Solutions Of Type IIB Supergravity Research Articles

Pin(d, d) covariance of pure spinor equations for supersymmetric vacua and non-Abelian T-duality

In a supersymmetric compactification of Type II supergravity, preservation of mathcal{N} = 1 supersymmetry in four dimensions requires that the structure group of the generalized tangent bundle TM ⨁ T∗M of the six dimensional internal manifold M is reduced from SO(6) to SU(3) × SU(3). This topological condition on the internal manifold implies existence of two globally defined compatible pure spinors Φ1 and Φ2 of non-vanishing norm. Furthermore, these pure spinors should satisfy certain first order differential equations. In this paper, we show that non-Abelian T-duality (NATD) is a solution generating transformation for these pure spinor equations. We first show that the pure spinor equations are covariant under Pin(d, d) transformations. Then, we use the fact NATD is generated by a coordinate dependent Pin(d, d) transformation. The key point is that the flux produced by this transformation is the same as the geometric flux associated with the isometry group, with respect to which one implements NATD. We demonstrate our method by studying NATD of certain solutions of Type IIB supergravity with SU(2) isometry and SU(3) structure.

On the stability of AdS backgrounds with \u03bb-deformed factors

We investigate the stability of the non-supersymmetric solutions of type-IIB supergravity having an unwarped AdS factor and λ-deformed subspaces found in [26]. Among the plethora of solutions we study the perturbative stability of backgrounds with an AdSn, with n = 3, 4, 6, factor. Our analysis is performed from a lower dimensional effective theory which we construct. We uncover the regions and isolated points in the parameter space of potential perturbative stability.

Tachyonic de Sitter Solutions of 10d Type II Supergravities

AbstractCosmological models of the early or late universe exhibit (quasi) de Sitter space‐times with different stability properties. Considering models derived from string theory, the swampland program does not provide for now a definite characterisation of this stability. In this work we focus on de Sitter solutions of 10d type II supergravities, candidates for classical de Sitter string backgrounds: surprisingly, all known examples are unstable with . We aim at proving the existence of such a systematic tachyon, and getting formally a bound on the value of . To that end, we develop three methods, giving us various sufficient conditions for having a tachyon upon assumptions, in analogy with de Sitter no‐go theorems. Our analysis eventually indicates the existence of variety of different tachyons, and related bounds on . We use this knowledge to find 10 new de Sitter solutions of type IIB supergravity, that have tachyons of a different kind, higher values and new 6d geometries. One solution even appears to be stable, with however non‐compact extra dimensions.

Resolution \xe0 la Kronheimer of mathbb {C}^3/Gamma singularities and the Monge\u2013Amp\xe8re equation for Ricci-flat K\xe4hler metrics in view of D3-brane solutions of supergravity

In this paper, we analyze the relevance of the generalized Kronheimer construction for the gauge/gravity correspondence. We begin with the general structure of D3-brane solutions of type IIB supergravity on smooth manifolds Y^Gamma that are supposed to be the crepant resolution of quotient singularities mathbb {C}^3/Gamma with Gamma a finite subgroup of SU(3). We emphasize that nontrivial 3-form fluxes require the existence of imaginary self-dual harmonic forms omega ^{2,1}. Although excluded in the classical Kronheimer construction, they may be reintroduced by means of mass deformations. Next we concentrate on the other essential item for the D3-brane construction, namely, the existence of a Ricci-flat metric on Y^Gamma . We study the issue of Ricci-flat Kähler metrics on such resolutions Y^Gamma , with particular attention to the case Gamma =mathbb {Z}_4. We advance the conjecture that on the exceptional divisor of Y^Gamma the Kronheimer Kähler metric and the Ricci-flat one, that is locally flat at infinity, coincide. The conjecture is shown to be true in the case of the Ricci-flat metric on mathrm{tot} K_{{mathbb {W}P}[112]} that we construct, i.e., the total space of the canonical bundle of the weighted projective space {mathbb {W}P}[112], which is a partial resolution of mathbb {C}^3/mathbb {Z}_4. For the full resolution, we have Y^{mathbb {Z}_4}={text {tot}} K_{mathbb {F}_{2}}, where mathbb {F}_2 is the second Hirzebruch surface. We try to extend the proof of the conjecture to this case using the one-parameter Kähler metric on mathbb {F}_2 produced by the Kronheimer construction as initial datum in a Monge–Ampère (MA) equation. We exhibit three formulations of this MA equation, one in terms of the Kähler potential, the other two in terms of the symplectic potential but with two different choices of the variables. In both cases, one can establish a series solution in powers of the variable along the fibers of the canonical bundle. The main property of the MA equation is that it does not impose any condition on the initial geometry of the exceptional divisor, rather it uniquely determines all the subsequent terms as local functionals of this initial datum. Although a formal proof is still missing, numerical and analytical results support the conjecture. As a by-product of our investigation, we have identified some new properties of this type of MA equations that we believe to be so far unknown.

