We study the gravity duals of symmetry-breaking deformations of superconformal field theories, AdS/CFT dual to Type IIB string theory on AdS_5 x Y where Y is a Sasaki-Einstein manifold. In these vacua both conformal invariance and baryonic symmetries are spontaneously broken. We present a detailed discussion of the supergravity moduli space, which involves flat form fields on asymptotically conical Calabi-Yau manifolds, and match this to the gauge theory vacuum moduli space. We discuss certain linearised fluctuations of the moduli, identifying the Goldstone bosons associated with spontaneous breaking of non-anomalous baryonic symmetries. The remaining moduli fields are related to spontaneous breaking of anomalous baryonic symmetries. We also elaborate on the proposal that computing condensates of baryon operators is equivalent to computing the partition function of a non-compact Euclidean D3-brane in the background supergravity solution, with fixed boundary conditions at infinity.
We give an explicit formulation of the time dependent AdS/CFT correspondence when there are multiple vacua present in Lorentzian signature. By computing sample two point functions we show how different amplitudes are related by cosmological particle production. We illustrate our methods in two example spacetimes: (a) a ``bubble of nothing'' in AdS space, and (b) an asymptotically locally AdS spacetime with a bubble of nothing on the boundary. In both cases the alpha vacua of de Sitter space make an interesting appearance.
The Schwarzschild, Schwarzschild-AdS, and Schwarzschild-de Sitter solutions all admit freely acting discrete involutions which commute with the continuous symmetries of the spacetimes. Intuitively, these involutions correspond to the antipodal map of the corresponding spacetimes. In analogy with the ordinary de Sitter example, this allows us to construct new vacua by performing a Mottola-Allen transform on the modes associated with the Hartle-Hawking, or Euclidean, vacuum. These vacua are the `alpha'-vacua for these black holes. The causal structure of a typical black hole may ameliorate certa…
In this paper we investigate the relation between the bulk and boundary in AdS/CFT. We first discuss the relation between the Poincare and the global vacua, and then study various probes of the bulk from the boundary theory point of view. We derive expressions for retarded propagators and note that objects in free fall look like expanding bubbles in the boundary theory. We also study several Yang-Mills theory examples where we investigate thermal screening and confinement using propagators. In the case of confinement we also calculate the profile of a flux tube and provide an alternative deriv…
AdS flux vacua with a parametric separation between the AdS and KK scales have been conjectured to be in the Swampland. We study flux compactifications of massive IIA supergravity with O6 planes which are claimed to allow moduli-stabilised and scale separated AdS$_3$ and AdS$_4$ vacua at arbitrary weak coupling and large volume. A recent refinement of the AdS Distance Conjecture is shown to be inconsistent with the class of AdS$_3$ vacua because the requisite discrete higher form symmetries are absent. We further perform a tree-level study of non-perturbative decays for the nonsupersymmetric v…
In this paper, we are looking for $\mathcal{N}=1$, AdS$_4$ sourceless vacua in type IIB. While several examples exist in type IIA , there exists only one example of such vacua in type IIB . Thanks to the framework of generalized geometry we were able to devise a semi-algorithmical method to look for sourceless vacua. We present this method, which can easily be generalized to more complex cases, and give two new vacua in type IIB.
We consider two infinite families of Non-Supersymmetric $AdS_4$ vacua, called Type 2) and Type 3) vacua, that arise in massive IIA supergravity with flux. We show that both families are perturbatively stable. We then examine non-perturbative decays of these vacua to other supersymmetric and non-supersymmetric $AdS_4$ vacua mediated by instantons in the thin wall approximation. We find that many decays are ruled out since the tension of the interpolating domain wall is too big compared to the energy difference in AdS units. In fact, within our approximations no decays of Type 2) vacua are allow…
We determine the conditions for maximally supersymmetric AdS_5 vacua of five-dimensional gauged N=2 supergravity coupled to vector-, tensor- and hypermultiplets charged under an arbitrary gauge group. In particular, we show that the unbroken gauge group of the AdS_5 vacua has to contain an U(1)_R-factor. Moreover we prove that the scalar deformations which preserve all supercharges form a Kahler submanifold of the ambient quaternionic Kahler manifold spanned by the scalars in the hypermultiplets.
