arXiv subjects
Publications and source records attributed to Michael Gutperle.
We study classical solutions of three dimensional higher spin gravity in the Chern-Simons formulation. We find solutions that generalize the BTZ black hole and carry spin-3 charge. The black hole entropy formula yields a result for the asymptotic growth of the partition function at finite spin-3 chemical potential. Along the way, we develop technology for computing AdS/CFT correlation functions involving higher spin operators.
In this paper we study half-BPS type IIB supergravity solutions with multiple $AdS_3\times S^3\times M_4$ asymptotic regions, where $M_4$ is either $T^4$ or $K_3$. These solutions were first constructed in [1] and have geometries given by the warped product of $AdS_2 \times S^2 \times M_4 $ over $Σ$, where $Σ$ is a Riemann surface. We show that the holographic boundary has the structure of a star graph, i.e. $n$ half-lines joined at a point. The attractor mechanism and the relation of the solutions to junctions of self-dual strings in six-dimensional supergravity are discussed. The solutions of [1] are constructed introducing two meromorphic and two harmonic functions defined on $Σ$. We focus our analysis on solutions corresponding to junctions of three different conformal field theories and show that the conditions for having a solution charged only under Ramond-Ramond three-form fields reduce to relations involving the positions of the poles and the residues of the relevant harmonic and meromorphic functions. The degeneration limit in which some of the poles collide is analyzed in detail. Finally, we calculate the holographic boundary entropy for a junction of three CFTs and obtain a simple expression in terms of poles and residues.
In this paper we compute the holographic boundary entropy for half-BPS Janus deformations of the $AdS_3\times S^3\times T^4$ vacuum of type IIB supergravity. Previous work \cite{Chiodaroli:2009yw} has shown that there are two independent deformations of this sort. In one case, the six-dimensional dilaton jumps across the interface, while the other case displays a jump of axion and four-form potential. In case of a jump of the six-dimensional dilaton, it is possible to compare the holographic result with the weak-coupling result for a two-dimensional interface CFT where the radii of the compactified bosons jump across the interface. We find exact agreement between holographic and CFT results. This is to be contrasted with the holographic calculation for the non-supersymmetric Janus solution, which agrees with the CFT result only at the leading order in the jump parameter. We also examine the implications of the holographic calculation in case of a solution with a jump in the axion, which can be associated with a deformation of the CFT by the $Z_2$-orbifold twist operator.
Type IIB supergravity admits Janus and multi-Janus solutions with eight unbroken supersymmetries that are locally asymptotic to AdS_3 x S^3 x M_4 (where M_4 is either T^4 or K_3). These solutions are dual to two or more CFTs defined on half-planes which share a common line interface. Their geometry consists of an AdS_2 x S^2 x M_4 fibration over a simply connected Riemann surface Sigma with boundary. In the present paper, we show that regular exact solutions exist also for surfaces Sigma which are not simply connected. Specifically, we construct in detail solutions for which Sigma has the topology of an annulus. This construction is generalized to produce solutions for any surface Sigma with the topology of an open string worldsheet with g holes.
Type IIB superstring theory has AdS_3 x S^3 x M_4 (where the manifold M_4 is either K_3 or T^4) solutions which preserve sixteen supersymmetries. In this paper we consider half-BPS solutions which are locally asymptotic to AdS_3 x S^3 x M_4 and preserve eight of the sixteen supersymmetries. We reduce the BPS equations and the Bianchi identity for the self-dual five-form field to a set of four differential equations. The complete local solution can be parameterized in terms of two harmonic and two holomorphic functions and all bosonic fields have explicit expressions in terms of these functions. We analyze the conditions for global regularity and construct new half-BPS Janus-solutions which have two asymptotic AdS_3 regions. In addition, our analysis proves the global regularity of a class of solutions with more than two asymptotic AdS_3 regions. Finally, we discuss the dual interpretation as a supersymmetric interface theory for the half-BPS Janus solutions carrying only Ramond-Ramond three-form charge.
