Antonio E. Goncalves

Mass and decay spectra of the piecewise uniform string

Abstract Mass and decay spectra are calculated for quantum massive excitations of a piecewise uniform bosonic string. The physical meaning of the critical temperatures characterising the radiation in the decay of a massive microstate in string theory is discussed.

Chern–Simons invariants on hyperbolic manifolds and topological quantum field theories

We derive formulas for the classical Chern–Simons invariant of irreducible SU(n)-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern–Simons invariant. On the basis of the Labastida–Mariño–Ooguri–Vafa conjecture we analyze a representation of the Chern–Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities.

Asymptotics of Elliptic Genera of Symmetric Products and Dyonic Black Hole Degeneracy

Abstract We calculate asymptotic expansions of elliptic genera for a supersymmetric sigma model on the N− fold symmetric product SNM of a Kahler manifold M and for N=2 superconformal field theory. Asymptotic expansions for the degeneracy of dyonic black hole spectrum are also derived.

Brane-black hole correspondence and the asymptotic properties of the quantum spectrum

The asymptotic properties of the density of quantum states for a fundamental (super)membrane are discussed in the semiclassical approach. Matching of the BPS part of the spectrum for a superstring and a supermembrane makes it possible to get stringy results via membrane calculations and vice versa. The brane-black hole correspondence (on the level of black hole states and brane microstates) is also studied.

Spectral Functions for Gauge Fields in Rindler-Like Spaces

A class of conformal deformations of Rindler-like spaces is analyzed. We study the spectral properties of the Laplace operators associated with p−forms and acting in these spaces and in their spatial sections. The spectral density of continuum spectrum and the spectral zeta functions related to the abelian p−forms in real compact hyperbolic manifolds are obtained.

Semiclassical limit for Chern-Simons theory on compact hyperbolic spaces

The invariant integration method for Chern-Simons theory defined on compact hyperbolic spaces of the form Γℍ3 is verified in the semiclassical approximation. The semiclassical limit for the partition function is calculated. The contribution to the sum over topologies in three-dimensional quantum gravity is briefly discussed.

Vacuum energy for the supersymmetric twisted D-brane in a constant electromagnetic field

We calculate the vacuum energy for the twisted SUSY D-brane on a toroidal background with constant magnetic or constant electric field. A numerical study of its behaviour for a toroidal D-brane (p = 2) in a constant electric field shows the presence of a stable minimum for untwisted or twisted versions of the theory. This indicates that such a background may be a reasonable ground state.