We show that for n-dimensional Einstein gravity coupled to a scalar field with mass-squared m_0^2=-n(n-2)/(4\ell^2), the first law of thermodynamics of (charged) AdS black holes will be modified by the boundary conditions of the scalar field at asymptotic infinity. Such scalars can arise in gauged supergravities in four and six dimensions, but not in five or seven. The result provides a guiding principle for constructing designer black holes and solitons in general dimensions, where the properties of the dual field theories depend on the boundary conditions.
We summarise the recent results in 1810.08093, where the Type IIB AdS$_6$ solutions T-dual to the Brandhuber-Oz solution to massive Type IIA supergravity are shown to fit within an extension to allow for delocalized 5- and 7-branes of the global AdS$_6 \times S^2$ solutions constructed by D'Hoker, Gutperle and Uhlemann. We show that the Abelian T-dual solution provides an explicit example of a Riemann surface with the topology of an annulus.
We consider two-dimensional geometries flowing away from an asymptotically AdS$_2$ spacetime. Macroscopically, flow geometries and their thermodynamic properties are studied from the perspective of dilaton-gravity models. We present a precise map constructing the fixed background metric from the boundary two-point function of a nearly massless matter field. We analyse constraints on flow geometries, viewed as solutions of dimensionally reduced theories, stemming from energy conditions. Microscopically, we construct computationally tractable RG flows in SYK-type models at vanishing and non-vani…
We obtain an AdS$_{2}$ solution to Type IIA supergravity with 4 Poincare supersymmetries, via non-Abelian T-duality with respect to a freely acting SL(2,$\mathbf{R}$) isometry group, operating on the AdS$_3\times$S$^3\times$CY$_2$ solution to Type IIB. That is, non-Abelian T-duality on AdS$_3$. The dual background obtained fits in the class of AdS$_2\times$S$^3\times$CY$_2$ solutions to massive Type IIA constructed in [1]. We propose and study a quiver quantum mechanics dual to this solution that we interpret as describing the backreaction of the baryon vertex of a D4-D8 brane intersection.
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 discuss, in terms of the AdS_3-CFT_2 correspondence, a one-parameter family of (asymptotically AdS_3) conical geometries which are generated by point masses and interpolate between AdS_3 and BTZ spacetimes. We show that these correspond to spectral flow in N= (4,4) SCFT_2 which interpolate between NS and R sectors. Our method involves representing the conical spaces as solutions of three-dimensional supergravity based on the supergroup SU(1,1|2) \times SU(1,1|2). The boundary CFT we use is based on the D1/D5 system. The correspondence includes comparing the Euclidean free energies between s…
We show that the first $AdS_6$ backgrounds in Type IIB supergravity known in the literature, namely those constructed via T-duality from the Brandhuber-Oz solution to massive IIA, fit within an extension of the global $AdS_6 \times S^2$ solutions with 7-branes warped over a Riemann surface $Σ$, recently classified by D'Hoker, Gutperle and Uhlemann, that describes delocalised 5-branes and 7-branes. The solution constructed through Abelian T-duality provides an explicit example of a Riemann surface with the topology of an annulus, that includes D7/O7-branes. In turn, the solution generated throu…
We investigate the AdS$_3$/CFT$_2$ correspondence for the Euclidean AdS$_3$ space compactified on a solid torus with the CFT field on the regularizing boundary surface in the bulk. Correlation functions corresponding to the bulk theory at finite temperature tend to the standard CFT correlation functions in the limit of removed regularization. In both regular and $Z_N$ orbifold cases, in the sum over geometries, the two-point correlation function for massless modes factors, up to divergent terms proportional to the volume of the $SL(2,Z)/Z}$ group, into the finite sum of products of the conform…
Expanding upon [arXiv:1404.4472, 1511.06079], we provide further detailed analysis of Bañados geometries, the most general solutions to the AdS3 Einstein gravity with Brown-Henneaux boundary conditions. We analyze in some detail the causal, horizon and boundary structure, and geodesic motion on these geometries, as well as the two class of symplectic charges one can associate with these geometries: charges associated with the exact symmetries and the Virasoro charges. We elaborate further the one-to-one relation between the coadjoint orbits of two copies of Virasoro group and Bañados geometrie…
