John Estes

Exact half-BPS Type IIB interface solutions. I. Local solution and supersymmetric Janus

The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold AdS4 ? S2 ? S2 ? ? with SO(2, 3) ? SO(3) ? SO(3) symmetry in terms of two holomorphic functions on a Riemann surface ?, 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 AdS5 ? S5 and supersymmetric Janus doped with D5 and/or NS5 branes, is deferred to a companion paper [1].

Exact half-BPS Type IIB interface solutions II: Flux solutions and multi-Janus

Regularity and topology conditions are imposed on the exact Type IIB solutions on AdS4 × S2 × S2 × Σ with 16 supersymmetries, which were derived in a companion paper [1]. 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 AdS5 × S5 (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 AdS5 × S5. The genus g ≥ 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 AdS5 × S5 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 = 4 super-Yang-Mills theories. Generally, the = 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.

Gravity duals of half-BPS Wilson loops

We explicitly construct the fully back-reacted half-BPS solutions in Type IIB supergravity which are dual to Wilson loops with 16 supersymmetries in = 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 AdS2 × S2 × S4 × Σ, with isometry group SO(2, 1) × SO(3) × 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 ≥ 0 hyperelliptic surface Σ, all of whose branch points lie on the real line. Each genus g solution has only a single asymptotic AdS5 × S5 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 AdS5 × S5 with 3 free parameters, while for genus g ≥ 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.

Interface Yang–Mills, supersymmetry, and Janus

Abstract We consider theories consisting of a planar interface with N = 4 super-Yang–Mills on either side and varying gauge coupling across the interface. The interface does not carry any independent degrees of freedom, but is allowed to support local gauge invariant operators, included with independent interface couplings. In general, both conformal symmetry and supersymmetry will be broken, but for special arrangements of the interface couplings, these symmetries may be restored. We provide a systematic classification of all allowed interface supersymmetries. We find new theories preserving eight and four Poincare supersymmetries, which get extended to sixteen and eight supersymmetries in the conformal limit, respectively with SU ( 2 ) × SU ( 2 ) , SO ( 2 ) × SU ( 2 ) internal symmetry. The Lagrangians for these theories are explicitly constructed. We also recover the theory with two Poincare supersymmetries and SU ( 3 ) internal symmetry proposed earlier as a candidate CFT dual to super-Janus. Since our new interface theories have only operators from the supergravity multiplet turned on, dual supergravity solutions are expected to exist. We speculate on the possible relation between the interface theory with maximal supersymmetry and the near-horizon limit of the D3–D5 system.

Ten-dimensional supersymmetric Janus solutions

Abstract 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 two-parameter family of solutions with 4 real 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.

Janus solutions in M-theory

We present a one-parameter deformation of the AdS4 × S7 vacuum, which is a regular solution in M-theory, invariant under SO(2,2) × SO(4) × 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) × SO(4) × U(1)2, preserves 12 supersymmetries, and provides a Janus-like interface/defect solution in ABJM theory.

Exact Half-BPS Flux Solutions in M-theory II: Global solutions asymptotic to AdS(7) x S**4

General local half-BPS solutions in M-theory, which have SO(2, 2) × SO(4) × SO(4) symmetry and are asymptotic to AdS7 × S4, 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.

Cosmological phases of the string thermal effective potential

In a superstring framework, the free energy density F can be determined unambiguously at the full string level once supersymmetry is spontaneously broken via geometrical fluxes. We show explicitly that only the moduli associated to the supersymmetry breaking may give relevant contributions. All other spectator moduli μI give exponentially suppressed contributions for relatively small (as compared to the string scale) temperature T and supersymmetry breaking scale M. More concisely, for μI>T and M, F takes the form F(T,M;μI)=F(T,M)+O[exp(−μIT),exp(−μIM)]. We study the cosmological regime where T and M are below the Hagedorn temperature scale TH. In this regime, F remains finite for any values of the spectator moduli μI. We investigate extensively the case of one spectator modulus μd corresponding to Rd, the radius-modulus field of an internal compactified dimension. We show that its thermal effective potential V(T,M;μ)=F(T,M;μ) admits five phases, each of which can be described by a distinct but different effective field theory. For late cosmological times, the Universe is attracted to a “Radiation-like evolution” with M(t)∝T(t)∝1/a(t)∝t−2/d. The spectator modulus μ(t) is stabilized either to the stringy enhanced symmetry point where Rd=1, or fixed at an arbitrary constant μ0>T,M. For arbitrary boundary conditions at some initial time, tE, μ(t) may pass through more than one effective field theory phase before its final attraction.

Superstring cosmology for N4 = 1 → 0 superstring vacua

We study the cosmology of perturbative heterotic superstring theory during the radiation-like era for semi-realistic backgrounds with initialN = 1 supersymmetry. This analysis is valid for times after the Hagedorn era (or alternatively ination era) but before the electroweak symmetry breaking transition. We nd an attraction to a radiation-like era with the ratio of the supersymmetry breaking scale to temperature stabilized. This provides a dynamical mechanism for setting the supersymmetry breaking scale and its corresponding hierarchy with the Planck scale. For the internal space, we nd that orbifold directions never decompactify, while toroidal directions may decompactify only when they are wrapped by certain geometrical uxes which break supersymmetry. This suggests a mechanism for generating spatial directions during the radiation-like era. Moreover, we show that certain moduli may be stabilized during the radiation-like era with masses near the supersymmetry breaking scale. In addition, the moduli do not dominate at late times, thus avoiding the cosmological moduli problem.

Exact half-BPS flux solutions in M-theory III: existence and rigidity of global solutions asymptotic to AdS(4) x S-7

The BPS equations in M-theory for solutions with 16 residual supersymmetries, SO(2,2) ? SO(4) ? SO(4) symmetry, and AdS4 ? S7 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 AdS4 ? S7 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 AdS7 ? S4. 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 AdS4 ? S7 and AdS7 ? S4 asymptotic regions.