Sine-Gordon theory with higher-spin N = 2 supersymmetry and the massless limit

Abstract

The sine-Gordon theory at β 2 8π = 2 (2n + 3) , n = 1, 2, 3, … , has a higher-spin generalization of the N = 2 supersymmetry with the central terms arising from the affine quantum group U q( sl (2)) . We observe that the algebraic determination of S-matrices (≈ quantum integrability) requires the saturation of the generalized Bogomolny bound. The S-matrix theory considered is a variant of the sine-Gordon theory at this value of the coupling whose spectrum consists of a doublet of fractionally charged solitons as well as that of anti-solitons in addition to the ordinary breathers. This is in contrast to the theory considered by Smirnov which is obtained by the truncation to the breathers. The allowed values for the fractional part of the fermion number are also determined. The central charge in the massless limit is found to be c = 1 from the TBA calculation for nondiagonal S-matrices. The attendant c = 1 conformal field theory is the gaussian model with Z 2 graded chiral algebra at the radius parameter r = 2n + 3 . In the course of the calculation, we find 4 n + 2 zero modes from the (anti-)soliton distributions.