On an exponential representation of the gravitational S-matrix

An exponential representation of the S-matrix provides a natural framework for understanding the semi-classical limit of scattering amplitudes. While sharing some similarities with the eikonal formalism it differs from it in details. Computationally, rules are simple because pieces that must be subtracted are given by combinations of unitarity cuts. Analyzing classical gravitational scattering to third Post-Minkowskian order in both maximal supergravity and Einstein gravity we find agreement with other approaches, including the contributions from radiation reaction terms. The kinematical relation for the two-body problem in isotropic coordinates follows immediately from this procedure, again with the inclusion of radiation reaction pieces up to third Post-Minkowskian order.

A novel way of constraining the α-attractor chaotic inflation through Planck data

Defining a scale of k-modes of the quantum fluctuations during inflation through the dynamical horizon crossing condition k = aH we go from the physical t variable to k variable and solve the equations of cosmological first-order perturbations self consistently, with the chaotic α-attractor type potentials. This enables us to study the behaviour of ns , r, nt and N in the k-space. Comparison of our results in the low-k regime with the Planck data puts constraints on the values of the α parameter through microscopic calculations. Recent studies had already put model-dependent constraints on the values of α through the hyperbolic geometry of a Poincaré disk: consistent with both the maximal supergravity model 𝒩 = 8 and the minimal supergravity model 𝒩 = 1, the constraints on the values of α are 1/3, 2/3, 1, 4/3, 5/3, 2, 7/3. The minimal 𝒩 = 1 supersymmetric cosmological models with B-mode targets, derived from these supergravity models, predicted the values of r between 10-2 and 10-3. Both in the E-model and the T-model potentials, we have obtained, in our calculations, the values of r in this range for all the constrained values of α stated above, within 68% CL. Moreover, we have calculated r for some other possible values of α both in low-α limit, using the formula r = 12α/N 2, and in the high-α limit, using the formula r = 4n/N, for n = 2 and 4. With all such values of α, our calculated results match with the Planck-2018 data with 68% or near 95% CL.

The holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

The massless irreducible representation in E theory and how bosons can appear as spinors

We study in detail the irreducible representation of [Formula: see text] theory that corresponds to massless particles. This has little algebra [Formula: see text] and contains 128 physical states that belong to the spinor representation of [Formula: see text]. These are the degrees of freedom of maximal supergravity in eleven dimensions. This smaller number of the degrees of freedom, compared to what might be expected, is due to an infinite number of duality relations which in turn can be traced to the existence of a subaglebra of [Formula: see text] which forms an ideal and annihilates the representation. We explain how these features are inherited into the covariant theory. We also comment on the remarkable similarity between how the bosons and fermions arise in [Formula: see text] theory.

Global properties of the conformal manifold for S-fold backgrounds

We study a one-parameter family of $$ \mathcal{N} $$ N = 2 anti-de Sitter vacua with U(1)2 symmetry of gauged four-dimensional maximal supergravity, with dyonic gauge group [SO(6) × SO(1, 1)] ⋉ ℝ12. These backgrounds are known to correspond to Type IIB S-fold solutions with internal manifold of topology S1 × S5. The family of AdS4 vacua is parametrized by a modulus χ. Although χ appears non-compact in the four-dimensional supergravity, we show that this is just an artefact of the four-dimensional description. We give the 10-dimensional geometric interpretation of the modulus and show that it actually has periodicity of $$ \frac{2\pi }{T} $$ 2 π T , which is the inverse radius of S1. We deduce this by providing the explicit D = 10 uplift of the family of vacua as well as computing the entire modulus-dependent Kaluza-Klein spectrum as a function of χ. At the special values χ = 0 and χ = $$ \frac{\pi }{T} $$ π T , the symmetry enhances according to U(1)2 → U(2), giving rise however to inequivalent Kaluza-Klein spectra. At χ = $$ \frac{\pi }{T} $$ π T , this realizes a bosonic version of the “space invaders” scenario with additional massless vector fields arising from formerly massive fields at higher Kaluza-Klein levels.

Unified non-metric (1, 0) tensor-Einstein supergravity theories and (4, 0) supergravity in six dimensions

