–Mills theories and Supergravity. They continue to play a key role in current developments in Early-Universe Cosmology. In this contribution we review models of inflation based on Supergravity with spontaneously broken local supersymmetry, with emphasis on the role of nilpotent superfields to describe a de Sitter phase of our Universe.

We review our recent results on dark matter from Starobinsky supergravity. In this context, a natural candidate for cold dark matter is the gravitino. On the other hand, assuming the supersymmetry broken at scales much higher than the electroweak scale, gravitinos are superheavy particles. In this case, they may be non-thermally produced during inflation, in turn originated by the scalaron field with Starobinsky’s potential. Assuming gravitinos as Lightest Supersymmetric Particles (LSSP), the non-thermal production naturally accounts for the right amount of cold dark matter. Metastability of the gravitino LSSP leads to observable effects of their decay, putting constraints on the corresponding Unstable or Decaying Dark Matters scenarios. In this model, the gravitino mass is controlled by the inflaton field and it runs with it. This implies that a continuous spectrum of superheavy gravitinos is produced during the slow-roll epoch. Implications in phenomenology, model building in Grand Unified Theory (GUT) scenarios, intersecting D-brane models and instantons in string theories are discussed.

The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of [Formula: see text] super-Yang–Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale "holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.

We review the geometric superspace approach to the boundary problem in supergravity, retracing the geometric construction of four-dimensional supergravity Lagrangians in the presence of a non-trivial boundary of spacetime. We first focus on pure N=1 and N=2 theories with negative cosmological constant. Here, the supersymmetry invariance of the action requires the addition of topological (boundary) contributions which generalize at the supersymmetric level the Euler-Gauss-Bonnet term. Moreover, one finds that the boundary values of the super field-strengths are dynamically fixed to constant values, corresponding to the vanishing of the OSp(N|4)-covariant supercurvatures at the boundary. We then consider the case of vanishing cosmological constant where, in the presence of a non-trivial boundary, the inclusion of boundary terms involving additional fields, which behave as auxiliary fields for the bulk theory, allows to restore supersymmetry. In all the cases listed above, the full, supersymmetric Lagrangian can be recast in a MacDowell-Mansouri(-like) form. We then report on the application of the results to specific problems regarding cases where the boundary is located asymptotically, relevant for a holographic analysis.

We discuss the properties of matter in a D-dimensional anti-de Sitter-type space–time induced dynamically by the recoil of a very heavy D(irichlet)-particle defect embedded in it. The particular form of the recoil geometry, which from a world sheet view point follows from logarithmic conformal field theory deformations of the pertinent sigma-models, results in the presence of both infrared and ultraviolet (spatial) cutoffs. These are crucial in ensuring the presence of mass gaps in scalar matter propagating in the D-particle recoil space–time. The analogy of this problem with the Liouville-string approach to QCD, suggested earlier by John Ellis and one of the present authors, prompts us to identify the resulting scalar masses with those obtained in the supergravity approach based on the Maldacena's conjecture, but without the imposition of any supersymmetry in our case. Within reasonable numerical uncertainties, we observe that agreement is obtained between the two approaches for a particular value of the ratio of the two cutoffs of the recoil geometry. Notably, our approach does not suffer from the ambiguities of the supergravity approach as regards the validity of the comparison of the glueball masses computed there with those obtained in the continuum limit of lattice gauge theories.

