Narrow Results

In this talk, we review the construction of two three-dimensional non-relativistic pure supergravity theories. One of these yields a supersymmetrization of Newton-Cartan gravity. The other one is a Chern-Simons theory with different bosonic equations of motion and matter couplings than Newton-Cartan gravity. We comment on the prospect of using these theories to construct non-relativistic supersymmetric field theories in curved backgrounds, that can be amenable to exact non-perturbative analysis via localization techniques.

The following sections are included:

• Introduction
• Ansatz, asymptotic behavior and charges
• Magnetized and squashed configurations
• Supersymmetric solutions
• Conclusions
• Acknowledgments
• References

Double field theory promotes the T-duality of closed string theory to a manifest symmetry, thus leading to a new perspective on the geometry experienced by stringy probes. In this contribution, we discuss the mathematical structure underlying the symmetries of double field theory, thus defining a DFT algebroid. We trace its origins in a large Courant algebroid defined over a doubled geometry, and show that after imposing a section condition the DFT algebroid reduces to a canonical Courant algebroid, as expected in generalized geometry.

We construct four dimensional QCD by using D4-branes and D8-branes in type IIA string theory and analyze it within the supergravity approximation. Replacing the D4-branes with the corresponding supergravity solution, a holographic five dimensional description of QCD is obtained. We show that various aspects of low energy (large N) QCD can be understood from this holographic description.

We present 11 and 10 dimensional supergravity descriptions of N=2 4-dimensional black holes. The problem is formulated in the context of type IIA string theory compactified on R^(3,1) × CY₃. The black holes are bound states of D4-branes wrapped on 4-cycles and D0-branes. We reduce the problem to a set of differential equations which describe black hole solutions in the lowest derivative supergravity theory. We argue that the full space-time is inherently 10 (or 11) dimensional. We then proceed to solve these equations in the near-horizon regime, which we define using ideas of “geometrical transitions” - where localized branes are replaced by smooth flux.

In the search for a classification of BPS backgrounds with flux, we look at geometries that arise when M-branes wrap supersymmetric cycles in Calabi-Yau manifolds. We find constraints on the differential forms in the back-reacted manifolds and discover that the calibration corresponding to the (background generating) M-brane is a co-closed form.

Recently, we proposed a holographic description of 4 dim QCD by using a D4/D8-brane system in type IIA string theory. (hep-th/0412141, hep-th/0507073 with T. Sakai) It was shown that the model nicely catches various features in QCD and hadron physics. Here we give an overview of the model and present some new results about construction of baryons in this framework.

We analyze the coupled supergravity and Yang–Mills system using holomorphy, near the rigid limit where the former decouples from the latter. We find that there appears generically a new mass scale around gM_pl where g is the gauge coupling constant and M_pl is the Planck scale. This is in accord with the weak-gravity conjecture proposed recently.

The maximal rank hyperbolic Kac–Moody algebra e₁₀ has been conjectured to play a prominent role in the unification of duality symmetries in string and M-theory. We review some recent developments supporting this conjecture.

I begin with some memories of Abdus Salam who was my PhD supervisor. After reviewing the theory of nonlinear realisations and Kac–Moody algebras, I explain how to construct the nonlinear realisation based on the Kac–Moody algebra E₁₁ and its vector representation. I explain how this field theory leads to dynamical equations which contain an infinite number of fields defined on a space–time with an infinite number of coordinates. I then show that these unique dynamical equations, when truncated to low level fields and the usual coordinates of space–time, lead to precisely the equations of motion of 11-dimensional supergravity theory. By taking different group decompositions of E₁₁ we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the nonlinear realisation should be thought of as a unified theory that is the low energy effective action for type II strings and branes. These results essentially confirm the E₁₁ conjecture given many years ago.

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.

Theories with elementary scalar degrees of freedom seem nowadays required for simple descriptions of the Standard Model and of the Early Universe. It is then natural to embed theories of inflation in supergravity, also in view of their possible ultraviolet completion in String Theory. After some general remarks on inflation in supergravity, we describe examples of minimal inflaton dynamics which are compatible with recent observations, including higher-curvature ones inspired by the Starobinsky model. We also discuss different scenarios for supersymmetry breaking during and after inflation, which include a revived role for non-linear realizations. In this spirit, we conclude with a discussion of the link, in four dimensions, between “brane supersymmetry breaking” and the super-Higgs effect in supergravity.