We construct new families of non-supersymmetric sourceless type IIA AdS4 vacua on those coset manifolds that also admit supersymmetric solutions. We investigate the spectrum of left-invariant modes and find that most, but not all, of the vacua are stable under these fluctuations. Generically, there are also no massless moduli.
We perform a systematic search for anti-de Sitter vacua of maximal supergravity with N>2 residual supersymmetries. We find that maximal supergravity admits two 1-parameter classes of N=3 and N=4 vacua, respectively. They are embedded, for the different values of an angular parameter, in the $ω$-rotated SO(8) (N=3) and SO(1,7) (N=4 and 3) gauged models. All vacua disappear in the limit when $ω$ tends to zero. We determine the mass spectra and the AdS-supermultiplet structure. These appear to be the first and only N>2 supersymmetric AdS vacua in maximal supergravity, aside from the N=8 vacua of …
We study supersymmetric AdS$_7$ vacua of massive type IIA string theory, which were argued to describe the near-horizon limit of NS5/D6/D8-brane intersections and to be holographically dual to 6D $(1,0)$ theories. We show, for the case without D8-brane charges, that such vacua do not admit any supersymmetry-breaking deformations. Our result implies that the dual $(1,0)$ theories do not have a conformal manifold, thus extending previously known results for supersymmetric deformations. It is also in line with the recent conjecture that non-supersymmetric AdS vacua are in the swampland.
We study AdS backgrounds of N=4 supergravity in four space-time dimensions which preserve all sixteen supercharges. We show that the graviphotons have to form a subgroup of the gauge group that consists of an electric and a magnetic SO(3)_+ x SO(3)_-. Moreover, these N=4 AdS backgrounds are necessarily isolated points in field space which have no moduli.
We classify the N=4 supersymmetric AdS5 backgrounds that arise as solutions of five-dimensional N=4 gauged supergravity. We express our results in terms of the allowed embedding tensor components and identify the structure of the associated gauge groups. We show that the moduli space of these AdS vacua is of the form SU(1,m)/(U(1)x SU(m)) and discuss our results regarding holographically dual N=2 SCFTs and their conformal manifolds.
We analyse type IIA Calabi-Yau orientifolds with background fluxes and D6-branes. Rewriting the F-term scalar potential as a bilinear in flux-axion polynomials yields a more efficient description of the Landscape of flux vacua, as they are invariant under the discrete shift symmetries of the 4d effective theory. In particular, expressing the extremisation conditions of the scalar potential in terms of such polynomials allows for a systematic search of vacua. We classify families of N=0 Minkowski, N=1 AdS and N=0 AdS flux vacua, extending previous findings in the literature to the Calabi-Yau co…
We use exceptional field theory to compute Kaluza-Klein mass spectra around ${\rm AdS_{3}}$ vacua that sit in half-maximal gauged supergravity in three dimensions. The formalism applies to any vacuum that arises from a consistent truncation of higher-dimensional supergravity, no matter what symmetries are preserved. We illustrate its efficiency by computing the spectra of ${\cal N}=(2,0)$ and ${\cal N}=(1,1)$ six-dimensional supergravities on ${\rm AdS_{3}}\times S^{3}$ and of type II supergravity on ${\rm AdS_{3}}\times S^{3}\times S^{3}\times S^{1}$.
