Supergravity Models Research Articles

Inflation, SUSY breaking, and primordial black holes in modified supergravity coupled to chiral matter

We propose a novel model of the modified (Starobinsky-like) old-minimal-type supergravity coupled to a chiral matter superfield, that can simultaneously describe multi-field inflation, primordial black hole (PBH) formation, dark matter (DM), and spontaneous supersymmetry (SUSY) breaking after inflation in a Minkowski vacuum. The PBH masses in our supergravity model of double slow-roll inflation, with a short phase of “ultra-slow-roll” between two slow-roll phases, are close to 10^{18} g. We find that a significant PBH fraction in the allowed mass window can be supplemented by spontaneous SUSY breaking in the vacuum with the gravitino mass close to the scalaron (inflaton) mass M of the order 10^{13} GeV. Our supergravity model favors the composite nature of DM as a mixture of PBH and heavy gravitinos as the lightest SUSY particles. The composite DM significantly relaxes fine-tuning needed for the whole PBH-DM. The PBH-DM fraction is derived, and the second-order gravitational wave background induced by the enhanced scalar perturbations is calculated. Those gravitational waves may be accessible by the future space-based gravitational interferometers.

Lower Tensor to Scalar Ratio in a SUGRA Motivated Inflationary Potential

A scalar potential obtained from the $D$-term in the Supergravity models, which dominates over $F$ term and is mainly responsible for the inflationary phase in the early universe, is studied. The potential with canonical kinetic terms for scalar fields in the Lagrangian, has a very slow roll feature in comparison to various other plateau type inflationary potentials. In this case, a much lower tensor-to-scalar ratio ($r$) of $\mathcal{O}(10^{-3})$ is achievable. The requirement of slow roll condition for the inflation potential implies that the up type neutral scalar and the down type neutral scalar in Supergravity models are with equal field strength at the time of inflation. If this relationship holds down to the electroweak scale for the corresponding $vev$ values of these fields, then it will indicate a higher SUSY breaking scale around 100 TeV. The predicted values of the inflationary observables are well within the 1-$\sigma$ bounds of the recent constraints from {\it Planck'18} observations. The era of reheating after the inflationary phase, is also studied and the bounds on the reheating temperature ($T_{re}$) is calculated for a different equation of states during reheating ($w_{re}$) for the {\it Planck'18} allowed values of the scalar spectral index ($n_s$). For our model with $w_{re}=2/3$ and $w_{re}=1$, after satisfying all the bounds due to gravitino overproduction, we can have big parameter space for $T_{re}$ which is well inside {\it Planck'18} 1-$\sigma$ bound on $n_s$.

Resonant superalgebras for supergravity

Considering supergravity theory is a natural step in the development of gravity models. This paper follows the “algebraic“ path and constructs possible extensions of the Poincaré and Anti-de-Sitter algebras, which inherit their basic commutation structure. Previously achieved results of this type are fragmentary and show only a limited fraction of possible algebraic realizations. Our paper presents the newly obtained symmetry algebras, evaluated within an efficient pattern-based computational method of generating the so-called ‘resonating’ algebraic structures. These supersymmetric extensions of algebras, going beyond the Poincaré and Anti-de Sitter ones, contain additional bosonic generators Z_{ab} (Lorentz-like), and U_a (translational-like) added to the standard Lorentz generator J_{ab} and translation generator P_{a}. Our analysis includes all cases up to two fermionic supercharges, Q_{alpha } and Y_{alpha }. The delivered plethora of superalgebras includes few past results and offers a vastness of new examples. The list of the cases is complete and contains all superalgebras up to two of Lorentz-like, translation-like, and supercharge-like generators (JP+Q)+(ZU+Y)=JPZU+QY. In the latter class, among 667 founded superalgebras, the 264 are suitable for direct supergravity construction. For each of them, one can construct a unique supergravity model defined by the Lagrangian. As an example, we consider one of the algebra configurations and provide its Lagrangian realization.

Phase transitions for deformations of JT supergravity and matrix models

We analyze deformations of mathcal{N} = 1 Jackiw-Teitelboim (JT) supergravity by adding a gas of defects, equivalent to changing the dilaton potential. We compute the Euclidean partition function in a topological expansion and find that it matches the perturbative expansion of a random matrix model to all orders. The matrix model implements an average over the Hamiltonian of a dual holographic description and provides a stable non-perturbative completion of these theories of mathcal{N} = 1 dilaton-supergravity. For some range of deformations, the supergravity spectral density becomes negative, yielding an ill-defined topological expansion. To solve this problem, we use the matrix model description and show the negative spectrum is resolved via a phase transition analogous to the Gross-Witten-Wadia transition. The matrix model contains a rich and novel phase structure that we explore in detail, using both perturbative and non-perturbative techniques.

