Induced Dilaton in Topologically Massive Quantum Field Theory

TL;DR

This paper explores how a topologically massive gravity theory coupled with scalar and gauge fields in three dimensions induces a dynamical dilaton field on the boundary, linking duality symmetries and string coupling.

Contribution

It demonstrates the emergence of the boundary dilaton from bulk topologically massive gravity and its transformation properties under dualities, revealing a dynamic link between bulk and boundary string theories.

Findings

Induces boundary dilaton from bulk topologically massive gravity.

Shows dilaton transforms correctly under duality, preserving mass gaps.

Establishes a connection between T-duality, S-duality, and dynamical string coupling.

Abstract

We consider the conformally-invariant coupling of topologically massive gravity to a dynamical massless scalar field theory on a three-manifold with boundary. We show that, in the phase of spontaneously broken Lorentz and Weyl symmetries, this theory induces the target space zero mode of the vertex operator for the string dilaton field on the boundary of the three-dimensional manifold. By a further coupling to topologically massive gauge fields in the bulk, we demonstrate directly from the three-dimensional theory that this dilaton field transforms in the expected way under duality transformations so as to preserve the mass gaps in the spectra of the gauge and gravitational sectors of the quantum field theory. We show that this implies an intimate dynamical relationship between T-duality and S-duality transformations of the quantum string theory. The dilaton in this model couples bulk and worldsheet degrees of freedom to each other and generates a dynamical string coupling.