Pure Supergravity Research Articles

Rigorous Holographic Bound on AdS Scale Separation.

We give an elementary proof of the following property of unitary, interacting four-dimensional N=2 superconformal field theories: At large central charge c, there exist at least sqrt[c] single-trace, scalar superconformal primary operators with dimensions Δ≲sqrt[c] (suppressing multiplicative logarithmic corrections). This follows from a stronger, more refined bound on the spectral density in terms of the asymptotic growth rate of the central charge. The proof employs known results on the structure of Coulomb branch operators. Interpreted holographically, this bounds the possible degree of scale separation in semiclassical AdS_{5} half-maximal supergravity. In particular, the bulk must contain an infinite tower of charged scalar states of energies parametrically below the large black hole threshold E_{BH}∼c. We address the extreme case of AdS_{5} pure supergravity, ruling it out as the asymptotic limit of certain sequences in theory space, though the general question remains open.

One‐Loop Effective Potential in Scherk–Schwarz Compactifications of Pure d=5$d=5$ Supergravities

AbstractWe perform a systematic analysis of the one‐loop effective potential of pure supergravities, with supersymmetry fully broken by a Scherk–Schwarz compactification on the circle, as a function of the radial modulus. We discuss the precise correspondence between the effective potential in the full compactified theory and its counterpart in the reduced theory. We confirm that is finite for any , in contrast to . We find that for broken supergravity is negative definite even after accounting for the Kaluza–Klein states. We outline a program for future work where the study of a different kind of Scherk‐Schwarz compactifications, still at the field theory level but with at least three extra dimensions, could lead to qualitatively new results.

Supergravities and branes from Hilbert-Poincaré series

The Molien-Weyl integral formula and the Hilbert-Poincaré series have proven to be powerful mathematical tools in relation to gauge theories, allowing to count the number of gauge invariant operators. In this paper we show that these methods can also be employed to construct Free Differential Algebras and, therefore, reproduce the associated pure supergravity spectrum and nonperturbative objects. Indeed, given a set of fields, the Hilbert-Poincaré series allows to compute all possible invariants and consequently derive the cohomology structure.

Precision test of gauge/gravity duality in D0-brane matrix model at low temperature

We test the gauge/gravity duality between the matrix model and type IIA string theory at low temperatures with unprecedented accuracy. To this end, we perform lattice Monte Carlo simulations of the Berenstein-Maldacena-Nastase (BMN) matrix model, which is the one-parameter deformation of the Banks-Fischler-Shenker-Susskind (BFSS) matrix model, taking both the large N and continuum limits. We leverage the fact that sufficiently small flux parameters in the BMN matrix model have a negligible impact on the energy of the system while stabilizing the flat directions so that simulations at smaller N than in the BFSS matrix model are possible. Hence, we can perform a precision measurement of the large N continuum energy at the lowest temperatures to date. The energy is in perfect agreement with supergravity predictions including estimations of α′-corrections from previous simulations. At the lowest temperature where we can simulate efficiently (T = 0.25λ1/3, where λ is the ’t Hooft coupling), the difference in energy to the pure supergravity prediction is less than 10%. Furthermore, we can extract the coefficient of the 1/N4 corrections at a fixed temperature with good accuracy, which was previously unknown.

Unifying the 6D mathcal{N} = (1, 1) string landscape

We propose an organizing principle for string theory moduli spaces in six dimensions with mathcal{N} = (1, 1), based on a rank reduction map, into which all known constructions fit. In the case of cyclic orbifolds, which are the main focus of the paper, we make an explicit connection with meromorphic 2D (s)CFTs with c = 24 (c = 12) and show how these encode every possible gauge symmetry enhancement in their associated 6D theories. These results generalize naturally to non-cyclic orbifolds, into which the only known string construction (to our awareness) also fits. This framework suggests the existence of a total of 47 moduli spaces: the Narain moduli space, 23 of cyclic orbifold type and 23 of non-cyclic type. Of these only 17 have known string constructions. Among the 30 new moduli spaces, 15 correspond to pure supergravity, for a total of 16 such spaces. A full classification of nonabelian gauge symmetries is given, and as a byproduct we complete the one for seven dimensions, in which only those of theories with heterotic descriptions were known exhaustively.