We study fully supersymmetric $AdS_6$ vacua of half-maxi\-mal $N=(1,1)$ gauged supergravity in six space-time dimensions coupled to $n$ vector multiplets. We show that the existence of $AdS_6$ backgrounds requires that the gauge group is of the form $G'\times G"\subset SO(4,n)$ where $G'\subset SO(3,m)$ and $G"\subset SO(1,n-m)$. In the $AdS_6$ vacua this gauge group is broken to its maximal compact subgroup $SO(3)\times H'\times H"$ where $H'\subset SO(m)$ and $H"\subset SO(n-m)$. Furthermore, the $SO(3)$ factor is the R-symmetry gauged by three of the four graviphotons. We further show that …
We give a classification of fully supersymmetric chiral ${\cal N}=(8,0)$ AdS$_3$ vacua in general three-dimensional half-maximal gauged supergravities coupled to matter. These theories exhibit a wealth of supersymmetric vacua with background isometries given by the supergroups OSp$(8|2,\mathbb{R})$, F(4), SU$(4|1,1)$, and OSp$(4^*|4)$, respectively. We identify the associated embedding tensors and the structure of the associated gauge groups. We furthermore compute the mass spectra around these vacua. As an off-spin we include results for a number of ${\cal N}=(7,0)$ vacua with supergroups OSp…
The moduli space of the supersymmetric massive IIA AdS4xS2(B4) vacua, where S2(B4) is a two-sphere bundle over a four-dimensional Kaehler-Einstein base B4, includes three independent parameters which can be thought of as corresponding to the sizes of AdS4, B4 and the S2 fiber. It might therefore be expected that these vacua do not suffer from the absence of scale separation. We show that the independence of the geometric moduli survives flux quantization. However, we uncover an attractor behavior whereby all sizes flow to equality in some neighborhood of spacetime independently of the initial …
We consider flux vacua attractor equations in type IIA string theory compactified on generalized geometries with orientifold projections. The four-dimensional N=1 superpotential in this compactification can be written as the sum of the Ramond-Ramond superpotential and a term described by (non)geometric flux charges. We exhibit a simple model in which supersymmetric AdS and Minkowski solutions are classified by means of discriminants of the two superpotentials. We further study various configurations without Ramond-Ramond flux charges. In this case we find supersymmetric AdS vacua both in the c…
We revisit various aspects of AdS$_4$ flux vacua with scale separation in type II supergravity and M-theory. We show that massless IIA allows both weakly and strongly coupled solutions for which the classical orientifold backreaction can be tuned small. This is explicitly verified by computing the backreaction at leading order in perturbation theory. We give evidence that the strongly coupled solutions can be lifted to scale-separated and sourceless (but classically singular) geometries in 11D supergravity.
The authors of arXiv:1610.01533 have recently proposed a stronger version of the weak gravity conjecture (WGC), based on which they concluded that all those non-supersymmetric AdS vacua that can be embedded within a constistent theory of quantum gravity necessarily develop instabilities. In this paper we further elaborate on this proposal by arguing that the aforementioned instabilities have a perturbative nature and arise from the crucial interplay between the closed and the open string sectors of the theory.
We consider D-dimensional Einstein gravity coupled to two U(1) fields and a dilaton with a scalar potential. We derive the condition that the analytical AdS black holes with two independent charges can be constructed. Turning off the cosmological constant, the extremal Reissner-Nordstrom black hole emerges as the harmonic superposition of the two U(1) building blocks. With the non-vanishing cosmological constant, our extremal solutions contain the near-horizon geometry of AdS_2 x R^{D-2} with or without a hyperscaling. We also obtain the magnetic AdS_{D-2} x Y^2 vacua where Y^2 can be R^2, S^2…
We consider genuine type IIB string theory (supersymmetric) brane intersections that preserve $(1+1)$D Lorentz symmetry. We provide the full supergravity solutions in their analytic form and discuss their physical properties. The Ansatz for the spacetime dependence of the different brane warp factors goes beyond the harmonic superposition principle. By studying the associated near-horizon geometry, we construct interesting classes of AdS$_3$ vacua in type IIB and highlight their relation to the existing classifications in the literature. Finally, we discuss their holographic properties.
We show how to construct supersymmetric warped AdS$_7$ vacua of massive IIA and AdS$_6$ vacua of IIB supergravity, using "half-maximal structures" of exceptional field theory. We use this formalism to obtain the minimal consistent truncations around these AdS vacua.
