Massless Boundary Sine-Gordon Model Coupled to External Fields

We investigate a generalization of the massless boundary sine-Gordon modelwith conformal invariance, which has been used to describe an array of D-branes(or rolling tachyon). We consider a similar action whose couplings are replacedwith external fields depending on the boundary coordinate. Even in the presenceof the external fields, this model is still solvable, though it does notmaintain the whole conformal symmetry. We obtain, to all orders in perturbationtheory in terms of the external fields, a simpler expression of the boundarystate and the disc partition function. As a by-product, we fix the relationbetween the bare couplings and the renormalized couplings which has beenappeared in papers on tachyon lump and rolling tachyon.Comment: 11pages, LaTe