Superradiant instability of extremal black holes in STU supergravity

We investigate the superradiant (in)stability of the extremal multicharge static black holes in the STU supergravity model, which reduce to the Reissner-Nordstr\"om (RN) black hole when all the charges are equal. We first show that the frequency of quasibound states is necessarily complex and obtain the corresponding superradiant condition. We then study the effective potential of the Schr\"odinger-like equation associated with the radial function of the charged scalar field. We find that trapping-well configurations can emerge with either a single peak or double peaks. We numerically obtain the corresponding unstable quasibound states, organized under the overtone number, as well as how the charged black holes deviate from the RN black hole. We find that the STU black holes are superradiantly unstable as long as not all the charges are equal, indicating that the superradiant stability of the extremal RN black hole is a fine-tuning result in the framework of the STU supergravity model.

Lie algebra expansions, non-relativistic matter multiplets and actions

We discuss a general methodology to provide rigid, off-shell matter multiplets and actions for recently constructed non-relativistic superalgebras. The technique is based on the Lie algebra expansion, which, in the context of supersymmetry, has so far been used to obtain non-relativistic on-shell supergravity models. We first explain how the Lie algebra expansion can be implemented to generate off-shell rigid multiplets on a flat background by developing an auxiliary framework where only the lowest order behavior of the spatial and temporal vielbein is relevant. We then provide explicit examples for the field content, the transformation rules as well as action principles for certain multiplets in three and four dimensions.

\u03b1\u2032-corrections to near extremal dyonic strings and weak gravity conjecture

We construct non-extremal dyonic string solutions in 6D minimal supergravity where the leading higher derivative corrections arise from either the type IIA string theory compactified on K3 or the heterotic string theory compactified on 4-torus. The thermodynamical quantities and Euclidean actions of the strings are computed. In the near extremal regime, we calculate the force felt by a probe fundamental string in the background of the macroscopic dyonic string with leading α′ corrections. We find that in both the IIA and heterotic setups, away from extremality, the attractive force overwhelms the repulsive force. However, close to extremality, the α′ corrections can reduce the attractive force in the isoentropic process, where the charges are fixed. This feature may be used as a new constraint for supergravity models with consistent quantum gravity embedding, in cases where the extremal limit coincides with the BPS limit and the higher derivative corrections do not affect the mass-to-charge ratio. By contrast, the α′ corrections can enhance the attractive force in the isothermal or isoenergetic processes.

Charge completeness and the massless charge lattice in F-theory models of supergravity

We prove that, for every 6D supergravity theory that has an F-theory description, the property of charge completeness for the connected component of the gauge group (meaning that all charges in the corresponding charge lattice are realized by massive or massless states in the theory) is equivalent to a standard assumption made in F-theory for how geometry encodes the global gauge theory by means of the Mordell-Weil group of the elliptic fibration. This result also holds in 4D F-theory constructions for the parts of the gauge group that come from sections and from 7-branes. We find that in many 6D F-theory models the full charge lattice of the theory is generated by massless charged states; this occurs for each gauge factor where the associated anomaly coefficient satisfies a simple positivity condition. We describe many of the cases where this massless charge sufficiency condition holds, as well as exceptions where the positivity condition fails, and analyze the related global structure of the gauge group and associated Mordell-Weil torsion in explicit F-theory models.

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 \U0001d4a9 = 8 and the minimal supergravity model \U0001d4a9 = 1, the constraints on the values of α are 1/3, 2/3, 1, 4/3, 5/3, 2, 7/3. The minimal \U0001d4a9 = 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.

Embeddings of integrable models in supergravity and their perturbative stability

We discuss the perturbative stability of an AdS 3 non-supersymmetric solution of the type-IIB supergravity, whose internal geometry is given by the direct product of a round three-sphere and two λ-deformed factors based on the coset CFTs SU(2)/U(1) and SL(2, ℝ)/SO(1,1). This solution admits a two-dimensional parametric space spanned by the inverse radius of the AdS 3 and the deformation parameter λ. Reality of the background imposes restrictions on the values of these parameters. Further limitations on the values of the inverse radius and the parameter λ arise after requiring the stability of the solution. Our approach relies on the study of scalar perturbations around the AdS 3 vacuum of a three-dimensional effective theory. This reveals the existence of a region in the parametric space where the Breitenlohner-Freedman bound is not violated.