Holographic Coulomb branch solitons, quasinormal modes, and black holes

Four-dimensional mathcal{N} = 4 supersymmetric Yang-Mills theory, at a point on the Coulomb branch where SU(N) gauge symmetry is spontaneously broken to SU(N − 1) × U(1), admits BPS solitons describing a spherical shell of electric and/or magnetic charges enclosing a region of unbroken gauge symmetry. These solitons have been proposed as gauge theory models for certain features of asymptotically flat extremal black holes. In the ’t Hooft large N limit with large ’t Hooft coupling, these solitons are holographically dual to certain probe D3-branes in the AdS5 × S5 solution of type IIB supergravity. By studying linearised perturbations of these D3-branes, we show that the solitons support quasinormal modes with a spectrum of frequencies sharing both qualitative and quantitative features with asymptotically flat extremal black holes.

Mathcal{N} = (0, 2) AdS3 solutions of type IIB and F-theory with generic fluxes

We consider the most general AdS3 solutions of type IIB supergravity admitting a dynamical SU(3) structure and preserving mathcal{N} = (0, 2) supersymmetry. The analysis is broken into three distinct classes depending on whether the dynamical SU(3) structure degenerates to a strict SU(3) structure. The first class we consider allows for a holomorphically varying axio-dilaton consistent with the presence of (p, q) 7-branes in addition to D3-branes and (p, q) 5-branes. In the remaining two classes the axio-dilaton may vary but does not do so holomorphically. The second class of solution allows for 5-branes and 1-branes but no D3-branes, whilst in the final class all branes can be present. We illustrate our results with examples of such solutions including a new infinite family with all fluxes but the axion turned on.

Kaluza-Klein spectroscopy for the Leigh-Strassler SCFT

We apply recently developed tools from exceptional field theory to calculate the full Kaluza-Klein spectrum of the AdS5 Pilch-Warner solution of type IIB supergravity. Through the AdS/CFT correspondence this yields detailed information about the spectrum of protected and unprotected operators of the four-dimensional mathcal{N} = 1 Leigh-Strassler SCFT, in the planar limit. We also calculate explicitly the superconformal index of the SCFT in this limit and show that it agrees precisely with the spectrum of protected operators in the supergravity calculation.

AdS2 \xd7 S2 \xd7 CY2 solutions in Type IIB with 8 supersymmetries

We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure of the space is AdS2 × S2 × CY2 × S1 fibered over an interval. These solutions can be related through double analytical continuations with those recently constructed in [1]. Both types of solutions are however dual to very different superconformal quantum mechanics. We show that our solutions fit locally in the class of AdS2 × S2 × CY2 solutions fibered over a 2d Riemann surface Σ constructed by Chiodaroli, Gutperle and Krym, in the absence of D3 and D7 brane sources. We compare our solutions to the global solutions constructed by Chiodaroli, D’Hoker and Gutperle for Σ an annulus. We also construct a cohomogeneity-two family of solutions using non-Abelian T-duality. Finally, we relate the holographic central charge of our one dimensional system to a combination of electric and magnetic fluxes. We propose an extremisation principle for the central charge from a functional constructed out of the RR fluxes.

