Employing uplift formulae, we uplift supersymmetric $AdS_6$ black holes from $F(4)$ gauged supergravity to massive type IIA and type IIB supergravity. In massive type IIA supergravity, we obtain supersymmetric $AdS_6$ black holes asymptotic to the Brandhuber-Oz solution. In type IIB supergravity, we obtain supersymmetric $AdS_6$ black holes asymptotic to the non-Abelian T-dual of the Brandhuber-Oz solution. For the uplifted black hole solutions, we calculate the holographic entanglement entropy. In massive type IIA supergravity, it precisely matches the Bekenstein-Hawking entropy of the black hole solutions.
We revisit non-rotating, dyonically charged, and supersymmetric AdS$_4$ black holes, which are solutions of $\mathcal{N}=2$ gauged supergravity with vector- and hyper-multplets. Uplifting the near horizon solutions to $D=11$ supergravity on seven-dimensional Sasaki-Einstein manifolds, we show that dyonic AdS$_4$ black holes correspond to AdS$_2$ solutions with electric and magnetic baryonic fluxes in $D=11$ supergravity. We identify the off-shell AdS$_4$ black hole solutions with parameters of $D=11$ AdS$_2$ solutions without imposing the equations of motion. We calculate the entropy of dyonic…
We find a new supersymmetric solution of type IIB supergravity which is the uplift of the GPPZ solution of maximal SO$(6)$ gauged supergravity in five dimensions. This background is expected to be holographically dual to an $\mathcal{N}=1^{*}$ supersymmetric mass deformation of four-dimensional $\mathcal{N}=4$ SYM. The ten-dimensional solution is singular in the region corresponding to the IR regime of the dual gauge theory and we discuss the physics of the singularity in some detail.
We consider flux compactification of type II string theory with local sources on SU(3)-structure manifolds. By adding pseudo-calibrated anti-$Dp$-branes wrapped on supersymmetric cycles we generalize all existing models so that the effective $d=4,$ ${\cal N}=1$ supergravity now includes a nilpotent multiplet. We present a new dictionary between string theory models and K{ä}hler potential $K$ and superpotential $W$ for these dS supergravities with a nilpotent multiplet and non-linearly realized local supersymmetry. In addition to KKLT and LVS with uplifting $\overline{D3}$-branes, we have now n…
In this note, we review our construction of de Sitter vacua in type IIB flux compactifications, in which moduli stabilization and D-term uplifting can be combined consistently with the supergravity constraints. Here, the closed string fluxes fix the dilaton and the complex structure moduli while perturbative quantum corrections to the Kähler potential stabilize the volume Kahler modulus in an AdS_4-vacuum. Then, magnetized D7-branes provide consistent supersymmetric D-term uplifting towards dS_4. Based on hep-th/0602253.
Recently it was found that a broad class of existing inflationary models based on supergravity can be significantly simplified if some of the standard, unconstrained chiral superfields are replaced by nilpotent superfields, associated with Volkov-Akulov supersymmetry. The same method allows to simplify the existing models of uplifting of AdS vacua in string theory. In this paper we will show that one can go well beyond simplifying the models that already exist. We will propose a broad class of new models of chaotic inflation based on supergravity with nilpotent superfields, which simultaneousl…
The quintessence-like potential of vacuum energy can meet the requirement from both quantum gravity and the accelerating expansion of the universe. The anti-de Sitter vacuum in string theory has to be lifted to the meta-stable de Sitter vacuum with positive vacuum energy density to explain the accelerating expansion of the universe. Based on the possible large scale Lorentz violation, we define an effective cosmological constant which depends not only on the bare cosmological constant but also on the Lorentz violation effect. We find the evolution of the effective cosmological constant exhibit…
An important ingredient in the construction of phenomenologically viable superstring models is the uplifting of Anti-de Sitter supersymmetric critical points in the moduli sector to metastable Minkowski or de Sitter vacua with broken supersymmetry. In all cases described so far, uplifting results in a displacement of the potential minimum away from the critical point and, if the uplifting is large, can lead to the disappearance of the minimum altogether. We propose a variant of F-term uplifting which exactly preserves supersymmetric critical points and shift symmetries at tree level. In spite …
We study in detail the stability properties of the simplest F-term uplifting mechanism consistent with the integration of heavy moduli. This way of uplifting vacua guarantees that the interaction of the uplifting sector with the moduli sector is consistent with integrating out the heavy fields in a supersymmetric way. The interactions between light and heavy fields are characterized in terms of the Kahler invariant function, G = K + log |W|^2, which is required to be separable in the two sectors. We generalize earlier results that when the heavy fields are stabilized at a minimum of the Kahler…
Moduli stabilization in the type IIA massive string theory so far was achieved only in the AdS vacua. The uplifting to dS vacua has not been performed as yet: neither the analogs of type IIB anti-D3 brane at the tip of the conifold, nor the appropriate D-terms have been identified. The hope was recently expressed that the F-term uplifting may work. We investigate this possibility in the context of a simplified version of the type IIA model developed in hep-th/0505160 and find that the F-term does not uplift the AdS vacua to dS vacua with positive CC. Thus it remains a challenging task to find …
Using the harmonic superspace method and the duality between real and complex representations of hypermultiplets, we compute the explicit scalar field expression of the quaternionic metric $G_{mn}$ of the moduli space SO(1,1)x[SO(4,k)/(SO(4)xSO(k))] of 6D N=2 supergravity with generic k Maxwell supermultiplets. The obtained metric includes the particular case k=20 associated with 10D type IIA superstring on K3. Uplifting to 7D N=2 supergravity is described and aspects of 6D/7D black attractor effective potentials are studied.
