Massless Thirring model in curved space: Thermal states and conformal anomaly

Abstract

The massless Thirring model of a self-interacting fermion field in a curved two-dimensional background spacetime is considered. The exact operator solution for the fields and the equation for the two-point function are given and used to examine the radiation emitted by a two-dimensional black hole. The radiation is found to be thermal in nature, confirming general predictions to this effect. We compute the particle spectrum of the Thirring fermions at finite temperature in Minkowski space and point out errors in a previous attempt at this calculation. Finally we calculate the vacuum expectation value of the stress tensor in an arbitrary two-dimensional spacetime by exploiting the connection between the thermal Hawking radiation from a black hole and the value of the so-called conformal trace anomaly. The latter is also computed quite independently, using dimensional regularization, from general considerations of the renormalization group. We find the stress tensor to be identical to the free-fermion case. Some discussion of the significance of this work for the second law of thermodynamics and black-hole entropy is given.