D3-Branes Wrapped on a Spindle.

We construct supersymmetric AdS_{3}×Σ solutions of minimal gauged supergravity in D=5, where Σ is a two-dimensional orbifold known as a spindle. Remarkably, these uplift on S^{5}, or more generally on any regular Sasaki-Einstein manifold, to smooth solutions of type IIB supergravity. The solutions are dual to d=2, N=(0,2) SCFTs and we show that the central charge for the gravity solution agrees with a field theory calculation associated with D3-branes wrapped on Σ.

A correspondence between Ricci-flat Kerr and Kaluza-Klein AdS black hole

We establish an explicit correspondence of Einstein gravity on the squashed spheres that are the U(1) bundles over ℂℙm to the Kaluza-Klein AdS gravity on the tori. This allows us to map the Ricci-flat Kerr metrics in odd dimensions with all equal angular momenta to charged Kaluza-Klein AdS black holes that can be lifted to become singly rotating M-branes and D3-branes. Furthermore, we find maps between Ricci-flat gravitational instantons to the AdS domain walls. In particular the supersymmetric bolt instantons correspond to domain walls that can be interpreted as distributed M-branes and D3-branes, whilst the non-supersymmetric Taub-NUT solutions yield new domain walls that can be lifted to become solutions in M-theory or type IIB supergravity. The correspondence also inspires us to obtain a new superpotential in the Kaluza-Klein AdS gravity in four dimensions.

Holographic and localization calculations of boundary F for mathcal{N} = 4 SUSY Yang-Mills theory

mathcal{N} = 4 Supersymmetric Yang-Mills (SYM) theory can be defined on a half-space with a variety of boundary conditions preserving scale invariance and half of the original supersymmetry; more general theories with the same symmetry can be obtained by coupling to a 3D SCFT at the boundary. Each of these theories is characterized by a quantity called “boundary F”, conjectured to decrease under boundary renormalization group flows. In this paper, we calculate boundary F for U(N) mathcal{N} = 4 SYM theory with the most general half-supersymmetric boundary conditions arising from string theory constructions with D3-branes ending on collections of D5-branes and/or NS5-branes. We first perform the calculation holographically by evaluating the entanglement entropy for a half-ball centered on the boundary using the Ryu-Takayanagi formula in the dual type IIB supergravity solutions. For boundary conditions associated with D3-branes ending on D5 branes only or NS5-branes only, we also calculate boundary F exactly by evaluating the hemisphere partition function using supersymmetric localization. The leading terms at large N in the supergravity and localization results agree exactly as a function of the t’ Hooft coupling λ.

Super Yang-Mills theories with inhomogeneous mass deformations

We construct the 4-dimensional mathcal{N}=frac{1}{2} and mathcal{N} = 1 inhomogeneously mass-deformed super Yang-Mills theories from the mathcal{N} = 1* and mathcal{N} = 2* theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the mathcal{N} = 4 super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the mathcal{N}=frac{1}{2} theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions.

Spatially modulated and supersymmetric mass deformations of mathcal{N} = 4 SYM

We study mass deformations of mathcal{N} = 4, d = 4 SYM theory that are spatially modulated in one spatial dimension and preserve some residual supersymmetry. We focus on generalisations of mathcal{N} = 1∗ theories and show that it is also possible, for suitably chosen supersymmetric masses, to preserve d = 3 conformal symmetry associated with a co-dimension one interface. Holographic solutions can be constructed using D = 5 theories of gravity that arise from consistent truncations of SO(6) gauged supergravity and hence type IIB supergravity. For the mass deformations that preserve d = 3 superconformal symmetry we construct a rich set of Janus solutions of mathcal{N} = 4 SYM theory which have the same coupling constant on either side of the interface. Limiting classes of these solutions give rise to RG interface solutions with mathcal{N} = 4 SYM on one side of the interface and the Leigh-Strassler (LS) SCFT on the other, and also to a Janus solution for the LS theory. Another limiting solution is a new supersymmetric AdS4× S1× S5 solution of type IIB supergravity.

