Smooth Horizonless Geometries Deep Inside the Black-Hole Regime

This Letter has been highlighted by the editors as an Editor's Suggestion.This Letter has been highlighted by the editors as an Editor's Suggestion

Non-Supersymmetric String Theory

A class of non-supersymmetric string backgrounds can be constructed using twists that involve space-time fermion parity. We propose a non-perturbative definition of string theory in these backgrounds via gauge theories with supersymmetry softly broken by twisted boundary conditions. The perturbative string spectrum is reproduced, and qualitative effects of the interactions are discussed. Along the way, we find an interesting mechanism for inflation. The end state of closed string tachyon condensation is a highly excited state in the gauge theory which, in all likelihood, does not have a geometric interpretation.Comment: 35 pages, 2 figures; revision adds a computation of the relevant orbifold state

Quantization of Integrable Systems and a 2d/4d Duality

We present a new duality between the F-terms of supersymmetric field theories defined in two- and four-dimensions respectively. The duality relates N=2 supersymmetric gauge theories in four dimensions, deformed by an Omega-background in one plane, to N=(2,2) gauged linear sigma-models in two dimensions. On the four dimensional side, our main example is N=2 SQCD with gauge group SU(L) and 2L fundamental flavours. Using ideas of Nekrasov and Shatashvili, we argue that the Coulomb branch of this theory provides a quantization of the classical Heisenberg SL(2) spin chain. Agreement with the standard quantization via the Algebraic Bethe Ansatz implies the existence of an isomorphism between the chiral ring of the 4d theory and that of a certain two-dimensional theory. The latter can be understood as the worldvolume theory on a surface operator/vortex string probing the Higgs branch of the same 4d theory. We check the proposed duality by explicit calculation at low orders in the instanton expansion. One striking consequence is that the Seiberg-Witten solution of the 4d theory is captured by a one-loop computation in two dimensions. The duality also has interesting connections with the AGT conjecture, matrix models and topological string theory where it corresponds to a refined version of the geometric transition.Comment: 51 pages, 7 figures. Additional comments, minor improvements and references adde

Revisiting random tensor models at large N via the Schwinger-Dyson equations

The Schwinger-Dyson Equations (SDEs) of matrix models are known to form (half) a Virasoro algebra and have become a standard tool to solve matrix models. The algebra generated by SDEs in tensor models (for random tensors in a suitable ensemble) is a specific generalization of the Virasoro algebra and it is important to show that these new symmetries determine the physical solutions. We prove this result for random tensors at large N. Compared to matrix models, tensor models have more than a single invariant at each order in the tensor entries and the SDEs make them proliferate. However, the specific combinatorics of the dominant observables allows to restrict to linear SDEs and we show that they determine a unique physical perturbative solution. This gives a new proof that tensor models are Gaussian at large N, with the covariance being the full 2-point function.Comment: 17 pages, many figure

Relating Gauge Theories via Gauge/Bethe Correspondence

In this note, we use techniques from integrable systems to study relations between gauge theories. The Gauge/Bethe correspondence, introduced by Nekrasov and Shatashvili, identifies the supersymmetric ground states of an N=(2,2) supersymmetric gauge theory in two dimensions with the Bethe states of a quantum integrable system. We make use of this correspondence to relate three different quiver gauge theories which correspond to three different formulations of the Bethe equations of an integrable spin chain called the tJ model.Comment: 30 pages, published in JHEP. LaTeX problem correcte

Optimal control models of the goal-oriented human locomotion

In recent papers it has been suggested that human locomotion may be modeled as an inverse optimal control problem. In this paradigm, the trajectories are assumed to be solutions of an optimal control problem that has to be determined. We discuss the modeling of both the dynamical system and the cost to be minimized, and we analyze the corresponding optimal synthesis. The main results describe the asymptotic behavior of the optimal trajectories as the target point goes to infinity

On Arnold's 14 `exceptional' N=2 superconformal gauge theories

We study the four-dimensional superconformal N=2 gauge theories engineered by the Type IIB superstring on Arnold's 14 exceptional unimodal singularities (a.k.a. Arnold's strange duality list), thus extending the methods of 1006.3435 to singularities which are not the direct sum of minimal ones. In particular, we compute their BPS spectra in several `strongly coupled' chambers. From the TBA side, we construct ten new periodic Y-systems, providing additional evidence for the existence of a periodic Y-system for each isolated quasi-homogeneous singularity with $\hat c<2$ (more generally, for each N=2 superconformal theory with a finite BPS chamber whose chiral primaries have dimensions of the form N/l).Comment: 73 pages, 7 figure

String Theory on Warped AdS_3 and Virasoro Resonances

We investigate aspects of holographic duals to time-like warped AdS_3 space-times--which include G\"odel's universe--in string theory. Using worldsheet techniques similar to those that have been applied to AdS_3 backgrounds, we are able to identify space-time symmetry algebras that act on the dual boundary theory. In particular, we always find at least one Virasoro algebra with computable central charge. Interestingly, there exists a dense set of points in the moduli space of these models in which there is actually a second commuting Virasoro algebra, typically with different central charge than the first. We analyze the supersymmetry of the backgrounds, finding related enhancements, and comment on possible interpretations of these results. We also perform an asymptotic symmetry analysis at the level of supergravity, providing additional support for the worldsheet analysis.Comment: 24 pages + appendice

The non-compact elliptic genus: mock or modular

We analyze various perspectives on the elliptic genus of non-compact supersymmetric coset conformal field theories with central charge larger than three. We calculate the holomorphic part of the elliptic genus via a free field description of the model, and show that it agrees with algebraic expectations. The holomorphic part of the elliptic genus is directly related to an Appell-Lerch sum and behaves anomalously under modular transformation properties. We analyze the origin of the anomaly by calculating the elliptic genus through a path integral in a coset conformal field theory. The path integral codes both the holomorphic part of the elliptic genus, and a non-holomorphic remainder that finds its origin in the continuous spectrum of the non-compact model. The remainder term can be shown to agree with a function that mathematicians introduced to parameterize the difference between mock theta functions and Jacobi forms. The holomorphic part of the elliptic genus thus has a path integral completion which renders it non-holomorphic and modular.Comment: 13 page

Thermal phases of D1-branes on a circle from lattice super Yang-Mills

We report on the results of numerical simulations of 1+1 dimensional SU(N) Yang-Mills theory with maximal supersymmetry at finite temperature and compactified on a circle. For large N this system is thought to provide a dual description of the decoupling limit of N coincident D1-branes on a circle. It has been proposed that at large N there is a phase transition at strong coupling related to the Gregory-Laflamme (GL) phase transition in the holographic gravity dual. In a high temperature limit there was argued to be a deconfinement transition associated to the spatial Polyakov loop, and it has been proposed that this is the continuation of the strong coupling GL transition. Investigating the theory on the lattice for SU(3) and SU(4) and studying the time and space Polyakov loops we find evidence supporting this. In particular at strong coupling we see the transition has the parametric dependence on coupling predicted by gravity. We estimate the GL phase transition temperature from the lattice data which, interestingly, is not yet known directly in the gravity dual. Fine tuning in the lattice theory is avoided by the use of a lattice action with exact supersymmetry.Comment: 21 pages, 8 figures. v2: References added, two figures were modified for clarity. v3: Normalisation of lattice coupling corrected by factor of two resulting in change of estimate for c_cri