Exact quasinormal modes for a special class of black holes

Analytic exact expressions for the quasinormal modes of scalar and electromagnetic perturbations around a special class of black holes are found in d\ge3 dimensions. It is shown that, the size of the black hole provides a bound for the angular momentum of the perturbation. Quasinormal modes appear when this bound is fulfilled, otherwise the excitations become purely damped.Comment: 8 pages, no figures. Slightly updated version of the plenary talk given at the General Relativity Conference: "50 Years of FaMAF and Workshop on Global Problems in Relativity", hosted during November 2006 at FaMAF, Universidad Nacional de Cordoba, Cordoba, Argentina

Colour analysis of degraded parchment

Multispectral imaging was employed to collect data on the degradation of an 18th century parchment by a series of physical and chemical treatments. Each sample was photographed before and after treatment by a monochrome digital camera with 21 narrow-band filters. A template-matching technique was used to detect the circular holes in each sample and a four-point projective transform to register the 21 images. Colour accuracy was verified by comparison of reconstructed spectra with measurements by spectrophotometer

The D^4 R^4 term in type IIB string theory on T^2 and U-duality

We propose a manifestly U-duality invariant modular form for the D^4 R^4 interaction in type IIB string theory compactified on T^2. It receives perturbative contributions upto two loops, and non-perturbative contributions from D-instantons and (p,q) string instantons wrapping T^2. We provide evidence for this modular form by showing that the coefficients at tree level and at one loop precisely match those obtained using string perturbation theory. Using duality, parts of the perturbative amplitude are also shown to match exactly the results obtained from eleven dimensional supergravity compactified on T^3 at one loop. Decompactifying the theory to nine dimensions, we obtain a U-duality invariant modular form, whose coefficients at tree level and at one loop agree with string perturbation theory.Comment: 25 pages, LaTe

Domain wall partition functions and KP

We observe that the partition function of the six vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP tau function and express it as an expectation value of charged free fermions (up to an overall normalization).Comment: 16 pages, LaTeX2

Regular quantum graphs

We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way incoming and outgoing channels at vertex scattering processes are connected. Symmetry properties of the quantum graph as well as its spectral statistics depend on the particular choice of permutation matrices, also called connectivity matrices, and can now be easily controlled. The method may find applications in the study of quantum random walks networks and may also prove to be useful in analysing universality in spectral statistics.Comment: 12 pages, 3 figure

Q-instantons

We construct the half-supersymmetric instanton solutions that are electric-magnetically dual to the recently discussed half-supersymmetric Q7-branes. We call these instantons `Q-instantons'. Whereas the D-instanton is most conveniently described using the RR axion \chi and the dilaton \phi, the Q-instanton is most conveniently described using a different set of fields \chi' and T, where \chi' is an axionic scalar. The real part of the Q-instanton on-shell action is a function of T and the imaginary part is linear in \chi'. Discrete shifts of the axion \chi' correspond to PSL(2,Z) transformations that are of finite order. These are e.g. pure S-duality transformations relating weak and strongly coupled regimes. We argue that near each orbifold point of the quantum axion-dilaton moduli space PSL(2,Z)\PSL(2,R)/SO(2) the higher order R^4 terms in the string effective action contain contributions from an infinite sum of single multiply-charged instantons with the Q-instantons corresponding to the orbifold points \tau=i,\rho where \tau is the complex axion-dilaton field.Comment: 29 pages, 1 figur

Large distance asymptotic behavior of the emptiness formation probability of the XXZ spin-1/2 Heisenberg chain

Using its multiple integral representation, we compute the large distance asymptotic behavior of the emptiness formation probability of the XXZ spin-1/2 Heisenberg chain in the massless regime.Comment: LPENSL-TH-10, 8 page

Automorphic properties of low energy string amplitudes in various dimensions

This paper explores the moduli-dependent coefficients of higher derivative interactions that appear in the low-energy expansion of the four-graviton amplitude of maximally supersymmetric string theory compactified on a d-torus. These automorphic functions are determined for terms up to order D^6R^4 and various values of d by imposing a variety of consistency conditions. They satisfy Laplace eigenvalue equations with or without source terms, whose solutions are given in terms of Eisenstein series, or more general automorphic functions, for certain parabolic subgroups of the relevant U-duality groups. The ultraviolet divergences of the corresponding supergravity field theory limits are encoded in various logarithms, although the string theory expressions are finite. This analysis includes intriguing representations of SL(d) and SO(d,d) Eisenstein series in terms of toroidally compactified one and two-loop string and supergravity amplitudes.Comment: 80 pages. 1 figure. v2:Typos corrected, footnotes amended and small clarifications. v3: minor corrections. Version to appear in Phys Rev

On correlation functions of integrable models associated to the six-vertex R-matrix

We derive an analog of the master equation obtained recently for correlation functions of the XXZ chain for a wide class of quantum integrable systems described by the R-matrix of the six-vertex model, including in particular continuum models. This generalized master equation allows us to obtain multiple integral representations for the correlation functions of these models. We apply this method to derive the density-density correlation functions of the quantum non-linear Schrodinger model.Comment: 21 page