We perform a systematic study, in eleven dimensional supergravity, of the geometry of wrapped brane configurations admitting $AdS_2$ limits. Membranes wrapping holomorphic curves in Calabi-Yau manifolds are found to exhibit some novel features; in particular, for fourfolds or threefolds, the gravitational effect of the branes on the overall transverse space is only weakly restricted by the kinematics of the Killing spinor equation. We also study the $AdS_2$ limits of the wrapped brane supergravity descriptions. For membranes wrapped in a two-fold, we derive a set of $AdS_2$ supersymmetry condi…
We study a relation between droplet configurations in the bubbling AdS geometries and a complex matrix model that describes the dynamics of a class of chiral primary operators in dual N=4 super Yang Mills (SYM). We show rigorously that a singlet holomorphic sector of the complex matrix model is equivalent to a holomorphic part of two-dimensional free fermions, and establish an exact correspondence between the singlet holomorphic sector of the complex matrix model and one-dimensional free fermions. Based on this correspondence, we find a relation of the singlet holomorphic operators of the comp…
We identify all symmetry superalgebras $\mathfrak{g}$ of near horizon geometries of black holes with a Killing horizon, assuming the solution is smooth and that the spatial cross section of the event horizon is compact without boundary. This includes all warped AdS$_2$ backgrounds with the most general allowed fluxes in 10- and 11-dimensional supergravities. If the index of a particular Dirac operator vanishes, we find that the even symmetry subalgebra decomposes as $\mathfrak{g}_0=\mathfrak{sl}(2,\mathbb{R})\oplus \mathfrak{t}_0$, where $\mathfrak{t}_0/\mathfrak{c}$ is the Lie algebra of a gr…
By using the approach introduced in arXiv:2107.09677 we construct non-BPS solutions of 6D $(1,0)$ supergravity coupled to two tensor multiplets as a perturbation of AdS$_3\times S^3$. These solutions are both regular and asymptotically AdS$_3\times S^3$, so according to the standard holographic framework they must have a dual CFT interpretation as non-supersymmetric heavy operators of the D1-D5 CFT. We provide quantitative evidence that such heavy CFT operators are bound states of a large number of light BPS operators that are mutually non-BPS.
We find soliton solutions in five-dimensional gauged supergravity, where a circle degenerates smoothly in the core of the geometry. In the family of solutions we consider, we find no completely smooth supersymmetric solutions, but we find discrete families of non-supersymmetric solitons. We discuss the relation to previous studies of the asymptotically flat case. We also consider gauged supergravities in four and seven dimensions, but fail to find any smooth solutions.
We investigate the ten dimensional origin of six dimensional F_4 variant supergravity with supersymmetric de Sitter background. We address first the issue of spontaneous compactification, showing that it consists of a warped compactification on a four sphere of a variant massive type IIA supergravity. Moreover we illustrate how the known D4-D8 brane solution, whose near horizon geometry yields AdS_6 x S^4, is accordingly modified to a system including Euclidean branes. Finally, we discuss the relation between this latter solution and the D4-D8 brane system, showing how it represents a generali…
Pure gravity in (2+1)-dimensions with negative cosmological constant is classically equivalent Chern-Simons gauge theory with gauge group SO(2; 2), which may be realized on chiral and antichiral gauge connections. This paper looks at half-AdS geometries i.e. those with a trivial rightmoving gauge connection while the left-moving connection is a standard (Banados-Teitelboim- Zanelli) BTZ connection. These are shown to be related by diffeomorphism to a BTZ geometry with different mass and angular momentum. Generically this is over-spinning, leading to a naked closed timelike curves. Other closel…
We consider all 1/2 BPS excitations of $AdS \times S$ configurations in both type IIB string theory and M-theory. In the dual field theories these excitations are described by free fermions. Configurations which are dual to arbitrary droplets of free fermions in phase space correspond to smooth geometries with no horizons. In fact, the ten dimensional geometry contains a special two dimensional plane which can be identified with the phase space of the free fermion system. The topology of the resulting geometries depends only on the topology of the collection of droplets on this plane. These so…
We extend the non-relativistic AdS/CFT correspondence to the fermionic fields. In particular we study the two point function of a fermionic operator in non-relativistic CFTs by making use of a massive fermion propagating in geometries with Schrodinger group isometry. Although the boundary of the geometries with Schrodinger group isometry differ from that in AdS geometries where the dictionary of AdS/CFT is established, using the general procedure of AdS/CFT correspondence, we see that the resultant two point function has the expected form for fermionic operators in non-relativistic CFTs, thoug…
