No abstract

We propose a novel prescription for computing the boundary stress tensor and charges of asymptotically de Sitter ͑dS͒ spacetimes from data at early or late time infinity. If there is a holographic dual to dS spaces, defined analogously to the AdS/conformal field theory correspondence, our methods compute the ͑Euclidean͒ stress tensor of the dual. We compute the masses of Schwarzschild-de Sitter black holes in four and five dimensions, and the masses and angular momenta of Kerr-de Sitter spaces in three dimensions. All these spaces are less massive than de Sitter space, a fact which we use to qualitatively and quantitatively relate de Sitter entropy to the degeneracy of possible dual field theories. Our results in general dimensions lead to a conjecture: Any asymptotically de Sitter spacetime with mass greater than de Sitter space has a cosmological singularity. Finally, if a dual to de Sitter space exists, the trace of our stress tensor computes the renormalized group ͑RG͒ equation of the dual field theory. Cosmological time evolution corresponds to RG evolution in the dual. The RG evolution of the c function is then related to changes in accessible degrees of freedom in an expanding universe.

We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure. The algorithm applies to crystals with broken time-reversal, particle-hole, and chiral symmetries in any dimension. The presented results match the mathematical structure underlying the topological classification of these crystals in terms of Ktheory, and therefore elucidate this abstract mathematical framework from a simple combinatorial perspective. Using a straightforward counting procedure, we classify the allowed topological phases in any possible two-dimensional crystal in class A. We also show how the same procedure can be used to classify the allowed phases for any three-dimensional space group. Employing these classifications, we study transitions between topological phases within class A that are driven by band inversions at high symmetry points in the first Brillouin zone. This enables us to list all possible types of phase transitions within a given crystal structure, and identify whether or not they give rise to intermediate Weyl semimetallic phases. arXiv:1612.02007v1 [cond-mat.mes-hall]

Using the AdS/CFT correspondence, we probe the scale-dependence of thermalization in strongly coupled field theories following a sudden injection of energy, via calculations of two-point functions, Wilson loops and entanglement entropy in d = 2, 3, 4. In the saddlepoint approximation these probes are computed in AdS space in terms of invariant geometric objects -geodesics, minimal surfaces and minimal volumes. Our calculations for two-dimensional field theories are analytical. In our strongly coupled setting, all probes in all dimensions share certain universal features in their thermalization: (1) a slight delay in the onset of thermalization, (2) an apparent non-analyticity at the endpoint of thermalization, (3) top-down thermalization where the UV thermalizes first. For homogeneous initial conditions the entanglement entropy thermalizes slowest, and sets a timescale for equilibration that saturates a causality bound over the range of scales studied. The growth rate of entanglement entropy density is nearly volume-independent for small volumes, but slows for larger volumes.