Using a theorem by Bonora-Pasti and Tonin on the existence of a solution for D=10N=1 Bianchi identities in the presence of a Lorentz Chern Simons term, we find an explicit parametrization of the superspace curvatures. Our solution depends only on one free parameter which can be reabsorbed in a field redefinition of the dilaton and of the gravitello. We emphasize that the essential point which enables us to obtain a closed form for the curvature parametrizations and hence for the supersymmetry transformation rules is the use of first order formalism. The spin connection is known once the torsion is known. This latter, rather than being identified with Hµνρ as it is usually done in the literature, is related to it by a differential equation which reduces to the algebraic relation Hµνρ = - 3Tµνρ e4/3σ only at γ1=0 (γ1 being proportional to κ/g2). The solution of the Bianchi identities exhibited in this paper corresponds to a D=10 anomaly free supergravity (AFS). This theory is unique in first order formalism but corresponds to various theories in second order formalism. Indeed the torsion equation is a differential equation which, in order to be solved must be supplemented with boundary conditions. One wonders whether supplemented with a judicious choice of boundary conditions for the torsion equation, AFS yields all the interaction terms found in the effective theory of the heterotic string (ETHS). In this respect two remarks are in order. Firstly it appears that solving the torsion equation iteratively with Tµνρ = -1/3Hµνρ e-4/3σ as starting point all the terms of ETHS except those with a ζ(3) coefficient show up. (Whether the coefficient agree is still to be checked.) Secondly, as shown in this paper the rheonomic solution of the super Poincaré Bianchi identities is unique. Hence additional interaction terms can be added to the Lagrangian only by modifying the rheonomic parametrization of the [Formula: see text]-curvature. The only assumption made in our paper is that [Formula: see text] has at most ψ∧ψ∧V components (sector (1,2)). Correspondingly the only room left for a modification of the present theory is the addition of a (0, 3) part in the rheonomic parametrization of [Formula: see text]. When this work was already finished a conjecture was published by Lechner Pasti and Tonin that such a generalization of AFS might exist and be responsible for the ζ(3) missing term. Indeed if we were able to solve the [Formula: see text]-Bianchi with this new (0, 3)-part then the torsion equation would be modified via new terms which, in second order formalism, lead to additional gravitational interactions. The equation of motion of Anomaly Free Supergravity can be worked out from the Bianchi identities: we indicate through which steps. The corresponding Lagrangian could be constructed with the standard procedures of the rheonomy approach. In this paper we limit ourselves to the bosonic sector of such a Lagrangian and we show that it can indeed be constructed in such a way as to produce the relation between Hµνρ and Tµνρ as a variational equation.

Abstract We construct $$ \mathcal{N} $$ N = (2, 2) supersymmetric AdS3 solutions of type IIB supergravity, dual to twisted compactifications of 4d $$ \mathcal{N} $$ N = 4 super-Yang-Mills on Riemann surfaces. We consider both theories with a regular topological twist, and a twist involving the isometry group of the Riemann surface. These solutions are interpreted as the near-horizon of black strings asymptoting to AdS5× S5. As evidence for the proposed duality we compute the central charge of the gravity solutions and show that it agrees with the field theory result.

Abstract We revisit the construction in four-dimensional gauged Spin(4) supergravity of the holographic duals to topologically twisted three-dimensional $$ \mathcal{N} $$ N = 4 field theories. Our focus in this paper is to highlight some subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion of finite counterterms and the necessity of a Legendre transformation to find the dual to the field theory generating functional. Studying the geometry of these supergravity solutions, we conclude that the gravitational free energy is indeed independent from the metric of the boundary, and it vanishes for any smooth solution.

Abstract Higher-derivative interactions and transformation rules of the fields in the effective field theories of the massless string states are strongly constrained by space-time symmetries and dualities. Here we use an exact formulation of ten dimensional $$ \mathcal{N} $$ N = 1 supergravity coupled to Yang-Mills with manifest T-duality symmetry to construct the first order α′-corrections of the heterotic string effective action. The theory contains a supersymmetric and T-duality covariant generalization of the Green-Schwarz mechanism that determines the modifications to the leading order supersymmetry transformation rules of the fields. We compute the resulting field-dependent deformations of the coefficients in the supersymmetry algebra and construct the invariant action, with up to and including four-derivative terms of all the massless bosonic and fermionic fields of the heterotic string spectrum.

