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arXiv · hep-th/0512219

Critical Boundary Sine-Gordon Revisited

M. Hasselfield·Taejin Lee·G. W. Semenoff·P. C. E. Stamp
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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.

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M. Hasselfield, Taejin Lee, G. W. Semenoff, P. C. E. Stamp. 2006-01-15. Critical Boundary Sine-Gordon Revisited. https://doi.org/10.1016/j.aop.2006.02.006

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