Inflationary physics and trans-Planckian conjecture in the stringy running vacuum model: from the phantom vacuum to the true vacuum

In previous works we have embedded the Running Vacuum Model (RVM) of Cosmology in the framework of string theory. Specifically, we considered a string-inspired Cosmology with primordial gravitational waves (GW) and gravitational anomalies, which were argued to lead, via appropriate condensation during the very-early-universe era, to dynamical inflation, of RVM type, without the need for extra inflaton fields. A crucial role for the associated slow-roll nature of the inflationary era was played by the fundamental axion field that exists in the gravitational multiplet of strings, viz. the Kalb-Ramond (KR) axion. In this paper, we study further this model and demonstrate several novel facts, completing our previous studies. We clarify the different roles played by the background KR axions, which constitute a form of stiff matter that dominates a pre-RVM-inflationary epoch of the Universe. We show that the KR axion when combined with the gravitational Chern-Simons contribution obey together a peculiar equation of state $p=-\rho$, with negative energy density $\rho < 0$, which we call `phantom vacuum'. Eventually, this state transmutes into the standard vacuum state thanks to the contribution from the gravitational Chern-Simons condensate, which makes the total $\rho_{\rm total} =-p_{\rm total} >0$. At this point the RVM vacuum picture emerges naturally, with an overall equation of state of true vacuum type. We find that our scenario is consistent with the trans-Planckian censorship hypothesis, given that the rate of change of the KR axion takes only sub-Planckian values. We also discuss some explicit scenarios on the creation of GWs within the context of supergravity models that could be embedded in our string theory framework. {Finally, we argue how the RVM in our context can help to alleviate the current tensions of the $\Lambda$CDM.}

Catastrophic production of slow gravitinos

We study gravitational particle production of the massive spin-$3/2$ Rarita-Schwinger field, and its close relative, the gravitino, in Friedmann-Robertson-Walker cosmological spacetimes. For masses lighter than the value of the Hubble expansion rate after inflation, ${m}_{3/2}\ensuremath{\lesssim}H$, we find catastrophic gravitational particle production, wherein the number of gravitationally produced particles is divergent, caused by a transient vanishing of the helicity-$1/2$ gravitino sound speed. In contrast with the conventional gravitino problem, the spectrum of produced particles is dominated by those with momentum at the UV cutoff. This suggests a breakdown of effective field theory, which might be cured by new degrees of freedom that emerge in the UV. We study the UV completion of the Rarita-Schwinger field, namely $\mathcal{N}=1$, $d=4$, supergravity. We reproduce known results for models with a single superfield and models with an arbitrary number of chiral superfields, find a simple geometric expression for the sound speed in the latter case, and extend this to include nilpotent constrained superfields and orthogonal constrained superfields. We find supergravity models where the catastrophe is cured and models where it persists. Insofar as quantizing the gravitino is tantamount to quantizing gravity, as is the case in any UV completion of supergravity, the models exhibiting catastrophic production are prime examples of four-dimensional effective field theories that become inconsistent when gravity is quantized, suggesting a possible link to the swampland program. We propose the gravitino swampland conjecture, which is consistent with and indeed follows from the Kachru-Kallosh-Linde-Trivedi and large volume scenarios for moduli stabilization in string theory.

Sequestered Inflation

AbstractWe construct supergravity models allowing to sequester the phenomenology of inflation from the Planckian energy scale physics. The procedure consists of two steps: At Step I we study supergravity models, which might be associated with string theory or M‐theory, and have supersymmetric Minkowski vacua with flat directions. At Step II we uplift these flat directions to inflationary plateau potentials. We find certain conditions which ensure that the superheavy fields involved in the stabilization of the Minkowski vacua at Step I are completely decoupled from the inflationary phenomenology.

IIB String Theory and Sequestered Inflation

AbstractWe develop sequestered inflation models, where inflation occurs along flat directions in supergravity models derived from type IIB string theory. It is compactified on a orientifold with generalized fluxes and O3/O7‐planes. At Step I, we use flux potentials which 1) satisfy tadpole cancellation conditions and 2) have supersymmetric Minkowski vacua with flat direction(s). The 7 moduli are split into heavy and massless Goldstone multiplets. At Step II we add a nilpotent multiplet and uplift the flat direction(s) of the type IIB string theory to phenomenological inflationary plateau potentials: α‐attractors with 7 discrete values . Their cosmological predictions are determined by the hyperbolic geometry inherited from string theory. The masses of the heavy fields and the volume of the extra dimensions change during inflation, but this does not affect the inflationary dynamics.

Swampland de Sitter conjectures in no-scale supergravity models

It is challenging to construct explicit and controllable models that realize de Sitter solutions in string compactifications. This difficulty is the main motivation for the refined de Sitter conjecture and the trans-Planckian censorship conjecture which forbid stable de Sitter solutions but allow metastable, unstable and rolling solutions in a theory consistent with quantum gravity. Inspired by this, we first study a toy de Sitter no-scale supergravity model and show that for particular choices of parameters it can be consistent with the refined de Sitter conjecture and the trans-Planckian censorship conjecture. Then we modify the model by adding rolling dynamics and show that the theory can become stable along the imaginary direction, where it would otherwise be unstable. We extend the model to multifield rolling and de Sitter fields, finding the parameter space where they can be compatible with the refined de Sitter conjecture. The modified models with rolling fields can be used to construct quintessence models to accommodate the accelerating expansion of the Universe.