We evaluate the backreaction of O6-planes in scale-separated $\text{AdS}_3$ flux vacua of massive Type IIA. Using the appropriate flux scaling we show that the corrections to the various background fields and moduli are controlled and subleading when going from smeared to localized sources. Similarly, the backreaction corrections to the scalar potential are parametrically small in the scale-separation limit, assuming always that the near-O6-plane singularities will find a resolution within string theory, even in the presence of a Romans mass. Our analysis is based on the equations of motion an…
We classify the non-supersymmetric, and perturbatively stable within $D=4$, AdS vacua of maximal $D=4$ supergravity with a dyonic ISO(7) gauging in a large sector of the supergravity. Seven such vacua are established within this sector, all of them giving rise to non-supersymmetric $\textrm{AdS}_{4} \times \textrm{S}^{6}$ type IIA backgrounds with and without non-trivial warpings and with internal fluxes. Then, we analyse the dynamics of various probe D$p$-branes in these backgrounds searching for potential brane-jet instabilities. In all these cases, such instabilities are absent. Finally, an…
It has recently been conjectured that string theory does not admit de Sitter critical points. This note points out that in several cases, including KKLT or racetrack models, this statement is equivalent to the absence of supersymmetric Minkowski or AdS solutions. This equivalence arises from establishing the positivity of the potential in a large-radius limit, requiring a turnover of the potential before reaching an AdS vacuum. For example, this conjecture is incompatible with the simplest 1-modulus KKLT AdS supersymmetric solution.
Singularities of Spin(7) manifolds are considered in the worldsheet approach, and it is argued that the internal CFT describing a singular spin(7) has an enhanced ${\cal SW}({3\over 2},{3\over 2},2)$ algebra tensored with ${\cal N}=1$ linear dilaton CFT, much like singular Calabi-Yau CFTs have a ${\cal N}=2$ linear dilaton tensored with a suitable ${\cal N}=2$ SCFT. Upon adding fundamental strings, these vacua are related to $AdS_3$ vacua with ${\cal N}=1$ supersymmetry, completing the worldsheet classification of $AdS_3$ vacua with NS flux.
We ask the question of classical integrability for certain (classes of) supergravity vacua that contain an AdS$_3$ factor arising in massive IIA and IIB theories and realizing various and different amounts of supersymmetry. Our approach is based on a well-established method of analytic non-integrability for Hamiltonian systems. To detect a non-integrable sector we consider a non-trivially wrapped string soliton and study its fluctuations. We answer in the negative for each and every one of the supergravity solutions. That is, of course, modulo very specific limits where the metrics reduce to t…
We construct a generalization of Witten's Kaluza-Klein instanton, where a higher-dimensional sphere (rather than a circle as in Witten's instanton) collapses to zero size and the geometry terminates at a bubble of nothing, in a low energy effective theory of M theory. We use the solution to exhibit instability of non-supersymmetric AdS_5 vacua in M Theory compactified on positive Kaehler-Einstein spaces, providing a further evidence for the recent conjecture that any non-supersymmetric anti-de Sitter vacuum supported by fluxes must be unstable.
We argue that supersymmetric higher-dimension operators in the effective actions of M-theory and IIB string theory do not affect the maximally supersymmetric vacua: $adS_4\times S^7$ and $adS_7\times S^4$ in M-theory and $adS_5\times S^5$ in IIB string theory. All these vacua are described in superspace by a fixed point with all components of supertorsion and supercurvature being supercovariantly constant. This follows from 32 unbroken supersymmetries and allows us to prove that such vacua are exact.