We study the possibility of using the D-term associated to an anomalous U(1) for the uplifting of AdS vacua (to dS or Minkowski vacua) in effective supergravities arising from string theories, particularly in the type IIB context put forward by Kachru, Kallosh, Linde and Trivedi (KKLT). We find a gauge invariant formulation of such a scenario (avoiding previous inconsistencies), where the anomalous D-term cannot be cancelled, thus triggering the uplifting of the vacua. Then, we examine the general conditions for this to happen. Finally, we illustrate the results by presenting different success…
It was shown in arXiv:1410.7168 that compactifying $D=6$, $\mathcal{N}=(1,0)$ ungauged supergravity coupled to a single tensor multiplet on S$^3$ one gets a particular $D=3$, $\mathcal{N}=4$ gauged supergravity which is a consistent reduction. We construct two supersymmetric black string solutions in this 3-dimensional model with one and two active scalars respectively. Uplifting the first, one gets a dyonic string solution in $D=6$ that has been known for a long time. Whereas, uplifting the second solution, one finds a very interesting configuration where magnetic strings are located uniforml…
Light cone gauge manifestly supersymmetric formulations of type IIB 10-dimensional supergravity in $AdS_5 \times S^5$ background and related boundary conformal field theory representations are developed. A precise correspondence between the bulk fields of IIB supergravity and the boundary operators is established. The formulations are given entirely in terms of light cone scalar superfields, allowing us to treat all component fields on an equal footing.
Construction of a five dimensional conformal supergravity (D=5 CSG) is attempted by applying the AdS/CFT correspondence to the F(4) AdS supergravity in six dimensions. As a first step, local transformation laws of D=5 CSG have been established, from which the Weyl weights of the various fields in D=5 can be predicted.
We obtain three and four dimensional conformal field theories with less than maximal supersymmetry by using their supergravity duals. These supergravity theories are type II on $AdS_5 \times CP^2$, IIA on $AdS_4 \times CP^3$, IIB on $AdS_5 \times S^5/Z_k$ and D=11 supergravity on $AdS_4 \times S^7/Z_k$. They are obtained from the spherically compactified ten and eleven dimensional theories by either Hopf reduction or by winding the U(1) fiber over the base.
Long ago, Achucarro and Townsend discovered that in three dimensions (3D) N-extended anti-de Sitter (AdS) supergravity exists in several incarnations, which were called the (p,q) AdS supergravity theories with non-negative integers p>=q such that N=p+q. Using the superspace approach to 3D N-extended supergravity developed in arXiv:1101.4013, we present three superfield formulations for N=2 supergravity that allow for well defined cosmological terms and supersymmetric AdS solutions. The conformal compensators corresponding to these theories are respectively: (i) a chiral scalar multiplet: (ii) …
We compute the index for the conifold gauge theory from type IIB supergravity (superstring) on AdS_5 \times T^{1,1}. We discuss its implication from the gauge theory viewpoint.
We work out the consistent AdS$_3\times S^3$ truncations of the bosonic sectors of both the six-dimensional ${\cal N}=(1,1)$ and ${\cal N}=(2,0)$ supergravity theories. They result in inequivalent three-dimensional half-maximal ${\rm SO}(4)$ gauged supergravities describing 32 propagating bosonic degrees of freedom apart from the non-propagating supergravity multiplet. We present the full non-linear Kaluza-Klein reduction formulas and illustrate them by explicitly uplifting a number of AdS$_3$ vacua.