Higher-derivative supergravity, AdS4 holography, and black holes

We use conformal supergravity techniques to study four-derivative corrections in four-dimensional gauged supergravity. We show that the four-derivative Lagrangian for the propagating degrees of freedom of the mathcal{N} = 2 gravity multiplet is determined by two real dimensionless constants. We demonstrate that all solutions of the two-derivative equations of motion in the supergravity theory also solve the four-derivative equations of motion. These results are then applied to explicitly calculate the regularized on-shell action for any asymptotically locally AdS4 solution of the two-derivative equations of motion. The four-derivative terms in the supergravity Lagrangian modify the entropy and other thermodynamic observables for the black hole solutions of the theory. We calculate these corrections explicitly and demonstrate that the quantum statistical relation holds for general stationary black holes in the presence of the four-derivative corrections. Employing an embedding of this supergravity model in M-theory we show how to use supersymmetric localization results in the holographically dual three-dimensional SCFT to determine the unknown coefficients in the four-derivative supergravity action. This in turn leads to new detailed results for the first subleading {N}^{frac{1}{2}} correction to the large N partition function of a class of three-dimensional SCFTs on compact Euclidean manifolds. In addition, we calculate explicitly the first subleading correction to the Bekenstein-Hawking entropy of asymptotically AdS4 black holes in M-theory. We also discuss how to add matter multiplets to the supergravity theory in the presence of four-derivative terms and to generalize some of these results to six- and higher-derivative supergravity.

Features of the inflaton potential and the power spectrum of cosmological perturbations

We discuss features of the inflaton potential that can lead to a strong enhancement of the power spectrum of curvature perturbations. We show that a steep decrease of the potential induces an enhancement of the spectrum by several orders of magnitude, which may lead to the production of primordial black holes. The same feature can also create a distinctive oscillatory pattern in the spectrum of gravitational waves generated through the scalar perturbations at second order. We study the additive effect of several such features. We analyse a simplified potential, but also discuss the possible application to supergravity models.

Automatic enhancement in 6D supergravity and F-theory models

We observe that in many F-theory models, tuning a specific gauge group G and matter content M under certain circumstances leads to an automatic enhancement to a larger gauge group G′ ⊃ G and matter content M′ ⊃ M. We propose that this is true for any theory G, M whenever there exists a containing theory G′, M′ that cannot be Higgsed down to G, M. We give a number of examples including non-Higgsable gauge factors, nonabelian gauge factors, abelian gauge factors, and exotic matter. In each of these cases, tuning an F-theory model with the desired features produces either an enhancement or an inconsistency, often when the associated anomaly coefficient becomes too large. This principle applies to a variety of models in the apparent 6D supergravity swampland, including some of the simplest cases with U(1) and SU(N) gauge groups and generic matter, as well as infinite families of U(1) models with higher charges presented in the prior literature, potentially ruling out all these apparent swampland theories.

Slow and safe gravitinos

It has been argued that supergravity models of inflation with vanishing sound speeds, $c_s$, lead to an unbounded growth in the production rate of gravitinos. We consider several models of inflation to delineate the conditions for which $c_s = 0$. In models with unconstrained superfields, we argue that the mixing of the goldstino and inflatino in a time-varying background prevents the uncontrolled production of the longitudinal modes. This conclusion is unchanged if there is a nilpotent field associated with supersymmetry breaking with constraint ${\bf S^2} =0$, i.e. sgoldstino-less models. Models with a second orthogonal constraint, ${\bf S(\Phi-\bar{\Phi})} =0$, where $\bf{\Phi}$ is the inflaton superfield, which eliminates the inflatino, may suffer from the over-production of gravitinos. However, we point out that these models may be problematic if this constraint originates from a UV Lagrangian, as this may require using higher derivative operators. These models may also exhibit other pathologies such as $c_s > 1$, which are absent in theories with the single constraint or unconstrained fields.

New Black Hole Solutions in N = 2 and N = 8 Gauged Supergravity

We review a special class of N=2 supergravity model that interpolates all the single-dilaton truncations of the maximal SO(8) gauged supergravity. We also provide explicit non-extremal, charged black hole solutions and their supersymmetric limits, asymptotic charges, thermodynamics and boundary conditions. We also discuss a suitable Hamilton–Jacobi formulation and related BPS flow equations for the supersymmetric configurations, with an explicit form for the superpotential function. Finally, we briefly analyze certain models within the class under consideration as consistent truncations of the maximal, N=8 gauged supergravity in four dimensions.