This thesis is divided in two parts, that can be read separately even if both use the possibility of replacing spinors with differential forms in theories with supersymmetry. The first part explores some recent results that have been obtained by applying the G-structure approach to type II supergravities. Using generalized complex geometry it is possible to reformulate the conditions for unbroken supersymmetry in type II supergravity in terms of differential forms. We use this result to find a classification for AdS7 and AdS6 solutions in type II supergravity. Concerning AdS7 solutions we find that in type IIB no solutions can be found, whereas in massive type IIA many new AdS7×M3 solutions are at disposal with the topology of the internal manifold M3 given by a three-sphere. We develop a classification for such solutions. Concerning AdS6 solutions, very few AdS6×M4 supersymmetric solutions are known in literature: one in massive IIA, and two IIB solutions dual to it. The IIA solution is known to be unique. We obtain a classification for IIB supergravity, by reducing the problem to two PDEs on a two-dimensional space Σ. The four-dimensional space M4 is then given by a fibration of S2 over Σ. We also explore other two contexts in which the G-structure approach has revealed its usefulness: first of all we derive the conditions for unbroken supersymmetry for a Mink2 (2,0) vacuum, arising from type II supergravity on a compact eight-dimensional manifold M8. When M8 enjoys SU(4)×SU(4) structure the resulting system is elegantly rewritten in terms of generalized complex geometry. Finally we rewrite the equations for ten-dimensional supersymmetry in a way formally identical to an analogous system in N = 2 gauged supergravity; this provides a way to look for lifts of BPS solutions without having to reduce the ten-dimensional action. The second part is devoted to study some aspects of two different Chern-Simons like theories: holomorphic Chern-Simons theory on a six-dimensional Calabi-Yau space and three-dimensional supersymmetric theories involving vector multiplets (both with Yang-Mills and Chern-Simons terms in the action). Concerning holomorphic Chern-Simons theory, we construct an action that couples the gauge field to off-shell gravitational backgrounds, comprising the complex structure and the (3,0)-form of the target space. Gauge invariance of this off-shell action is achieved by enlarging the field space to include an appropriate system of Lagrange multipliers, ghost and ghost-for-ghost fields. From this reformulation it is possible to uncover a twisted supersymmetric algebra for this model that strongly constrains the anti-holomorphic dependence of physical correlators. Concerning three-dimensional theories, we will develop a new way of computing the exact partition function of supersymmetric three-dimensional gauge theories, involving vector supermultiplet only. Our approach will reduce the problem of computing the exact partition function to the problem of solving an anomalous Ward identity. To obtain such a result we will describe the coupling of three-dimensional topological gauge theories to background topological gravity. The Seifert condition for manifolds supporting global supersymmetry is elegantly deduced from the topological gravity BRST transformations. We will show how the geometrical moduli that affect the partition function can be characterized cohomologically. In the Seifert context Chern-Simons topological (framing) anomaly is BRST trivial and we will compute explicitly the corresponding local Wess-Zumino functional. As an application, we obtain the dependence on the Seifert moduli of the partition function of three-dimensional supersymmetric gauge theory on the squashed sphere by solving the anomalous topological Ward identities, in a regularization independent way and without the need of evaluating any functional determinant.

This thesis is devoted to a discussion of two-dimensional theories with (0,2) supersymmetry. Examples of two-dimensional (0,2) gauged linear sigma models (GLSMs) are constructed for various spaces including Grassmannians, complete intersections in Grassmannians, and non-complete intersections such as Pfaffians. Generalizations of (2,2) Toda dual theories to (0,2) Toda-like theories are also discussed and some examples are given, including products of projective spaces and del Pezzo surfaces. Correlation functions are computed to show the examples are the correct mirror models.
Ph. D.

The motivation for supersymmetry. The algebra, the superspace, and the representations. Field theory models and the non-renormalisation theorems. Spontaneous and explicit breaking of super-symmetry. The generalisation of the Montonen–Olive duality conjecture in supersymmetric theories. The remarkable properties of extended supersymmetric theories. A brief discussion of twisted supersymmetry in connection with topological field theories. Attempts to build a supersymmetric extention of the standard model and its experimental consequences. The property of gauge supersymmetry to include general relativity and the supergravity models.