Critical Boundary Sine-Gordon Revisited

TL;DR

This paper revisits the boundary sine-Gordon model in 2D quantum field theory, providing explicit solutions, analyzing dualities, and exploring special boundary states with rational radii, advancing understanding of boundary states and dualities.

Contribution

It offers an explicit fermionic expression for boundary states in the sine-Gordon model and explores their duality properties and special rational radius boundary states.

Findings

Boundary states are sine-Gordon states across the SL(2,C) family.

Derived explicit fermionic boundary state expressions.

Identified a strong-weak coupling T-duality generalization.

Abstract

We revisit the exact solution of the two space-time dimensional quantum field theory of a free massless boson with a periodic boundary interaction and self-dual period. We analyze the model by using a mapping to free fermions with a boundary mass term originally suggested in ref.[22]. We find that the entire SL(2,C) family of boundary states of a single boson are boundary sine-Gordon states and we derive a simple explicit expression for the boundary state in fermion variables and as a function of sine-Gordon coupling constants. We use this expression to compute the partition function. We observe that the solution of the model has a strong-weak coupling generalization of T-duality. We then examine a class of recently discovered conformal boundary states for compact bosons with radii which are rational numbers times the self-dual radius. These have simple expression in fermion variables. We postulate sine-Gordon-like field theories with discrete gauge symmmetries for which they are the appropriate boundary states.