The BPS equations in M-theory for solutions with 16 residual supersymmetries, $SO(2,2)\times SO(4)\times SO(4)$ symmetry, and $AdS_4 \times S^7$ asymptotics, were reduced in [arXiv:0806.0605] to a linear first order partial differential equation on a Riemann surface with boundary, subject to a non-trivial quadratic constraint. In the present paper, suitable regularity and boundary conditions are imposed for the existence of global solutions. We seek regular solutions with multiple distinct asymptotic $AdS_4 \times S^7$ regions, but find that, remarkably, such solutions invariably reduce to multiple covers of the M-Janus solution found by the authors in [arXiv:0904.3313], suggesting rigidity of the half-BPS M-Janus solution. In particular, we prove analytically that no other smooth deformations away from the M-Janus solution exist, as such deformations invariably violate the quadratic constraint. These rigidity results are contrasted to the existence of half-BPS solutions with non-trivial 4-form fluxes and charges asymptotic to $AdS_7 \times S^4$. The results are related to the possibility of M2-branes to end on M5-branes, but the impossibility of M5-branes to end on M2-branes, and to the non-existence of half-BPS solutions with simultaneous $AdS_4 \times S^7$ and $AdS_7 \times S^4$ asymptotic regions.
We present a one-parameter deformation of the AdS_{4} x S^{7} vacuum, which is a regular solution in M-theory, invariant under SO(2,2) x SO(4) x SO(4), and which preserves 16 supersymmetries. The solution corresponds to a holographic realization of a Janus-like interface/defect theory, despite the absence of a dilaton in M-theory. The 2+1-dimensional CFT dual results from the maximally symmetric CFT through the insertion of a dimension 2 operator which is localized along a 1+1-dimensional linear interface/defect, thereby partially breaking the superconformal symmetry. The solution admits a regular ABJM reduction to a quotient solution which is invariant under SO(2,2) x SO(4) x U(1)^2, preserves 12 supersymmetries, and provides a Janus-like interface/defect solution in ABJM theory.
In this paper, we construct Euclidean instanton and wormhole solutions in $d=4$, N=2 supergravity theories with hypermultiplets. The analytic continuation of the hypermultiplet action, involving pseudoscalar axions, is discussed using the approach originally developed by Coleman which determines the apparence of boundary terms. In particular, we investigate the conditions obtained by requiring the action to be positive-definite once the boundary terms are taken into account. The case of two hypermultiplets parameterizing the coset $G_{2,2}/SU(2)\times SU(2)$ is studied in detail. Orientifold projections which reduce the supersymmetry to N=1 are also discussed.
General local half-BPS solutions in M-theory, which have $SO(2,2)\times SO(4)\times SO(4)$ symmetry and are asymptotic to $AdS_{7}\times S^{4}$, were constructed in exact form by the authors in [arXiv:0806.0605]. In the present paper, suitable regularity conditions are imposed on these local solutions, and corresponding globally well-defined solutions are explicitly constructed. The physical properties of these solutions are analyzed, and interpreted in terms of the gravity duals to extended 1+1-dimensional half-BPS defects in the 6-dimensional CFT with maximal supersymmetry.
We establish a correspondence between certain Lie superalgebras with 16 fermionic generators, and half-BPS solutions to supergravities with 32 supersymmetries. Three cases are discussed. For Type IIB supergravity, we relate semi-simple Lie superalgebras H with 16 fermionic generators which are subalgebras of PSU(2,2|4), to families of half-BPS solutions which are invariant under H, and locally asymptotic to AdS_5 x S^5. Similarly, for M-theory, we relate semi-simple Lie superalgebras H with 16 fermionic generators which are subalgebras of OSp(8^*|4) or OSp(8|4,R) to families of half-BPS solutions which are invariant under H, and locally asymptotic to AdS_7 x S^4 or AdS_4 x S^7 respectively. Possible enhancements to more than 16 supersymmetries, such as 24, are also analyzed. The classification of semi-simple subalgebras of PSU(2,2|4), OSp(8^*|4), and OSp(8|4,R) derived in this paper, leads us to conjecture the existence of various new families of half-BPS solutions to Type IIB supergravity and M-theory.
