Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3

We study classical open string solutions with a null polygonal boundary in AdS_3 in relation to gluon scattering amplitudes in N=4 super Yang-Mills at strong coupling. We derive in full detail the set of integral equations governing the decagonal and the dodecagonal solutions and identify them with the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon models. By evaluating the free energy in the conformal limit we compute the central charges, from which we observe general correspondence between the polygonal solutions in AdS_n and generalized parafermions.Comment: 25 pages, 4 figures, v2: a figure and references added, minor corrections, v3: references added, minor corrections, to appear in JHE

Strain-induced partially flat band, helical snake states, and interface superconductivity in topological crystalline insulators

Topological crystalline insulators in IV-VI compounds host novel topological surface states consisting of multi-valley massless Dirac fermions at low energy. Here we show that strain generically acts as an effective gauge field on these Dirac fermions and creates pseudo-Landau orbitals without breaking time-reversal symmetry. We predict the realization of this phenomenon in IV-VI semiconductor heterostructures, due to a naturally occurring misfit dislocation array at the interface that produces a periodically varying strain field. Remarkably, the zero-energy Landau orbitals form a flat band in the vicinity of the Dirac point, and coexist with a network of snake states at higher energy. We propose that the high density of states of this flat band gives rise to interface superconductivity observed in IV-VI semiconductor multilayers at unusually high temperatures, with non-BCS behavior. Our work demonstrates a new route to altering macroscopic electronic properties to achieve a partially flat band, and paves the way for realizing novel correlated states of matter.Comment: Accepted by Nature Physic

Asymptotic analysis of an elastic rod with rounded ends

We derive a one-dimensional model for an elastic shuttle, that is, a thin rod with rounded ends and small fixed terminals, by means of an asymptotic procedure of dimension reduction. In the model, deformation of the shuttle is described by a system of ordinary differential equations with variable degenerating coefficients, and the number of the required boundary conditions at the end points of the one-dimensional image of the rod depends on the roundness exponent m is an element of(0,1). Error estimates are obtained in the case m is an element of(0,1/4) by using an anisotropic weighted Korn inequality, which was derived in an earlier paper by the authors. We also briefly discuss boundary layer effects, which can be neglected in the case m is an element of(0,1/4) but play a crucial role in the formulation of the limit problem for m >= 1/4.Peer reviewe

BPS States in Omega Background and Integrability

We reconsider string and domain wall central charges in N=2 supersymmetric gauge theories in four dimensions in presence of the Omega background in the Nekrasov-Shatashvili (NS) limit. Existence of these charges entails presence of the corresponding topological defects in the theory - vortices and domain walls. In spirit of the 4d/2d duality we discuss the worldsheet low energy effective theory living on the BPS vortex in N=2 Supersymmetric Quantum Chromodynamics (SQCD). We discuss some aspects of the brane realization of the dualities between various quantum integrable models. A chain of such dualities enables us to check the AGT correspondence in the NS limit.Comment: 48 pages, 10 figures, minor changes, references added, typos correcte