Equações de campo efetivas para cordas bosônicas com simetria de Weyl

Abstract

In this work we analyze the quantization of a closed bosonic string theory by means of the Feynnman path integral. We study the dynamics of a string under the action of three different fields: a Lorentzian metric, a 2-form and a scalar field. The action of the string has invariance under the Weyl group in the smooth module of world-sheet metrics, and the preservation of such symmetry is equivalently associated to the nullity of the trace of the energy-momentum tensor in the world-sheet. When we quantize the theory, this trace, which comes from the effective action at the 1-loop level, is non-trivial and depends on the beta functions of the theory’s renormalization group. We show that the Weyl invariance of the theory is preserved if the background fields satisfy a system of field equations, one of which is a modified form of the Einstein field equations.