Pure supersymmetric AdS and the Swampland

We point out that pure supergravity theories in AdS with enough supersymmetry lead, upon taking the large radius limit, to flat space quantum gravities with a nonperturbatively exact global symmetry, and are therefore in the Swampland. The argument applies to any AdS supergravity with gauged R-symmetry group, including truncations of most well known examples, such as AdS5 without the S5 or AdS4 without the S7. This demonstrates that extreme scale separation, at least with enough supersymmetry, is not realizable. Moreover pure AdS theories are also in conflict with some other Swampland principles including the Weak Gravity Conjecture and the (generalized) Distance Conjecture.

Consistent Deformations for a Non-Standard D = 6 Topological BF Model from a BRST-Symmetry-Based Cohomological Approach

This paper falls under the heading of constructing consistent self-couplings in topological BF models. Our endeavor is of interest in the context of pure gravity, General Relativity, and super-gravity in Ashtekar formalism, which allow for certain economic formulations in terms of self-coupled BF theories in the presence of certain extra-constraints. More precisely, herein we address the construction of a special class of D=6 self-interactions for a collection of topological BF models with a non-standard field spectrum. Our methodology relies on a deformation method based on the relationship between antifield–BRST symmetry and the non-trivial gauge symmetries of a given field theory and implemented via the computation of certain precise spaces of the local BRST cohomology corresponding to the free limit. This cohomological BRST approach is applied to the starting free model under standard “selection rules” from Quantum Field Theory. Our findings are completely new and reveal a self-interacting topological BF model in D=6 with a complex gauge structure that is entirely read from the expression of the fully deformed solution to the classical master equation (the canonical generator of the antifield–BRST symmetry), and includes a generalization of the famous D=2 gravity in BF formulation.

Gravitini zero modes riding on top of multiple black holes

We study gravitini zero modes in four dimensional $\mathcal{N}=2$ pure supergravity theory. The gravitini zero modes we study are solutions to the Rarita-Schwinger equations of motion in the background of the purely bosonic Majumdar-Papapetrou background. We start with a very generic ansatz for the gravitini that involves 32 ansatz functions and reduce the Rarita-Schwinger equations to a set of linear coupled partial differential equations on ${\mathbf{R}}^{3}$: the kind familiar from electromagnetism with divergences, curls, etc. We first show how the gravitini zero modes due to broken supersymmetries arise in this setup and how they solve the equations on ${\mathbf{R}}^{3}$. Then we go on and obtain other solutions to these equations: the ``extra'' fermion zero modes, parametrized by four integration constants (one of the integration constants corresponds to the gravitini zero modes due to broken supersymmetries). A careful analysis of pure gauge solutions reveals that we have four independent extra zero modes.

Mathcal{N} = 2 AdS4 supergravity, holography and Ward identities

We develop in detail the holographic framework for an mathcal{N} = 2 pure AdS supergravity model in four dimensions, including all the contributions from the fermionic fields and adopting the Fefferman-Graham parametrization. We work in the first order formalism, where the full superconformal structure can be kept manifest in principle, even if only a part of it is realized as a symmetry on the boundary, while the remainder has a non-linear realization. Our study generalizes the results presented in antecedent literature and includes a general discussion of the gauge-fixing conditions on the bulk fields which yield the asymptotic symmetries at the boundary. We construct the corresponding super- conformal currents and show that they satisfy the related Ward identities when the bulk equations of motion are imposed. Consistency of the holographic setup requires the super- AdS curvatures to vanish at the boundary. This determines, in particular, the expression of the super-Schouten tensor of the boundary theory, which generalizes the purely bosonic Schouten tensor of standard gravity by including gravitini bilinears. The same applies to the superpartner of the super-Schouten tensor, the conformino. Furthermore, the vanishing of the supertorsion poses general constraints on the sources of the three-dimensional boundary conformal field theory and requires that the super-Schouten tensor is endowed with an antisymmetric part proportional to a gravitino-squared term.

