UV and IR analyses of the mass spectrum in the sine-Gordon model

We study the mass spectrum of the sine-Gordon model on a cylinder in the UV and IR regime. This is done by numerical diagonalization of the XXZ spin chain in a transverse field which is a convenient regularization. Our results strongly confirm the conjecture of Klassen and Melzer that sine-Gordon and massive Thirring models are not equivalent when defined on a finite cylinder. We obtain that the first two breathers have equal scaling dimensions, contrary to the conjecture claimed in literature