We analyze general N = 2 supersymmetric AdS4 solutions of type IIB supergravity. Utilizing a set of pure spinor equations directly adapted to N = 2, the necessary and sufficient conditions for supersymmetry are reduced to a concise system of partial differential equations for two functions which determine the solutions. We show that using this system analytic solutions can be generated, thus potentially expanding the rather limited set of known AdS4 solutions in type IIB supergravity.
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.
This paper presents a detailed discussion of the issue of supergravity perturbations around the flat five dimensional superspace required for manifest superspace formulations of the supergravity side of the AdS_{5}/CFT_{4} Correspondence.
In this paper we propose a generalization of N=4 three dimensional AdS supergravity to the noncommutative case. This is a supersymmetric version of the results presented in hep-th/0201103. We show that it continues to admit an N=4 supersymmetric solution which is the noncommutative couterpart of AdS_3 space. Some other solutions are also discussed.
The quadratic action for physical fields of type IIB supergravity model on $AdS_5\times S^5$ is derived starting from the recently found covariant action. All boundary terms that have to be added to the action to be used in the AdS/CFT correspondence are determined.
We present a family of N=1 supersymmetric backgrounds in type-IIA supergravity and their lifts to eleven-dimensional supergravity. These are of the form $AdS_5 \times X^5$ and are characterised by an $SU(2)$ structure. The internal space, $X^5$, is obtained from the known Sasaki-Einstein manifolds, $Y^{p,q}$, via an application of non-Abelian T-duality.
We discuss the spectrum of states of IIB supergravity on $AdS_5\times S^5$ in a manifest $SU(2,2/4)$ invariant setting. The boundary fields are described in terms of N=4 superconformal Yang-Mills theory and the proposed correspondence between supergravity in $AdS_5$ and superconformal invariant singleton theory at the boundary is formulated in an N=4 superfield covariant language.
In this paper we derive the Anti de Sitter counterpart of the super-Maxwell algebra presented recently by Bonanos et.\ al. Then we gauge this algebra and derive the corresponding supergravity theory, which turns out to be described by the standard N=1 supergravity lagrangian, up to topological terms.
We find explicit supergravity solutions which describe branes in the AdS_3 x S^3 background. These solutions preserve 8 of the 16 supersymmetries of this background, and are consistent with kappa-symmetry. These represent new 1/2-BPS states of string theory.
We present the complete Kaluza-Klein spectrum resulting from the compactification of IIB supergravity on S^5/Z_3. Knowledge of this spectrum allows us to perform a holographic computation of the difference of central charges c-a of the dual SU(N)^3 quiver gauge theory. We find the numerical value c-a=3/16, in exact agreement with the field theory result.
We find a large class of supersymmetric solutions in the $AdS_3 \times S^3$ background with NS fluxes. This two-parameter family of solutions preserves 8 of the 16 supersymmetries of the background.
We determine the AdS exchange diagrams needed for the computation of 4--point functions of chiral primary operators in the SCFT_2 dual to the D=6 N=4b supergravity on the AdS_3\times S^3 background and compute the corresponding cubic couplings. We also address the issue of consistent truncation.
We consider superconformal field theories in three and six dimensions with eight supercharges which can be realized on the world-volume of M-theory branes sitting at orbifold singularities. We find that they should admit a N=4 and N=2 supergravity dual in AdS_4 and AdS_7, respectively. We discuss the characteristics of the corresponding gauged supergravities.
The standard formulation of the AdS/CFT correspondence is incomplete since it requires adding to a supergravity action some a priori unknown boundary terms. We suggest a modification of the correspondence principle based on the Hamiltonian formulation of the supergravity action, which does not require any boundary terms. Then all the boundary terms of the standard formulation naturally appear by passing from the Hamiltonian version to the Lagrangian one. As examples the graviton part of the supergravity action on the product of $AdS_{d+1}$ with a compact Einstein manifold $\cal E$ and fermions…
We construct the supergravity solution for fully localized D2/D6 intersection. The near horizon limit of this solution is the supergravity dual of supersymmetric Yang-Mills theory in 2+1 dimensions with flavor. We use this solution to formulate mirror symmetry of 2+1 dimensional gauge theories in the language of AdS/CFT correspondence. We also construct the supergravity dual of a non-commutative gauge theory with fundamental matter.
Motivated by the AdS_6/CFT_5 correspondence, we study general supersymmetric solutions of massive type IIA supergravity, consisting of a warped product of six-dimensional anti-de Sitter space AdS_6 with a four-dimensional Riemannian manifold M_4, and fluxes compatible with the SO(5,2) symmetry. We find that the only local solution of this form is the warped AdS_6 x_w S^4 solution, originally discovered by Brandhuber and Oz. We discuss the supersymmetric properties of this solution.
