Perturbative String Thermodynamics near Black Hole Horizons

We provide further computations and ideas to the problem of near-Hagedorn string thermodynamics near (uncharged) black hole horizons, building upon our earlier work JHEP 1403 (2014) 086. The relevance of long strings to one-loop black hole thermodynamics is emphasized. We then provide an argument in favor of the absence of $\alpha'$-corrections for the (quadratic) heterotic thermal scalar action in Rindler space. We also compute the large $k$ limit of the cigar orbifold partition functions (for both bosonic and type II superstrings) which allows a better comparison between the flat cones and the cigar cones. A discussion is made on the general McClain-Roth-O'Brien-Tan theorem and on the fact that different torus embeddings lead to different aspects of string thermodynamics. The black hole/string correspondence principle for the 2d black hole is discussed in terms of the thermal scalar. Finally, we present an argument to deal with arbitrary higher genus partition functions, suggesting the breakdown of string perturbation theory (in $g_s$) to compute thermodynamical quantities in black hole spacetimes.Comment: 51 pages, v2: matches published versio

Knot Homology from Refined Chern-Simons Theory

We formulate a refinement of SU(N) Chern-Simons theory on a three-manifold via the refined topological string and the (2,0) theory on N M5 branes. The refined Chern-Simons theory is defined on any three-manifold with a semi-free circle action. We give an explicit solution of the theory, in terms of a one-parameter refinement of the S and T matrices of Chern-Simons theory, related to the theory of Macdonald polynomials. The ordinary and refined Chern-Simons theory are similar in many ways; for example, the Verlinde formula holds in both. We obtain new topological invariants of Seifert three-manifolds and torus knots inside them. We conjecture that the knot invariants we compute are the Poincare polynomials of the sl(n) knot homology theory. The latter includes the Khovanov-Rozansky knot homology, as a special case. The conjecture passes a number of nontrivial checks. We show that, for a large number of torus knots colored with the fundamental representation of SU(N), our knot invariants agree with the Poincare polynomials of Khovanov-Rozansky homology. As a byproduct, we show that our theory on S^3 has a large-N dual which is the refined topological string on X=O(-1)+O(-1)->P^1; this supports the conjecture by Gukov, Schwarz and Vafa relating the spectrum of BPS states on X to sl(n) knot homology. We also provide a matrix model description of some amplitudes of the refined Chern-Simons theory on S^3.Comment: 73 pages, 8 figures; minor corrections and improvements in presentatio

Inversion mechanism for the transport current in type-II superconductors

The longitudinal transport problem (the current is applied parallel to some bias magnetic field) in type-II superconductors is analyzed theoretically. Based on analytical results for simplified configurations, and relying on numerical studies for general scenarios, it is shown that a remarkable inversion of the current flow in a surface layer may be predicted under a wide set of experimental conditions. Strongly inhomogeneous current density profiles, characterized by enhanced transport toward the center and reduced, or even negative, values at the periphery of the conductor, are expected when the physical mechanisms of flux depinning and consumption (via line cutting) are recalled. A number of striking collateral effects, such as local and global paramagnetic behavior, are predicted. Our geometrical description of the macroscopic material laws allows a pictorial interpretation of the physical phenomena underlying the transport backflow.Comment: 8 pages, 6 figures (Best quality pictures are available by author's contact

In Search of Fundamental Discreteness in 2+1 Dimensional Quantum Gravity

Inspired by previous work in 2+1 dimensional quantum gravity, which found evidence for a discretization of time in the quantum theory, we reexamine the issue for the case of pure Lorentzian gravity with vanishing cosmological constant and spatially compact universes of genus larger than 1. Taking as our starting point the Chern-Simons formulation with Poincare gauge group, we identify a set of length variables corresponding to space- and timelike distances along geodesics in three-dimensional Minkowski space. These are Dirac observables, that is, functions on the reduced phase space, whose quantization is essentially unique. For both space- and timelike distance operators, the spectrum is continuous and not bounded away from zero.Comment: 29 pages, 18 figure

The Lagrange spectrum of a Veech surface has a Hall ray

We study Lagrange spectra of Veech translation surfaces, which are a generalization of the classical Lagrange spectrum. We show that any such Lagrange spectrum contains a Hall ray. As a main tool, we use the boundary expansion developed by Bowen and Series to code geodesics in the corresponding Teichm\"uller disk and prove a formula which allows to express large values in the Lagrange spectrum as sums of Cantor sets.Comment: 30 pages, 5 figures. Minor revisio