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arXiv:hep-th/9410117 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Correlation functions along a massless flow

Gesualdo Delfino A, Giuseppe Mussardo, P. Simonetti

Published Jun 15, 1995• 66 citations
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Abstract

A nonperturbative method based on the form factor bootstrap approach is proposed for the analysis of correlation functions of two-dimensional massless integrable theories and applied to the massless flow between the tricritical Ising and the critical Ising models.
DOI
10.1103/physrevd.51.r6620

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A bstract For QFTs in AdS the boundary correlation functions remain conformal even if the bulk theory has a scale. This allows one to constrain RG flows with numerical conformal bootstrap methods. We apply this idea to flows between two-dimensional CFTs, focusing on deformations of the tricritical and ordinary Ising model. We provide non-perturbative constraints for the boundary correlation functions of these flows and compare them with conformal perturbation theory in the vicinity of the fixed points. We also reproduce a completely general constraint on the sign of the TT‾T\overline{T }TT deformation in two dimensions.
For QFTs in AdS the boundary correlation functions remain conformal even if the bulk theory has a scale. This allows one to constrain RG flows with numerical conformal bootstrap methods. We apply this idea to flows between two-dimensional CFTs, focusing on deformations of the tricritical and ordinary Ising model. We provide non-perturbative constraints for the boundary correlation functions of these flows and compare them with conformal perturbation theory in the vicinity of the fixed points. We also reproduce a completely general constraint on the sign of the TTˉT\bar TTTˉ deformation in two dimensions.
We derive a systematic construction for form factors of relevant fields in the thermal perturbation of the tricritical Ising model, an integrable model with scattering amplitudes described by the E7{E}_{7}E7​ bootstrap. We find a new type of recursive structure encoding the information in the bound state fusion structure, which fully determines the form factors of the perturbing field and the order/disorder fields, for which we present a mathematical proof. Knowledge of these form factors enables the systematic computation of correlation functions and dynamical structure factors in systems whose dynamics is governed by the vicinity of a fixed point in the tricritical Ising universality class.
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