The ultrashort unitary (4, 0) supermultiplet of 6d superconformal algebra OSp(8∗|8) reduces to the CPT-self conjugate supermultiplet of 4d superconformal algebra SU(2, 2|8) that represents the fields of maximal N = 8 supergravity. The graviton in the (4, 0) multiplet is described by a mixed tensor gauge field which can not be identified with the standard metric in 6d. Furthermore the (4, 0) supermultiplet can be obtained as a double copy of (2, 0) conformal supermultiplet whose interacting theories are non-Lagrangian. It had been suggested that an interacting non-metric (4, 0) supergravity theory might describe the strongly coupled phase of 5d maximal supergravity. In this paper we study the implications of the existence of an interacting non-metric (4, 0) supergravity in 6d. The (4, 0) theory can be truncated to non-metric (1, 0) supergravity coupled to 5,8 and 14 self-dual tensor multiplets that reduce to three of the unified magical supergravity theories in d = 5. This implies that the three infinite families of unified N = 2, 5d Maxwell-Einstein supergravity theories (MESGTs) plus two sporadic ones must have uplifts to unified non-metric (1, 0) tensor Einstein supergravity theories (TESGT) in d = 6. These theories have non-compact global symmetry groups under which all the self-dual tensor fields including the gravitensor transform irreducibly. Four of these theories are uplifts of the magical supergravity theories whose scalar manifolds are symmetric spaces. The scalar manifolds of the other unified theories are not homogeneous spaces. We also discuss the exceptional field theoretic formulations of non-metric unified (1, 0) tensor-Einstein supergravity theories and conclude with speculations concerning the existence of higher dimensional non-metric supergravity theories that reduce to the (4, 0) theory in d = 6.

E 9 exceptional field theory. Part II. The complete dynamics

We construct the first complete exceptional field theory that is based on an infinite-dimensional symmetry group. E9 exceptional field theory provides a unified description of eleven-dimensional and type IIB supergravity covariant under the affine Kac-Moody symmetry of two-dimensional maximal supergravity. We present two equivalent formulations of the dynamics, which both rely on a pseudo-Lagrangian supplemented by a twisted self-duality equation. One formulation involves a minimal set of fields and gauge symmetries, which uniquely determine the entire dynamics. The other formulation extends $$ {\mathfrak{e}}_9 $$ e 9 by half of the Virasoro algebra and makes direct contact with the integrable structure of two-dimensional supergravity. Our results apply directly to other affine Kac-Moody groups, such as the Geroch group of general relativity.

Old and new vacua of 5D maximal supergravity

We look for critical points with U(2) residual symmetry in 5-dimensional maximally supersymmetric gauged supergravity, by varying the embedding tensor, rather than directly minimizing the scalar potential. We recover all previously known vacua and we find four new vacua, with different gauge groups and cosmological constants. We provide the first example of a maximal supergravity model in D ≥ 4 having critical points with both positive and vanishing cosmological constant. For each vacuum we also compute the full mass spectrum. All results are analytic.

Microscopic wormholes, extra-dimensions and cold dark matter from N = 2 maximal supergravity with Gauss–Bonnet corrections

In this paper, we have discussed a (1 + 9)-dimensional open cosmological model motivated from N = 2 maximal supergravity arguments characterized by the presence of a wormhole connected to the extra dimensions part and a Gauss–Bonnet (GB) curvature corrections. The universe is dominated by dark energy and cold dark matter (CDM) which emerged from extra dimensions as supported by recent phenomenological and observational arguments. By assuming that the wormhole in the outer/inner regions of the halos of galaxies is characterized by a CDM profile density, it was revealed that the universe is expanding acceleratedly with time, dominated by a microscopic traversable wormhole and dark energy. The role of the dominance of the GB term is discussed and the model is confronted with astrophysical observations.

Non-perturbative aspects of gauge theories from gauge-gravity dualities

In this Ph.D. Thesis we consider two speci˝c supergravities which are well-established within the literature on holography, and which are known to provide the low-energy e˙ective description of either superstring theory or M-theory: the six-dimensional half-maximal theory of Romans, and the maximal supergravity in seven dimensions.We implement their dimensional reduction by compactifying on an S1 and T 2, respectively, to obtain a ˝ve-dimensional sigma-model coupled to grav-ity. Spectra of bosonic excitations are computed numerically by considering ˝eld ˛uctuations on background geometries which holographically realise con-˝nement. We furthermore propose a diagnostic tool to detect mixing e˙ects between scalar resonances and the pseudo-NambuGoldstone boson associated with spontaneous breaking of conformal invariance: the dilaton. This test con-sists of neglecting a certain component of the spin-0 ˛uctuation variables, ef-fectively disregarding their back-reaction on the underlying geometry; where discrepancies arise compared to the complete calculation we infer dilaton mix-ing. For both theories this analysis evinces a parametrically light dilaton.For each supergravity we uncover a tachyonic instability within their param-eter space; motivated by these pathological ˝ndings we proceed to conduct an investigation into their respective phase structures, reasoning that there must necessarily exist some mechanism by which these instabilities are rendered phys-ically inaccessible. We compile a comprehensive catalogue of geometrically dis-tinct backgrounds admissible within each theory, and derive general expressionsfor their holographically renormalised free energy F. Another numerical rou-tine is employed to systematically extract data for some special deformationparameters, and F is plotted in units of an appropriate universal scale.Our analysis proves fruitful: each theory exhibits clear evidence of a ˝rst-order phase transition which induces the spontaneous decompacti˝cation of the shrinking circular dimension before the instability manifests, favouring instead a class of singular solutions. The aforementioned dilaton resonance appears only along a metastable portion of the branch of con˝ning backgrounds.