Massless Boundary Sine-Gordon Model Coupled to External Fields

TL;DR

This paper extends the massless boundary sine-Gordon model by incorporating external boundary-dependent fields, maintaining solvability and providing explicit expressions for boundary states and partition functions, with implications for D-branes and tachyon dynamics.

Contribution

It introduces a solvable generalization of the boundary sine-Gordon model with external fields and derives explicit all-order expressions for key physical quantities.

Findings

Derived a simplified boundary state expression.

Obtained the disc partition function in the presence of external fields.

Fixed the relation between bare and renormalized couplings.

Abstract

We investigate a generalization of the massless boundary sine-Gordon model with conformal invariance, which has been used to describe an array of D-branes (or rolling tachyon). We consider a similar action whose couplings are replaced with external fields depending on the boundary coordinate. Even in the presence of the external fields, this model is still solvable, though it does not maintain the whole conformal symmetry. We obtain, to all orders in perturbation theory in terms of the external fields, a simpler expression of the boundary state and the disc partition function. As a by-product, we fix the relation between the bare couplings and the renormalized couplings which has been appeared in papers on tachyon lump and rolling tachyon.