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…
In this note we show that the IIB supergravity solutions of the form AdS$_6\times M_4$ found by Apruzzi et al. are related to the local solutions found by D'Hoker et al. We also discuss how the global regular solutions found by D'Hoker et al. are mapped to the parameterization of Apruzzi et al.
We calculate the dimensions of operators in three and six dimensional superconformal field theories by using the duality between these theories at large N and D=11 supergravity on $AdS_{4/7} \times S^{7/4}$. We find that for the duality relations to work the Kaluza--Klein masses given in the supergravity literature must be rescaled and/or shifted.
We review some recent results on the construction in superspace of 3D N=2 AdS supergravities and on the formulation of rigid supersymmetric theories in (1,1) and (2,0) AdS superspaces.
Four-point functions of R-currents are discussed within Anti-de Sitter supergravity. In particular, we compute Witten diagrams with graviton and gauge boson exchange in the high energy Regge limit. Assuming validity of the AdS/CFT correspondence, our results apply to R-current four-point functions of N=4 super Yang-Mills theory at strong coupling.
It is shown that local symmetry transformations of the maximal AdS supergravity in seven-dimensional anti de Sitter space induce those of the N=(2,0) conformal supergravity on the six-dimensional boundary at infinity. Boundary values of the AdS supergravity fields form a supermultiplet of the conformal supergravity.
We obtain the complete local solutions with 16 supersymmetries to Type IIB supergravity on a space-time of the form $AdS_{2}\times S^{6}$ warped over a Riemann surface $Σ$ in terms of two locally holmorphic functions on $Σ$. We construct the general Ansatz for the bosonic supergravity fields and supersymmetry generators compatible with the $SO(2,1)\oplus SO(7)$ isometry algebra of space-time, which extends to the corresponding real form of the exceptional Lie superalgebra $F(4)$. We reduce the BPS equations to this Ansatz, obtain their general local solutions, and show that these local solutio…
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.
The maximally supersymmetric Freund-Rubin vacua for eleven dimensional supergravity, namely $AdS_4 \times S^7$ and $AdS_7 \times S^4$, admit an analytic continuation to $S^4 \times S^7$. From the full harmonic expansions on $S^4 \times S^7$, it is shown that by analytical continuation to either $AdS_4$, or to $AdS_7$, the detailed structure of the Kaluza-Klein spectrum can be obtained for both vacua in a unified manner. The results are shown to be related by a simple rule which interchanges the spacetime and internal space representations. We also obtain the linearized field equations for the …
The Kaluza-Klein spectrum of D=5 simple supergravity compactified on S^3 is studied. A classical background solution which preserves maximal supersymmetry is fulfilled by the geometry of AdS_2\times S^3. The physical spectrum of the fluctuations is classified according to SU(1,1|2)\times SU(2) symmetry, which has a very similar structure to that in the case of compactification on AdS_3\times S^2.
We study the structure of the supersymmetric moduli spaces of ${\cal N}=1$ and ${\cal N}=2$ supergravity theories in $AdS_4$ backgrounds. In the ${\cal N}=1$ case, the moduli space cannot be a complex submanifold of the Kähler field space, but is instead real with respect to the inherited complex structure. In ${\cal N}=2$ supergravity the same result holds for the vector multiplet moduli space, while the hypermultiplet moduli space is a Kähler submanifold of the quaternionic-Kähler field space. These findings are in agreement with AdS/CFT considerations.
We derive necessary and sufficient conditions for N=1 compactifications of (massive) IIA supergravity to AdS(4) in the language of SU(3) structures. We find new solutions characterized by constant dilaton and nonzero fluxes for all form fields. All fluxes are given in terms of the geometrical data of the internal compact space. The latter is constrained to belong to a special class of half-flat manifolds.
In this paper we propose the identification in AdS4 N = 2 gauged supergravity of the coefficient $τ_{RR}$ of 3D N = 2 SCFTs. We constraint the structure of this function in supergravity by combining the results from unitarity, holography and localization. We show that our conjectured function is minimized by the exact R-charge, corresponding to a gravitational attractor for the scalars in the special geometry. We identify this mechanism with the supergravity dual of the $τ_{RR}$-minimization. We check this proposal in the ABJM model, comparing with the expectations from localization and the Ad…
We consider the minimal off-shell formulation for four-dimensional N=2 supergravity with a cosmological term, in which the second compensator is an improved tensor multiplet. We use it to derive a linearized supergravity action (and its dual versions) around the anti-de Sitter (AdS) background in terms of three N=2 off-shell multiplets: an unconstrained scalar superfield, vector and tensor multiplets. This allows us to deduce the structure of the supercurrent multiplet associated with those supersymmetric theories which naturally couple to the supergravity formulation chosen, with or without a…
It is shown that the supersymmetric extension of the Stelle-West formalism permits the construction of an action for $(3+1)$-dimensional N=1 supergravity with cosmological constant genuinely invariant under the $OSp(4/1).$ Since the action is invariant under the supersymmetric extension of the $AdS$ group, the supersymmetry algebra closes off shell without the need for auxiliary fields. The limit case $m\to 0$, i.e.$(3+1)$ -dimensional N=1 supergravity invariant under the Poincaré supergroup is also discussed.