We construct and analyze dual N = 4 supersymmetric gauge theories in three dimensions with unitary and symplectic gauge groups. The gauge groups and the field content of the theories are encoded in quiver diagrams. The duality exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters. We analyze the classical and the quantum moduli spaces of the theories and construct an explicit mirror map between the mass parameters and the the Fayet-Iliopoulos parameters of the dual. The results generalize the relation between ALE spaces and moduli spaces of SU(n) and SO(2n) instantons. We interpret some of these results from the string theory viewpoint, for SU(n) by analyzing T-duality and extremal transitions in type II string compactifications, for SO(2n) by using D-branes as probes. Finally, we make a proposal for the moduli space of vacua of these theories in the absence of matter.1 The Hilbert schemes of k points on complex surfaces have recently appeared as the moduli spaces of D-branes [8,9] 1 persymmetric gauge theories in three dimensions. In section 3 we define the dual gauge theories associated with quiver diagrams. We present the proposed dualities, the Higgs and Coulomb branches of the theories and the mirror map between the mass and FI parameters. In section 4 we study the first proposed family of dualities for U(k) gauge theories. We start by providing the first evidence to this duality proposal by counting the dimensions of the Higgs and Coulomb branches as well as the number of mass and FI terms. We then study how the quantum corrections to the metric on the Coulomb branch fit into the mirror picture. We compute the one-loop corrections to the hyperkähler metric on the Coulomb branch of the A-model and compare to the exact metric on the Higgs branch of the B-model. The comparison yields strong support for the mirror map between the mass terms of the A-model and the FI terms of the B-model. In section 5 we analyze the structure of the Coulomb, Higgs and mixed branches for various mass and FI parameters. We observe a complete agreement of their dimensions which provide further evidence for the duality. In particular, we complete the proof of the mirror map by fixing the ambiguities left after the one-loop computation. We show how the proposed duality completely determines the quantum moduli space of vacua. In section 6 we examine type II string compactifications that in the field theory limit yield the A-model. The gauge symmetry and matter fields arise by wrapping D-branes around vanishing cycles and we use T-duality and extremal transitions to explain the gauge theory duality from a stringy viewpoint. In section 7 we study the second proposed family of dualities for Sp(k) gauge theories. We provide the counting evidence for this duality proposal, study the quantum corrections, derive the mirror map and use D-brane probes and the Type I -M-theory duality to further support the gauge theory picture. In section 8 we study the third proposed family of dualities for U(k) n gauge theorie...

We study conformal field theories in two dimensions separated by domain walls, which preserve at least one Virasoro algebra. We develop tools to study such domain walls, extending and clarifying the concept of 'folding' discussed in the condensed-matter literature. We analyze the conditions for unbroken supersymmetry, and discuss the holographic duals in AdS3 when they exist. One of the interesting observables is the Casimir energy between a wall and an anti-wall. When these separate free scalar field theories with different target-space radii, the Casimir energy is given by the dilogarithm function of the reflection probability. The walls with holographic duals in AdS3 separate two sigma models, whose target spaces are moduli spaces of Yang-Mills instantons on T4 or K3. In the supergravity limit, the Casimir energy is computable as classical energy of a brane that connects the walls through AdS3. We compare this result with expectations from the sigma-model point of view. * Unité mixte du CNRS et de l'Ecole Normale Supérieure, UMR 8549. * The language is somewhat loose, because strictly-speaking a CFT has no asymptotic particle states. A more accurate phrasing, in two dimensions, is that the boundary state maps holomorphic into antiholomorphic fields, in a way that commutes with the action of the Virasoro algebra. † More precisely, the tensor product of the theory on one side and of the 'conjugate' theory, with left-and right-movers interchanged, on the other side. ‡ The light-cone coordinates are taken to be x ± = t ± x, so that ∂ ± = 1 2 (∂ t ± ∂ x ). * * We thank Volker Schomerus for pointing out these arguments.

We study string compactifications with sixteen supersymmetries. The moduli space for these compactifications becomes quite intricate in lower dimensions, partly because there are many different irreducible components. We focus primarily, but not exclusively, on compactifications to seven or more dimensions. These vacua can be realized in a number ways: the perturbative constructions we study include toroidal compactifications of the heterotic/type I strings, asymmetric orbifolds, and orientifolds. In addition, we describe less conventional M and F theory compactifications on smooth spaces. The last class of vacua considered are compactifications on singular spaces with non-trivial discrete fluxes.We find a number of new components in the string moduli space. Contained in some of these components are M theory compactifications with novel kinds of "frozen" singularities. We are naturally led to conjecture the existence of new dualities relating spaces with different singular geometries and fluxes. As our study of these vacua unfolds, we also learn about additional topics including: F theory on spaces without section, automorphisms of del Pezzo surfaces, and novel physics (and puzzles) from equivariant K-theory. Lastly, we comment on how the data we gain about the M theory three-form might be interpreted.

Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in 2, 3, and 4 dimensions to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest, and sets a timescale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volumeindependent for small volumes, but slows for larger volumes. In this setting, the UV thermalizes first.