Holographic entanglement entropy and complexity of microstate geometries

We study holographic entanglement entropy and holographic complexity in a two-charge, frac{1}{4} -BPS family of solutions of type IIB supergravity, controlled by one dimensionless parameter. All the geometries in this family are asymptotically AdS3×\U0001d54a3×\U0001d54b4 and, varying the parameter that controls them, they interpolate between the global AdS3× \U0001d54a3× \U0001d54b4 and the massless BTZ3× \U0001d54a3× \U0001d54b4 geometry. Due to AdS/CFT duality, these geometries are dual to pure CFT heavy states.We find that there is no emergence of entanglement shadow for all the values of the parameter and we discuss the relation with the massless BTZ result, underlying the relevance of the nature of the dual states.We also compute the holographic complexity of formation of these geometries, finding a nice monotonic function that interpolates between the pure AdS3 result and the massless BTZ one.

Holomorphic waves of black hole microstructure

We obtain the largest families constructed to date of frac{1}{8} -BPS solutions of type IIB supergravity. They have the same charges and mass as supersymmetric D1-D5-P black holes, but they cap off smoothly with no horizon. Their construction relies on the structure of superstratum states, but allows the momentum wave to have an arbitrary shape. Each family is based on an arbitrary holomorphic function of one variable. More broadly, we show that the most general solution is described by two arbitrary holomorphic functions of three variables. After exhibiting several new families of such “holomorphic superstrata,” we reformulate the BPS backgrounds and equations in holomorphic form and show how this simplifies their structure. The holomorphic formulation is thus both a fundamental part of superstrata as well as an effective tool for their construction. In addition, we demonstrate that holomorphy provides a powerful tool in establishing the smoothness of our solutions without constraining the underlying functions. We also exhibit new families of solutions in which the momentum waves of the superstrata are highly localized at infinity but diffuse and spread into the infra-red limit in the core of the superstratum. Our work also leads to some results that can be tested within the dual CFT.

Heating up holography for single-trace Joverline{T} deformations

We study thermodynamic aspects of a tractable toy model of holography for extremal Kerr black holes proposed in [1]. On the gravity side, the theory can be described by the worldsheet action of string theory on a warped AdS3 background supported by NS-NS flux. Once we turn on temperature, the deformed background is described by a black string solution of type IIB supergravity that features a locally warped AdS3 factor. The dual field theory is conjectured to be a single-trace version of a Joverline{T} -deformed CFT at finite temperature. As evidence for the correspondence we show that the spectrum of strings winding on the deformed background agrees with the spectrum of Joverline{T} -deformed CFTs. Furthermore, we show that the gravitational charges of the black string match the averaged charges of a thermal ensemble in the dual field theory. Finally, we reproduce the Bekenstein-Hawking entropy of the black string from the microscopic density of states of Joverline{T} -deformed CFTs.

S-folds and (non-)supersymmetric Janus solutions

The S-fold description of Janus-type solutions of type IIB supergravity is investigated. This is done by first studying a U(1) × U (1) invariant sector of the four­ dimensional dyonically-gauged [SO(1) × SO(6)] × ℝ12 maximal supergravity that arises upon reduction of type IIB supergravity on ℝ × S5. Two AdS4 solutions preserving SU(3) and SO (6) gauge symmetry together with mathcal{N} = 1 and mathcal{N} = 0 supersymmetry are found within this sector. Fetching techniques from the E 7(7) exceptional field theory, these solutions are uplifted to ten-dimensional S-folds of type IIB Janus-type solutions of the form AdS4 × ℝ × M5. The solutions presented here are natural candidates for the holographic duals of three-dimensional mathcal{N} = 1 and mathcal{N} = 0 interface super-Yang-Mills theories with SU(3) and SU(4) internal symmetry.