The plethora of recent and forthcoming data on the cosmic microwave background (CMB) data are stimulating a new wave of inflationary model-building. Naturalness suggests that the appropriate framework for models of inflation is supersymmetry. This should be combined with gravity in a supergravity theory, whose specific no-scale version has much to commend it, e.g. its derivation from string theory and the flat directions in its effective potential. Simple no-scale supergravity models yield predictions similar to those of the Starobinsky R + R² model, though some string-motivated versions make alternative predictions. Data are beginning to provide interesting constraints on the rate of inflaton decay into Standard Model particles. In parallel, LHC and other data provide significant constraints on no-scale supergravity models, which suggest that some sparticles might have masses close to present experimental limits.

This work summarises recent progress obtained by the mini-superpspace quantization of N = 1, d = 4 supergravity, formulated in the framework of the Bianchi IX cosmological model. The emphasis is put on three main results: the completeness of the solution space obtained, the elements suggesting a hidden Kac-Moody structure of the theory and those leading to conjecture an avoidance of the cosmological singularity by some branches of the wave function of the Universe.

We consider the construction of a transgression field theory invariant under the Poincare supergroup ${\mathcal{P}}_5$, modulo boundary terms. The transgression action is constructed from the lagrangian for five dimensional Chern–Simons supergravity through the introduction of two 1-forms gauge connections valuated in the corresponding Lie superalgebra. These conections are associated to linear and nonlinear realizations of the Poincaré supergroup. From a dimensional reduction of the transgression field theory we get a four dimensional gauged Wess–Zumino–Witten action whose fields are the original gauge fields of the Chern–Simons theory plus the set of tensorial and spinorials functions relating the gauge conections corresponding to the parameterized coordinates of the coset space ${\mathcal{P}}_5/SO(1,4)$ in the adjoint representation. The resulting action and its equations of motion are studied.

In this paper we present a model for accelerated expansion of the universe, both during inflation and the present stage of the expansion, from four dimensional 𝒩 = 1 supergravity. We evaluate the tensor-to-scalar ratio (r ≈ 0.00034), the scalar spectral index (n_s ≈ 0.970) and the running spetral index (dn_s/dk ≈ −6 × 10⁻⁵), and we notice that these parameters are in agreement with Planck+WP+lensing data and with BICEP2/Keck and Planck joint analysis, at 95% CL. The number of e-folds is 50 or higher. The reheating period has an associated temperature T_R ˜ 10¹² GeV, which agrees with the one required by thermal leptogenesis. Regarding the scalar field as dark energy, the autonomous system for it in the presence of a barotropic fluid provides a stable fixed point that leads to a late-time accelerated expansion of the universe, with an equation of state that mimics the cosmological constant (ω_Φ ≈ −0.997).

Klein-Gordon equation is the starting point of the scattering and gauge/gravity calculations for black holes. Thus, studying its separability and probing the residua associated with the black hole horizons are key issues that constitute the core of the calculations for the black hole internal structure. One can write the radial part of the Klein-Gordon equation in a specific form that reveals the pole structure of the horizon equation. The residua of the poles reflect the physical properties, namely surface gravities and angular velocities associated with respective horizons. We start with the Kerr black hole by showing the correspondence of the residua of the poles and the monodromy exponents. Then we study the cases of the most general nonextremal black hole solutions in four and five dimensional gauged supergravity.

After a brief discussion of RR and NS fluxes, we consider the T-duality family of fluxes whose prototype is the Scherk-Schwarz reduction of the S-dual of the RR scalar of IIB supergravity. We give a complete classification of these fluxes, including the ones that are non-geometric, and we explain their relation with dual mixed-symmetry potentials. We point out that the non-geometric fluxes turn out to be dual to potentials containing nine antisymmetric indices. Our analysis suggests that all these fluxes can be understood in the context of double field theory, although for the non-geometric ones one expects a violation of the strong constraint.

We define an algebraic characterization of half supersymmetric branes in supergravity theories with different amount of supersymmetry. We furthermore illustrate how this classification can be used as starting point to explain the orbits stratification for extremal black holes.

We discuss the construction and basic properties of a recently constructed 𝒩 = 1 supergravity theory in 4 dimensions with spontaneously broken local supersymmetry, called ‘de Sitter supergravity’. The theory has a cosmological constant that can be positive, zero or negative. Nilpotent multiplets and non-linear Volkov-Akulov supersymmetry play an important role in the construction. We shortly discuss some recent extensions of the theory.