The dS/CFT correspondence is illuminated through an analysis of massive scalar field theory in d-dimensional de Sitter space. We consider a one-parameter family of dS-invariant vacua related by Bogolyubov transformations and compute the corresponding Green functions. It is shown that none of these Green functions correspond to the one obtained by analytic continuation from AdS. Among this family of vacua are in (out) vacua which have no incoming (outgoing) particles on past (future) infinity. Surprisingly, it is shown that in odd spacetime dimensions the in and out vacua are the same, implying…
We study $AdS_3$ supersymmetric vacua in N=4 and N=8, three dimensional gauged supergravities, with scalar manifolds $(\frac{SO(4,4)}{SO(4)\times SO(4)})^2$ and $\frac{SO(8,8)}{SO(8)\times SO(8)}$, non-semisimple Chern-Simons gaugings $SO(4)\ltimes {\bf R}^6$ and $(SO(4)\ltimes {\bf R}^6)^2$, respectively. These are in turn equivalent to SO(4) and $SO(4)\times SO(4)$ Yang-Mills theories coupled to supergravity. For the N=4 case, we study renormalization group flows between UV and IR $AdS_3$ vacua with the same amount of supersymmetry: in one case, with (3,1) supersymmetry, we can find an analy…
Conformal deformations manifest in the AdS/CFT correspondence as boundary conditions on the AdS field. Heretofore, double-trace deformations have been the primary focus in this context. To better understand multitrace deformations, we revisit the relationship between the generating AdS partition function for a free bulk theory and the boundary CFT partition function subject to arbitrary conformal deformations. The procedure leads us to a formalism that constructs bulk fields from boundary operators. Using this formalism, we independently replicate the holographic RG flow narrative to go on to …
We calculate the scalar quasinormal modes of warped $AdS_3$ black holes analytically. We find that in general they are not in agreement with the prediction of the usual AdS/CFT correspondence. Nevertheless, for the black hole not deviating far from BTZ black hole, the quasinormal frequencies are still well consistent with AdS/CFT correspondence.
In this letter we examine some structural aspects of the AdS/CFT such as the way of obtaining the expectation value of product of operators of the CFT, and ideas that should be considered when a proof of AdS/CFT is under consideration.
We study N=1 compactification of IIB supergravity to AdS4. The internal manifold must have SU(2)-structure. By putting some restrictions on the SU(2) torsion classes, we can perform an exhaustive scan of all possible solutions on group manifolds. We show that sourceless solutions don't exist and that the presence of O5 and O7 orientifolds is mandatory. We also find a new solution and relate it by T-duality to a known type IIA solution with O6 planes.
In this note we study the mass spectrum of type IIB flux compactifications. We first give a general discussion of the mass matrix for F-term vacua in four-dimensional N=1 supergravity theories and then specialize to type IIB Calabi-Yau orientifold compactifications in the presence of geometric and non-geometric fluxes. F-term vacua in this setting are in general AdS$_4$ vacua for which we compute the conformal dimensions of operators dual to the scalar fields. For the mirror-dual of the DGKT construction we find that one-loop corrections to the complex-structure moduli space lead to real-value…
We show how all known N=2, d=4,5,6 maximally supersymmetric vacua (Hpp-waves and aDSxS solutions) are related through dimensional reduction/oxidation preserving all the unbroken supersymmetries. In particular we show how the N=2, d=5 family of vacua (which are the near-horizon geometry of supersymmetric rotating black holes) interpolates between aDS_2xS^3 and aDS_3xS^2 in parameter space and how it can be dimensionally reduced to an N=2, d=4 dyonic Robinson-Bertotti solution with geometry aDS_2xS^2 and oxidized to an N=2, d=6 solution with aDS_3xS^3 geometry (which is the near-horizon of the s…
In the context of AdS3/CFT2, we address spacetimes with a certain sort of internal infinity as typified by the extreme BTZ black hole. The internal infinity is a null circle lying at the end of the black hole's infinite throat. We argue that such spacetimes may be described by a product CFT of the form CFT-L * CFT-R, where CFT-R is associated with the asymptotically AdS boundary while CFT-L is associated with the null circle. Our particular calculations analyze the CFT dual of the extreme BTZ black hole in a linear toy model of AdS3/CFT2. Since the BTZ black hole is a quotient of AdS3, the dua…
We present a new Type IIB supergravity background of the warped form AdS$_4\times \mathcal{M}_6$ with dilaton, $B$-field and all Ramond-Ramond fluxes turned on. We obtain the solution by applying non-Abelian T-duality to a certain representative of a class of AdS$_4$ backgrounds in massive IIA supergravity. By explicitly constructing the Killing spinor of the seed solution and using an argument involving Kosmann spinorial Lie derivative we demonstrate that the background is supersymmetric.