A holographic kaleidoscope for mathcal{N} = 1*

We study in detail the recently-found family of asymptotically AdS5× S5 type IIB supergravity solutions dual to the mathcal{N} = 1* SYM theory with equal masses. The backgrounds exhibit a naked singularity and are labelled by a dimensionless parameter, λ, which is interpreted as the ratio of the gaugino condensate and the mass in the dual field theory. When |λ| < 1 we show that the naked singularity is due to a smeared distribution of polarized (p, q) five-branes. For this range of parameters we study the nature of the singularity using probe strings and show that the dual line operators exhibit screening behavior. These features are in line with the physics anticipated in the work of Polchinski-Strassler. For |λ| = 1 the naked singularity has qualitatively different behavior which has no clear brane interpretation. We show that when λ = 1 the singularity can be excised and replaced by a smooth Euclidean supergravity solution with an S4 boundary.

Strongly coupled N=4 supersymmetric Yang-Mills plasma on the Coulomb branch. II. Transport coefficients and hard probe parameters

We study $\mathcal{N} = 4$ super Yang-Mills theory on the Coulomb branch (cSYM) by using its Type IIB supergravity dual. We compute the transport coefficients, and hard probe parameters of $\mathcal{N} = 4$ cSYM at finite temperature $T$. We use the rotating black 3-brane solution of Type IIB supergravity with a single non-zero rotation parameter $r_{0}$ after analytically continuing $r_{0}\rightarrow -ir_{0}$, and in an ensemble where the Hawking temperature $T$ and a scalar condensate $<\mathcal{O}>\sim r_{0}^4$ are held fixed. We find that the bulk viscosity to entropy density ratio of the large black hole branch decreases with temperature and has a maxima around the critical temperature $T_{c}$ while, for the small black hole branch, it increases with temperature. The other transport coefficients and parameters of hard probes, such as the conductivity, jet quenching parameter, drag force, and momentum diffusion coefficients of the large black hole branch increase with temperature and asymptote to their conformal value while, for the small black hole branch, they decrease with temperature.

Strongly coupled N=4 supersymmetric Yang-Mills plasma on the Coulomb branch. I. Thermodynamics

We study $\mathcal{N} = 4$ super Yang-Mills theory on the Coulomb branch (cSYM) in the strong coupling limit by using the AdS/CFT correspondence. The dual geometry is the rotating black 3-brane Type IIB supergravity solution with a single non-zero rotation parameter $r_{0}$ which sets a fixed mass scale corresponding to the scalar condensate $<\mathcal{O}>\,\,\sim r_{0}^4$ in the Coulomb branch. We introduce a new ensemble where $T$ and $<\mathcal{O}>$ are held fixed, i.e., the free energy $F(T,<\mathcal{O}>)$ is a function of $T$ and $<\mathcal{O}>$. We compute the equation of state (EoS) of $\mathcal{N} = 4$ cSYM at finite $T$, as well as the heavy quark-antiquark potential and the quantized mass spectrums of the scalar and spin-2 glueballs at $T=0$. By computing the Wilson loop (minimal surface) at $T=0$, we determine the heavy quark-antiquark potential $V(L)$ to be the Cornell potential, which is confining for large separation $L$. At $T\neq 0$, we find two black hole branches: the large black hole and small black hole branches. For the large black hole branch, that has positive specific heat, we find qualitatively similar EoS to that of pure Yang-Mills theory on the lattice. For the small black hole branch, that has negative specific heat, we find an EoS where the entropy and energy densities decrease with $T$. We also find a second-order phase transition between the large and small black hole branches with critical temperature $T_c=T_{min}$.