All symmetric space AdS(n) solutions of ten-dimensional type IIA and type IIB supergravity are constructed for n>2. There are a total of 26 geometries. Out of these only 7 allow for supersymmetries and these are the well known backgrounds coming from near-horizon limits of (intersecting) branes in ten or eleven dimensions and preserving 32, 16 or 8 supersymmetries.
We derive the full Kaluza-Klein spectrum of type IIB supergravity compactified on AdS_5 x T^{11} with T^{11} = (SU(2) x SU(2))/U(1). From the knowledge of the spectrum and general multiplet shortening conditions, we make a refined test of the AdS/CFT correspondence, by comparison between various shortenings of SU(2,2|1) supermultiplets on AdS_5 and different families of boundary operators with protected dimensions. Additional towers of long multiplets with rational dimensions, that are not protected by supersymmetry, are also predicted from the supergravity analysis.
We will study the AdS/CFT correspondence in an intermediate region between the strong form of this correspondence (string theory on AdS being dual to a boundary CFT), and the weak form of this correspondence (supergravity on AdS being dual to a boundary CFT). We will go beyond the supergravity approximation in the AdS by using the fact that strings have an extended structure. We will also calculate the CFT dual to such string corrections in the bulk, and demonstrate that they are consistent with the strong form of the AdS/CFT correspondence. So, even though the conformal dimensions of both the…
We study $N=2$ gauged supergravity with $U(1)$ gauge group coupled to $n_v$ vector multiplets and find quite general analytic solutions for quarter-BPS black holes with mass, NUT and dyonic Maxwell charges. The solutions we find have running scalar fields and flow in the IR region to a horizon geometry of the form AdS$_2\times Σ_g$.
By identifying a bosonic consistent truncation from the 1/4-BPS wrapped M5-brane geometry of Maldacena, Strominger and Witten in D = 11 supergravity and finding a supersymmetric extension, we recover an N = 2 D = 3 supergravity theory. Reductions of a large class of supersymmetric solutions corresponding to wrapped M2 and M5-branes lead to black strings and warped AdS3 solutions preserving supersymmetry. With a view to AdS/CMT applications, we also construct a numerical hairy BTZ black hole and, as a preliminary step in this direction, determine the conductivity of the dual CFT.
We derive from a general formulation of pure spinor string theory on type IIA backgrounds the specific form of the action for the AdS_4 x P^3 background. We provide a complete geometrical characterization of the structure of the superfields involved in the action.
In this thesis we study maximally supersymmetric solutions of gauged supergravity theories, with special focus on anti-de Sitter solutions. The latter are relevant in the context of the AdS/CFT correspondence. In the first part we classify all maximally supersymmetric solutions of all gauged or deformed supergravity theories in $D \geq 3$ space-time dimensions. In the second part we exclusively study maximally supersymmetric AdS$_D$ solutions of gauged supergravities in dimensions $D \geq 4$. We discuss the structure of the allowed gauge groups as well as possible supersymmetry preserving defo…
We obtain the pseudo-supergravity extension of the D-dimensional Kaluza-Klein theory, which is the circle reduction of pure gravity in D+1 dimensions. The fermionic partners are pseudo-gravitino and pseudo-dilatino. The full Lagrangian is invariant under the pseudo-supersymmetric transformation, up to quadratic order in fermion fields. We find that the theory possesses a U(1) global symmetry that can be gauged so that all the fermions are charged under the Kaluza-Klein vector. The gauging process generates a scalar potential that has a maximum, leading to the AdS vacuum. Whist the highest dime…
We study the supersymmetric solutions of 11-dimensional supergravity with a factor of $AdS_2$ made of M2-branes. Such solutions can provide gravity duals of superconformal quantum mechanics, or through double Wick rotation, the generic bubbling geometry of M-theory which are 1/16-BPS. We show that, when the internal manifold is compact, it should take the form of a warped U(1)-fibration over an 8-dimensional Kahler space.