We identify 219 AdS$_4$ solutions in four-dimensional dyonically gauged ISO(7) $\mathcal{N}=8$ supergravity and present some of their properties. One of the new solutions preserves $\mathcal{N}=1$ supersymmetry and provides a rare explicit example of an AdS$_4$ vacuum dual to a 3d SCFT with no continuous global symmetry. There are also two new non-supersymmetric solutions for which all 70 scalar fields in the supergravity theory have masses above the BF bound. All of these AdS$_4$ solutions can be uplifted to massive type IIA supergravity. Motivated by this we present the low lying operator sp…
We introduce the AdS/CFT correspondence as a natural extension of QFT in a fixed AdS background. We start by reviewing some general concepts of CFT, including the embedding space formalism. We then consider QFT in a fixed AdS background and show that one can define boundary operators that enjoy very similar properties as in a CFT, except for the lack of a stress tensor. Including a dynamical metric in AdS generates a boundary stress tensor and completes the CFT axioms. We also discuss some applications of the bulk geometric intuition to strongly coupled QFT. Finally, we end with a review of th…
Only two kinds of compactification are known that lead to four-dimensional supersymmetric AdS vacua with moduli stabilisation and separation of scales at tree-level. The most studied ones are compactifications of massive IIA supergravity on SU(3) structures with smeared O6 planes, for which a general ten-dimensional expression for the solution in terms of the SU(3) structure was found. Less studied are compactifications of IIB supergravity with smeared O5/O7 planes. In this paper we derive a general ten-dimensional expression for the smeared O5/O7 solutions in terms of SU(2) structures. For a …
We argue that the Maldacena-Nunez no-go theorem excluding Minkowski and de Sitter vacua in flux compactifications can be extended to exclude anti-de Sitter (AdS) vacua for which the Kaluza-Klein scale is parametrically smaller than the AdS length scale. As a practical application of this observation we demonstrate that the mechanism to resolve O6 singularities in massive type IIA at the classical level is likely not to occur in AdS compactifications with scale separation. We furthermore remark that a compactification to four observable dimensions implies a large cosmological hierarchy.
On the branes behind scale-separated AdS$_{3}$ flux vacua
Universidad de Oviedo（奥维耶多大学）；Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA)（阿斯图里亚斯空间科学与技术大学研究所）；Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学）
We study maximally supersymmetric Anti-de Sitter backgrounds in consistent N=2 truncations of type IIB supergravity compactified on the Sasaki-Einstein manifold $T^{1,1}$. In particular, we focus on truncations that contain fields coming from the nontrivial second and third cohomology forms on $T^{1,1}$. These give rise to N=2 supergravity coupled to two vector- and two hypermultiplets (Betti-vector truncation) or one vector- and three hypermultiplets (Betti-hyper truncation), respectively. We find that both truncations admit AdS$_5$ backgrounds with the gauge group always being broken but con…
We find new twisted Yangian symmetries of the AdS/CFT reflection matrices for the Y=0 maximal giant graviton and D5-brane. These new symmetries originate from the known secret symmetries of the Yangian symmetry of the AdS/CFT S-matrix.
We study five-dimensional $N=4$ gauged supergravity coupled to five vector multiplets with $SO(2)_D\times SO(3)\times SO(3)$ gauge group. There are four supersymmetric $AdS_5$ vacua in the truncation to $SO(2)_{\textrm{diag}}$ invariant scalars. Two of these vacua preserve the full $N=4$ supersymmetry with $SO(2)_D\times SO(3)\times SO(3)$ and $SO(2)_D\times SO(3)_{\textrm{diag}}$ symmetries. These have an analogue in $N=4$ gauged supergravity with $SO(2)\times SO(3)\times SO(3)$ gauge group. The other two $AdS_5$ vacua preserve only $N=2$ supersymmetry with $SO(2)_{\textrm{diag}}\times SO(3)$…
Mack has conjectured that all conformal field theories are equivalent to string theories. We explore the example of the two-dimensional minimal model CFTs and confirm that the Mellin transformed amplitudes have the desired properties of string theory in three-dimensional anti-de Sitter spacetime.