We construct BPS geometries describing normalizable excitations of AdS_2 x S^2. All regular horizon-free solutions are parameterized by two harmonic functions in R^3 with sources along closed curves. This local structure is reminiscent of the "bubbling solutions" for the other AdS cases, however, due to peculiar asymptotic properties of AdS_2, one copy of R^3 does not cover the entire space, and we discuss the procedure for analytic continuation, which leads to a nontrivial topological structure of the new geometries. We also study supersymmetric brane probes on the new geometries, which repre…
Recently, 1/2-BPS AdS bubble solutions have been obtained by Lin, Lunin and Maldacena, which correspond to Fermi droplets in phase space in the dual CFT picture. They can be thought of as generalisations of 1/2-BPS AdS black hole solutions in five or seven dimensional gauged supergravity. In this paper, we extend these solutions by invoking additional gauge fields and scalar fields in the supergravity Lagrangians, thereby obtaining AdS bubble generalisations of the previously-known multi-charge AdS black solutions of gauged supergravity. We also obtain analogous AdS bubble solutions in four-di…
We give a description of supermembranes in nontrivial target-space geometries. A special class are the $AdS_4\times S^7$ and $AdS_7\times S^4$ spaces that have the maximal number of 32 supersymmetries.
We study supersymmetric AdS_4 x X_7 solutions of 11-dim supergravity where the tri-Sasakian space X_7 has generically U(1)^2\times SU(2)_R isometry. The compact and regular 7-dim spaces X_7=S(t_1,t_2,t_3) is originated from 8-dim hyperkahler quotient of a 12-dim flat hyperkahler space by U(1) and belongs to the class of the Eschenburg space. We calculate the volume of X_7 and that of the supersymmetric five cycle via localization. From this we discuss the 3-dim dual superconformal field theories with \CN=3 supersymmetry.
We provide a classification of near-horizon geometries of supersymmetric, asymptotically anti-de Sitter, black holes of five-dimensional U(1)^3-gauged supergravity which admit two rotational symmetries. We find three possibilities: a topologically spherical horizon, an S^1 \times S^2 horizon and a toroidal horizon. The near-horizon geometry of the topologically spherical case turns out to be that of the most general known supersymmetric, asymptotically anti-de Sitter, black hole of U(1)^3-gauged supergravity. The other two cases have constant scalars and only exist in particular regions of thi…
We investigate the complexity=volume proposal in the case of Janus AdS$_3$ geometries, both at zero and finite temperature. The leading contribution coming from the Janus interface is a logarithmic divergence, whose coefficient is a function of the dilaton excursion. In the presence of the defect, complexity is no longer topological and becomes temperature-dependent. We also study the time evolution of the extremal volume for the time-dependent Janus BTZ black hole. This background is not dual to an interface but to a pair of entangled CFTs with different values of the couplings. At late times…
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 AdS$_3 \times \mathbb{S}^3 \times \mathbb{T}^4$ and, varying the parameter that controls them, they interpolates between the global AdS$_3 \times \mathbb{S}^3 \times \mathbb{T}^4$ and the massless BTZ$_3 \times \mathbb{S}^3 \times \mathbb{T}^4$ geometry. Due to AdS/CFT duality, these geometries are dual to pure CFT heavy states. We find that there is n…
We carry out a general analysis of the representations of the superconformal algebras SU(2,2/N), OSp(8/4,R) and OSp(8^*/4) and give their realization in superspace. We present a construction of their UIR's by multiplication of the different types of massless superfields ("supersingletons"). Particular attention is paid to the so-called "short multiplets". Representations undergoing shortening have "protected dimension" and correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary confo…
The mapping between bulk supergravity fields in anti-de Sitter space and operators in the dual boundary conformal field theory usually relies heavily on the available global symmetries. In the present work, we study a generalization of this mapping to time dependent situations, for the simple case of collapsing shock waves in two spacetime dimensions. The construction makes use of analyticity of the conformal field theory and the properties of the asymptotic bulk geometry to reconstruct the non-analytic bulk observables. Many of the features of this construction are expected to apply to higher…