The Super-Stückelberg procedure and dS in pure supergravity.

Understanding de Sitter space in supergravity-and string theory-has led to an intense amount of work for more than two decades, largely motivated by the discovery of the accelerated expansion of the Universe in 1998. In this paper, we consider a non-trivial generalization of unimodular gravity to minimal supergravity, which allows for de Sitter solutions without the need of introducing any matter. We formulate a superspace version of the Stückelberg procedure, which restores diffeomorphism and local supersymmetry invariance. This introduces the goldstino associated with spontaneous breaking of supersymmetry in a natural way. The cosmological constant and gravitino mass are related to the vacuum expectation value of the components of a Lagrange multiplier imposing a super-unimodularity condition.

Black holes and general Freudenthal transformations

We study General Freudenthal Transformations (GFT) on black hole solutions in Einstein-Maxwell-Scalar (super)gravity theories with global symmetry of type E7. GFT can be considered as a 2-parameter, a, b ∈ ℝ, generalisation of Freudenthal duality: xto {x}_F= ax+btilde{x} , where x is the vector of the electromagnetic charges, an element of a Freudenthal triple system (FTS), carried by a large black hole and tilde{x} is its Freudenthal dual. These transformations leave the Bekenstein-Hawking entropy invariant up to a scalar factor given by a2 ± b2. For any x there exists a one parameter subset of GFT that leave the entropy invariant, a2 ± b2 = 1, defining the subgroup of Freudenthal rotations. The Freudenthal plane defined by spanℝ{x, tilde{x} } is closed under GFT and is foliated by the orbits of the Freudenthal rotations. Having introduced the basic definitions and presented their properties in detail, we consider the relation of GFT to the global symmetries or U-dualities in the context of supergravity. We consider explicit examples in pure supergravity, axion-dilaton theories and N = 2, D = 4 supergravities obtained from D = 5 by dimensional reductions associated to (non-degenerate) reduced FTS’s descending from cubic Jordan Algebras.

Are all supergravity theories Yang–Mills squared?

Using simple symmetry arguments we classify the ungauged D=4, N=2 supergravity theories, coupled to both vector and hyper multiplets through homogeneous scalar manifolds, that can be built as the product of N=2 and N=0 matter-coupled Yang–Mills gauge theories. This includes all such supergravities with two isolated exceptions: pure supergravity and the T3 model.

Ghostbusters in f (R) supergravity

f (R) supergravity is known to contain a ghost mode associated with higher-derivative terms if it contains Rn with n greater than two. We remove the ghost in f (R) supergravity by introducing auxiliary gauge field to absorb the ghost. We dub this method as the ghostbuster mechanism [1]. We show that the mechanism removes the ghost super-multiplet but also terms including Rn with n ≥ 3, after integrating out auxiliary degrees of freedom. For pure supergravity case, there appears an instability in the resultant scalar potential. We then show that the instability of the scalar potential can be cured by introducing matter couplings in such a way that the system has a stable potential.

Uniqueness of mathcal{N} = 2 and 3 pure supergravities in 4D

After proving the impossibility of consistent non-minimal coupling of a real Rarita-Schwinger gauge field to electromagnetism, we re-derive the necessity of introducing the graviton in order to couple a complex Rarita-Schwinger gauge field to electromagnetism, with or without a cosmological term, thereby obtaining mathcal{N} = 2 pure supergravity as the only possibility. These results are obtained with the BRST-BV deformation method around the flat and (A)dS backgrounds in 4 dimensions. The same method applied to nv vectors, mathcal{N} real spin-3/2 gauge fields and at most one real spinor field also requires gravity and yields mathcal{N} = 3 pure supergravity as well as mathcal{N} = 1 pure supergravity coupled to a vector supermultiplet, with or without cosmological terms. Independently of the matter content, we finally derive strong necessary quadratic constraints on the possible gaugings for an arbitrary number of spin-1 and spin-3/2 gauge fields, that are relevant for larger supergravities.