In this paper we present supersymmetric instanton and non-supersymmetric wormhole solutions for the universal hypermultiplet sector of $d=4$ N=2 supergravity theories. Instantons and wormholes are constructed as saddle points dominating transition amplitudes between states of definite axionic shift charge, using an approach due to Coleman and Lee. Our solutions are constructed in terms of the conserved Noether charges associated with the global SU(2,1) symmetry of the universal hypermultiplet action. The conditions imposed by regularity on the charges are discussed.
The complete eleven-dimensional supergravity solutions with 16 supersymmetries on manifolds of the form $AdS_3 \times S^3 \times S^3 \times Σ$, with isometry $SO(2,2) \times SO(4) \times SO(4)$, and with either $AdS_4 \times S^7$ or $AdS_7 \times S^4$ boundary behavior, are obtained in exact form. The two-dimensional parameter space $Σ$ is a Riemann surface with boundary, over which the product space $AdS_3 \times S^3 \times S^3$ is warped. By mapping the reduced BPS equations to an integrable system of the sine-Gordon/Liouville type, and then mapping this integrable system onto a linear equation, the general local solutions are constructed explicitly in terms of one harmonic function on $Σ$, and an integral transform of two further harmonic functions on $Σ$. The solutions to the BPS equations are shown to automatically solve the Bianchi identities and field equations for the 4-form field, as well as Einstein's equations. The solutions we obtain have non-vanishing 4-form field strength on each of the three factors of $AdS_3 \times S^3 \times S^3$, and include fully back-reacted M2-branes in $AdS_7 \times S^4$ and M5-branes in $AdS_4 \times S^7$. No interpolating solutions exist with mixed $AdS_4 \times S^7$ and $AdS_7 \times S^4$ boundary behavior. Global regularity of these local solutions, as well as the existence of further solutions with neither $AdS_4 \times S^7$ nor $AdS_7 \times S^4$ boundary behavior will be studied elsewhere.
We study aspects of a recently proposed exact time dependent black hole solution of IIB string theory using the AdS/CFT correspondence. The dual field theory is a thermal system in which initially a vacuum density for a non-conserved operator is turned on. We can see that in agreement with general thermal field theory expectation the system equilibrates: the expectation value of the non-conserved operator goes to zero exponentially and the entropy increases. In the field theory the process can be described quantitatively in terms of a thermofield state and exact agreement with the gravity answers is found.
Nonlocal stringy versions of the Nambu-Jona-Lasinio and Gross-Neveu models arise in a certain limit of holographic QCD. We analyze the phase structure at finite density and temperature at strong coupling in terms of probe branes in the gravity dual. Comparison with the phase structure of the local field theory models shows qualitative agreement with some aspects, and disagreement with others. Finally, we explain how to construct the Landau potentials for these models by taking the probe branes off-shell.
The reduced field equations and BPS conditions are derived in Type IIB supergravity for configurations of the Janus type, characterized by an $AdS_4$-slicing of $AdS_5$, and various degrees of internal symmetry and supersymmetry. A generalization of the Janus solution, which includes a varying axion along with a varying dilaton, and has SO(6) internal symmetry, but completely broken supersymmetry, is obtained analytically in terms of elliptic functions. A supersymmetric solution with 4 conformal supersymmetries, SU(3) internal symmetry, a varying axion along with a varying dilaton, and non-trivial $B_{(2)}$ field, is derived analytically in terms of genus 3 hyper-elliptic integrals. This supersymmetric solution is the 10-dimensional Type IIB dual to the $\N=1$ interface super-Yang-Mills theory with SU(3) internal symmetry previously found in the literature.