The "pole-skipping" phenomenon reflects that the retarded Green's function is not unique at a pole-skipping point in momentum space $(ω,k)$. We explore the universality of the pole-skipping in different geometries. In holography, near horizon analysis of the bulk equation of motion is a simpler way to derive a pole-skipping point and we use this method in Lifshitz, AdS$_2$ and Rindler geometries. We also study the complex hydrodynamic analyses and find that the dispersion relations in terms of dimensionless variables $\fracω{2πT}$ and $\frac{\vert k\vert}{2πT}$ pass through pole-skipping point…
We carry out a general analysis of the representations of the superconformal algebras OSp(8/4,R) and OSp(8*/2N) in terms of harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless conformal superfields ("supersingletons"). Particular attention is paid to the so-called "short multiplets". Representations undergoing shortening have "protected dimension" and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in bound…
We study aspects of confinement in two deformed versions of the AdS/CFT correspondence - the GPPZ dual of N=1* Yang Mills, and the Yang Mills* N=0 dual. Both geometries describe discrete glueball spectra which we calculate numerically. The results agree at the 10% level with previous AdS/CFT computations in the Klebanov Strassler background and AdS Schwarzchild respectively. We also calculate the spectra of bound states of the massive fermions in these geometries and show that they are light, so not decoupled from the dynamics. We then study the behaviour of Wilson loops in the 10d lifts of th…
We show how to implement T-duality along non-abelian isometries in backgrounds with non-vanishing Ramond fields. When the dimension of the isometry group is odd (even) the duality swaps (preserves) the chirality of the theory. In certain cases a non-abelian duality can result in a massive type-IIA background. We provide two examples by dualising SU(2) isometry subgroups in $AdS_5\times S^5$ and $AdS_3\times S^3\times T^4$. The resultant dual geometries inherit the original AdS factors but have transverse spaces with reduced isometry and preserve only half of the original supersymmetry. The non…
We investigate some universal features of AdS/CFT models of heavy quark energy loss. In addition, as a specific example, we examine quark damping in the spinning D3-brane solution dual to N=4 SU(N_c) super Yang-Mills at finite temperature and R-charge chemical potential.
We extend the classification of supersymmetric locally AdS$_3$ geometries, beyond BTZ black holes, to the Banados geometries, noting that supersymmetries are in one-to-one correspondence with solutions to the Hill differential condition. We show that the number of global supersymmetries is an orbit invariant quantity and identify geometries with zero, one, two, three and four global supersymmetries. As an application of our classification, we exploit supersymmetry, which is preserved locally in the bulk, to determine space-like co-dimension two surfaces in AdS$_3$. In the process, we by-pass g…
We study hidden symmetries, the symmetries associated with the Killing tensors, of the near horizon geometry of odd-dimensional Kerr-AdS-NUT black hole in two limits: generic extremal and extremal vanishing horizon (EVH) limits. Starting from Kerr-AdS-NUT black hole in ellipsoidal coordinates which admits integrable geodesic equations, we obtain the near horizon extremal/EVH geometries and their principal and Killing tensors by taking the near horizon limit. We explicitly demonstrate that geodesic equations are separable and integrable on theses near horizon geometries. We also compute the con…
We quantize the moduli space of supersymmetric microstates describing four-dimensional black holes with AdS$_2$$\times$S$^2$ asymptotics. To acquire the commutation relations of quantization, we find the symplectic form that is imposed in the Type IIB SUGRA and defined in the space of solutions parameterized by one complex harmonic function in ${R}^3$ with sources distributed along closed curves.
We consider stationary extremal black hole solutions of the Einstein-Maxwell equations with a negative cosmological constant in four dimensions. We determine all non-static axisymmetric near-horizon geometries (with non-toroidal horizon topology) and all static near-horizon geometries for black holes of this kind. This allows us to deduce that the most general near-horizon geometry of an asymptotically globally AdS(4) rotating extremal black hole, is the near-horizon limit of extremal Kerr-Newman-AdS(4). We also identify the subset of near-horizon geometries which are supersymmetric. Finally, …
The AdS-bubble solutions interestingly mimic Schrödinger-like geometries when expressed in light-cone coordinates. These D$p$ bubble vacuas exhibit asymmetric scaling property with a negative dynamical exponent of time $a<0$, but are smooth geometries. Through a time-like T-duality we map these vacua to E$p$-brane bubbles with $a>0$ in type II* super-strings. We obtain an expression for the entanglement entropy for `bubble E3-branes'. It is argued that the entropy from E3-bubbles has to be the lowest.
