Excited state Destri-De Vega equation for sine-Gordon and restricted sine-Gordon models

Abstract

We derive a generalization of the Destri -De Vega equation governing the scaling functions of some excited states in the Sine-Gordon theory. In particular configurations with an even number of holes and no strings are analyzed and their UV limits found to match some of the conformal dimensions of the corresponding compactified massless free boson. Quantum group reduction allows to interpret some of our results as scaling functions of excited states of Restricted Sine-Gordon theory, i.e. minimal models perturbed by φ 13 in their massive regime. In particular we are able to reconstruct the scaling functions of the off-critical deformations of all the scalar primary states on the diagonal of the Kac-table.

A next-to-leading Lüscher formula

“…In both cases, we obtained exact agreement between our NLO Lüscher-like formulas and the expansions of the well known NLIEs [41][42][43][44], at least for excitations belonging to the U(1) sectors, in the same way as for the Gross-Neveu model. In the sine-Gordon case we needed to use a generalized version of the identities (4.9):…”

New families of flows between two-dimensional conformal field theories

“…Setting ζ = β 2 /(8π−β 2 ), it can be shown that for ζ = p/(q−p) and α = 1/p, the ground-state energy of the φ 13 perturbation of a general minimal model M p,q is also matched [23,24,[27][28][29]. (Note that this definition of ζ is thus in line with the one given in the introduction.)…”

“…The previously-studied sequence (1.1), (1.2) is picked out by the monotonicity of the function c eff as a function of r. In all other cases, somewhat to our surprise, we found that the effective central charge undergoes a number of oscillations as it interpolates between its short and long distance limits. Our approach differs from the TBA method, and is much closer to that of the papers [20][21][22][23][24][25][26], in that a single nonlinear integral equation (NLIE) is proposed to describe infinitely-many different perturbed conformal field theories, each being picked out by an appropriate choice of certain parameters. For massless flows, the one previous example of such an equation was found by Al.…”

Solving the AdS/CFT Y-system

“…Apart from some exceptional cases (Lee-Yang model, SS-model, Wess-Zumino cosets) both the TBA system and the Y-system are infinite. However, Destri and de Vega noticed [2] that the infinite TBA system for the vacuum of the Sine-Gordon model can be reduced to only one non-linear integral equation, and this was later generalized to excited states [3]. For the models with higher rank groups of symmetries a similar reduction to a few integral equations is usually possible.…”