We explicitly construct the fully back-reacted half-BPS solutions in Type IIB supergravity which are dual to Wilson loops with 16 supersymmetries in $\mathcal{N}=4$ super Yang-Mills. In a first part, we use the methods of a companion paper to derive the exact general solution of the half-BPS equations on the space $AdS_2 \times S^2 \times S^4 \times Σ$, with isometry group $SO(2,1)\times SO(3) \times SO(5)$ in terms of two locally harmonic functions on a Riemann surface $Σ$ with boundary. These solutions, generally, have varying dilaton and axion, and non-vanishing 3-form fluxes. In a second part, we impose regularity and topology conditions. These non-singular solutions may be parametrized by a genus $g \geq 0$ hyperelliptic surface $Σ$, all of whose branch points lie on the real line. Each genus $g$ solution has only a single asymptotic $AdS_5 \times S^5$ region, but exhibits $g$ homology 3-spheres, and an extra $g$ homology 5-spheres, carrying respectively RR 3-form and RR 5-form charges. For genus 0, we recover $AdS_5 \times S^5$ with 3 free parameters, while for genus $g \geq 1$, the solution has $2g+5$ free parameters. The genus 1 case is studied in detail. Numerical analysis is used to show that the solutions are regular throughout the $g=1$ parameter space. Collapse of a branch cut on $Σ$ subtending either a homology 3-sphere or a homology 5-sphere is non-singular and yields the genus $g-1$ solution. This behavior is precisely expected of a proper dual to a Wilson loop in gauge theory.
The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold $AdS_4 \times S^2 \times S^2 \times Σ$ with $SO(2,3) \times SO(3) \times SO(3)$ symmetry in terms of two holomorphic functions on a Riemann surface $Σ$, which generally has a boundary. This is achieved by reducing the BPS equations using the above symmetry requirements, proving that all solutions of the BPS equations solve the full Type IIB supergravity field equations, mapping the BPS equations onto a new integrable system akin to the Liouville and Sine-Gordon theories, and mapping this integrable system to a linear equation which can be solved exactly. Amongst the infinite class of solutions, a non-singular Janus solution is identified which provides the AdS/CFT dual of the maximally supersymmetric Yang-Mills interface theory discovered recently. The construction of general classes of globally non-singular solutions, including fully back-reacted $AdS_5 \times S^5$ and supersymmetric Janus doped with D5 and/or NS5 branes, is deferred to a companion paper.
Regularity and topology conditions are imposed on the exact Type IIB solutions on $AdS_4 \times S^2 \times S^2 \times Σ$ with 16 supersymmetries, which were derived in a companion paper. We construct an infinite class of regular solutions with varying dilaton, and non-zero 3-form fluxes. Our solutions may be viewed as the fully back-reacted geometries of $AdS_5 \times S^5$ (or more generally, Janus) doped with D5 and/or NS5 branes. The solutions are parametrized by the choice of an arbitrary genus $g$ hyper-elliptic Riemann surface $Σ$ with boundary, all of whose branch points are restricted to lie on a line. For genus 0, the Janus solution with 16 supersymmetries and 6 real parameters is recovered; its topology coincides with that of $AdS_5 \times S^5$. The genus $g\geq 1$ solutions are parametrized by a total of $4g+6$ real numbers, $2g-1$ of which are the real moduli of $Σ$. The solutions have $2g+2$ asymptotic $AdS_5 \times S^5$ regions, $g$ three-spheres with RR 3-form charge, and another $g$ with NSNS 3-form charge. Collapse of consecutive branch points of $Σ$ yields singularities which correspond to D5 and NS5 branes in the probe limit. It is argued that the AdS/CFT dual gauge theory to each of our solutions consists of a 2+1-dimensional planar interface on which terminate $2g+2$ half-Minkowski 3+1-dimensional space-time $\mathcal{N}=4$ super-Yang-Mills theories. Generally, the $\\mathcal{N}=4$ theory in each Minkowski half-space-time may have an independent value of the gauge coupling, and the interface may support various operators, whose interface couplings are further free parameters of the dual gauge theory.