We develop a new hybrid WKB technique to compute boundary-to-boundary scalar Green functions in asymptotically-AdS backgrounds in which the scalar wave equation is separable and is explicitly solvable in the asymptotic region. We apply this technique to a family of six-dimensional $\frac{1}{8}$-BPS asymptotically AdS$_3\,\times\,$S$^3$ horizonless geometries that have the same charges and angular momenta as a D1-D5-P black hole with a large horizon area. At large and intermediate distances, these geometries very closely approximate the extremal-BTZ$\,\times\,$S$^3$ geometry of the black hole, …
We derive a complete geometrical characterisation of a large class of $AdS_3$, $AdS_4$ and $AdS_5$ supersymmetric spacetimes in eleven-dimensional supergravity using G-structures. These are obtained as special cases of a class of supersymmetric $\mathbb{R}^{1,1}$, $\mathbb{R}^{1,2}$ and $\mathbb{R}^{1,3}$ geometries, naturally associated to M5-branes wrapping calibrated cycles in manifolds with $G_2$, SU(3) or SU(2) holonomy. Specifically, the latter class is defined by requiring that the Killing spinors satisfy the same set of projection conditions as for wrapped probe branes, and that there …
We prove the existence of a new class of BPS saturated M-branes. They are in one-to-one correspondence with the Freund--Rubin compactifications of M-theory on either (AdS_4) x (G/H) or (AdS_7) x (G/H), where G/H is the seven (or four) dimensional Einstein coset manifolds classified long ago in the context of Kaluza Klein supergravity. The G/H M-branes are solitons that interpolate between flat space at infinity and the old Kaluza-Klein compactifications at the horizon. They preserve N/2 supersymmetries where N is the number of Killing spinors of the (AdS) x (G/H) vacuum. A crucial ingredient i…
It has been proven in arXiv:1303.0853 that all regular supersymmetric near-horizon geometries in minimal five-dimensional gauged supergravity admit automatic supersymmetry enhancement. Using this result, the integrability conditions associated with the existence of the additional supersymmetry are analysed, and the near-horizon geometries are determined explicitly. We show that they all correspond to previously constructed examples. Hence, there are no supersymmetric black ring solutions in minimal five-dimensional gauged supergravity.
A class of $AdS_2\times Σ_2$, with $Σ_2$ being a two-sphere or a hyperbolic space, solutions within four-dimensional $N=4$ gauged supergravity coupled to three-vector multiplets with dyonic gauging is identified. The gauged supergravity has non-semisimple $SO(3)\ltimes (\mathbf{T}^3,\hat{\mathbf{T}}^3)$ gauge group and can be obtained from a consistent truncation of eleven-dimensional supergravity on a tri-sasakian manifold. The maximally symmetric vacua contain $AdS_4$ geometries with $N=1,3$ supersymmetry corresponding to $N=1$ and $N=3$ superconformal field theories (SCFTs) in three dimensi…
We review the issue of chronology protection and show how string theory can solve it in the half BPS sector of AdS/CFT. According to the LLM prescription, half BPS excitations of AdS_5 x S^5 geometries in type IIB string theory can be mapped into free fermion configurations. We show that unitarity of the theory describing these fermions is intimately related to the protection of the chronology in the dual geometries.
We study strings on orbifolds of $AdS_{5}\times S^5$ by SU(2) discrete groups in the Penrose limit. We derive the degenerate metrics of pp wave of $AdS_{5}\times S^5/Γ$ using ordinary $ADE$ and affine $\wildtilde{ADE}$ singularities of complex surfaces and results on ${\cal N}=4$ CFT$_4$'s. We also give explicit metric moduli depencies for abelian and non abelian orbifolds.