Entropy of black holes in $$\mathcal {N}=2$$N=2 supergravity

Using the formalism of isolated horizons, we construct space of solutions of asymptotically flat extremal black holes in $$\mathcal {N}=2$$ pure supergravity in 4 dimensions. We prove that the laws of black hole mechanics hold for these black holes. Further, restricting to constant area phase space, we show that the spherical horizons admit a Chern–Simons theory. Standard way of quantizing this topological theory and counting states confirms that entropy is indeed proportional to the area of horizon.

Remarks on a SUSY exact action in 3D supergravity

We consider 2+1 dimensional off-shell N = 1 pure supergravity that is constructed from graviton, gravitino and auxiliary field. We show that the $R^2$ supersymmetric invariant and $R^2_{\mu \nu}$ supersymmetric invariant are expressed as local supersymmetric exact terms up to mass terms for gravitino. In both cases, the mass parameter is proportional to the off-shell supersymmetric cosmological constant.

Pure gravities via color-kinematics duality for fundamental matter

We give a prescription for the computation of loop-level scattering amplitudes in pure Einstein gravity, and four-dimensional pure supergravities, using the color-kinematics duality. Amplitudes are constructed using double copies of pure (super-)Yang-Mills parts and additional contributions from double copies of fundamental matter, which are treated as ghosts. The opposite-statistics states cancel the unwanted dilaton and axion in the bosonic theory, as well as the extra matter supermultiplets in supergravities. As a spinoff, we obtain a prescription for obtaining amplitudes in supergravities with arbitrary non-self-interacting matter. As a prerequisite, we extend the color-kinematics duality from the adjoint to the fundamental representation of the gauge group. We explain the numerator relations that the fundamental kinematic Lie algebra should satisfy. We give nontrivial evidence supporting our construction using explicit tree and loop amplitudes, as well as more general arguments.

Pure de Sitter supergravity

Using superconformal methods we derive an explicit de Sitter supergravity action invariant under spontaneously broken local ${\cal N}=1$ supersymmetry. The supergravity multiplet interacts with a nilpotent goldstino multiplet. We present a complete locally supersymmetric action including the graviton and the fermionic fields, gravitino and goldstino, no scalars. In the global limit when supergravity multiplet decouples, our action reproduces the Volkov-Akulov theory. In the unitary gauge where goldstino vanishes we recover pure supergravity with the positive cosmological constant. The classical equations of motion, with all fermions vanishing, have a maximally symmetric solution: de Sitter space.

ℛ2 supergravity

We formulate R2 pure supergravity as a scale invariant theory built only in terms of superfields describing the geometry of curved superspace. The standard supergravity duals are obtained in both “old” and “new” minimal formulations of auxiliary fields. These theories have massless fields in de Sitter space as they do in their non supersymmetric counterpart. Remarkably, the dual theory of R2 supergravity in the new minimal formulation is an extension of the Freedman model, describing a massless gauge field and a massless chiral multiplet in de Sitter space, with inverse radius proportional to the Fayet-Iliopoulos term. This model can be interpreted as the “de-Higgsed” phase of the dual companion theory of R + R2 supergravity.

Supersymmetry breaking and inflation from higher curvature supergravity

The generic embedding of the $R+R^2$ higher curvature theory into old-minimal supergravity leads to models with rich vacuum structure in addition to its well-known inflationary properties. When the model enjoys an exact R-symmetry, there is an inflationary phase with a single supersymmetric Minkowski vacuum. This appears to be a special case of a more generic set-up, which in principle may include R-symmetry violating terms which are still of pure supergravity origin. By including the latter terms, we find new supersymmetry breaking vacua compatible with single-field inflationary trajectories. We discuss explicitly two such models and we illustrate how the inflaton is driven towards the supersymmetry breaking vacuum after the inflationary phase. In these models the gravitino mass is of the same order as the inflaton mass. Therefore, pure higher curvature supergravity may not only accommodate the proper inflaton field, but it may also provide the appropriate hidden sector for supersymmetry breaking after inflation has ended.