We study integrable deformations of AdS/CFT by focusing upon three kinds of warped AdS_3 geometries, 1) space-like warped AdS_3, 2) time-like warped AdS_3 and 3) null warped AdS_3. These geometries are embedded into type IIB supergravity solutions and are regarded as consistent string backgrounds. By restricting the classical motion of strings on the warped AdS_3xS^1 subspace, the Landau-Lifshitz sigma models are derived by taking the fast-moving limit. The first two warped AdS_3 spaces correspond to anisotropic deformations of the sl(2) spin chain and the last one to Jordanian deformations. A…
We construct large classes of non-BPS smooth horizonless geometries that are asymptotic to AdS$_3\times$S$^3\times$T$^4$ in type IIB supergravity. These geometries are supported by electromagnetic flux corresponding to D1-D5 charges. We show that Einstein equations for systems with eight commuting Killing vectors decompose into a set of Ernst equations, thereby admitting an integrable structure. This feature, which can a priori be applied to other AdS$_D\times\mathcal{C}$ settings in supergravity, allows us to use solution-generating techniques associated with the Ernst formalism. We explicitl…
We find a new example of an asymptotically $AdS_5 \times S^5$ geometry which has an entanglement shadow: that is, a region of spacetime which no Ryu-Takayanagi minimal surface enters. Our example is a particular case of the supersymmetric LLM geometries. Our results illustrate how minimal surfaces, which holographically geometrize entanglement entropy, can fail to probe the whole of spacetime, posing a challenge for attempts to directly reconstruct holographic geometries from the entanglement entropies of the dual field theory. We also comment on the relation to previous investigations of mini…
We study the Regge limit of 4-point AdS$_3 \times S^3$ correlators in the tree-level supergravity approximation and provide various explicit checks of the relation between the eikonal phase derived in the bulk picture and the anomalous dimensions of certain double-trace operators. We consider both correlators involving all light operators and HHLL correlators with two light and two heavy multi-particle states. These heavy operators have a conformal dimension proportional to the central charge and are pure states of the theory, dual to asymptotically AdS$_3 \times S^3$ regular geometries. Devia…
We describe the geometry of the R x SO(3) x SO(6) x U(1) invariant half-BPS M-theory configurations considered in LLM in terms of their electrostatic variables. We discuss both regular configurations, such as AdS_4 x S^7 and AdS_7 x S^4 vacua or simple excited solutions, and singular ones such as the superstar geometries. This allows us to identify the appropriate boundary conditions describing the most general smooth and superstar-like singular configurations. We also compute their masses, matching the expected result from their microscopic interpretation, but now at finite radius of curvatur…
In Conformal Field Theories with a gravitational AdS dual it is possible to calculate the entanglement entropy of a region $A$ holographically by using the Ryu-Takayanagi formula. In this work we consider systems that are in a pure state that is not the vacuum. We study in particular the 2D Conformal Field Theory dual to type IIB string theory on AdS$_3 \times S^3 \times T^4$ and focus on the $1/4$-BPS states described holographically by the 2-charge microstate geometries. We discuss a general prescription for the calculation of the entanglement entropy in these geometries that are asymptotica…
A geometric torsion dynamics leading to an effective curvature in a second order formalism on a D4-brane is revisited with a renewed interest. We obtain two effective $AdS_4$ brane geometries on a vacuum created pair of $(D{\bar D})_3$-brane. One of them is shown to describe an AdS Schwarzschild spinning black hole and the other is shown to describe a spinning black hole bound state. It is argued that a D-instanton in a vacuum created anti D3-brane within a pair may describe a quintessence. It may seen to incorporate a varying vacuum energy density in a brane universe. We consider the effectiv…
In the holographic AdS/QCD approach, the confinement/deconfinement transition is associated with the Hawking-Page transition of a thermal anti-de Sitter (AdS) space to an AdS black hole. In the case of the hard wall model, the thermal transition takes place in the planar AdS thanks to the introduction of an infrared cut-off in the geometry. The corresponding thermodynamic entropy of the $SU(N) $ gauge theory jumps from proportional to $N^0$ in the confined hadronic phase to proportional to $N^2$ in the plasma phase, corresponding to the presence of the color degrees of freedom. The Hawking-Pag…
The seven and nine dimensional geometries associated with certain classes of supersymmetric $AdS_3$ and $AdS_2$ solutions of type IIB and D=11 supergravity, respectively, have many similarities with Sasaki-Einstein geometry. We further elucidate their properties and also generalise them to higher odd dimensions by introducing a new class of complex geometries in $2n+2$ dimensions, specified by a Riemannian metric, a scalar field and a closed three-form, which admit a particular kind of Killing spinor. In particular, for $n\ge 3$, we show that when the geometry in $2n+2$ dimensions is a cone we…
