Form factor relocalisation and interpolating renormalisation group flows from the staircase model

We investigate the staircase model, introduced by Aliosha Zamolodchikov through an analytic continuation of the sinh-Gordon S-matrix to describe interpolating flows between minimal models of conformal field theory in two dimensions. Applying the form factor expansion and the c-theorem, we show that the resulting c-function has the same physical content as that found by Zamolodchikov from the thermodynamic Bethe Ansatz. This turns out to be a consequence of a nontrivial underlying mechanism, which leads to an interesting localisation pattern for the spectral integrals giving the multi-particle contributions. We demonstrate several aspects of this form factor relocalisation, which suggests a novel approach to the construction of form factors and spectral sums in integrable renormalisation group flows with non-diagonal scattering.We investigate the staircase model, introduced by Aliosha Zamolodchikov through an analytic continuation of the sinh-Gordon S-matrix to describe interpolating flows between minimal models of conformal field theory in two dimensions. Applying the form factor expansion and the c-theorem, we show that the resulting c-function has the same physical content as that found by Zamolodchikov from the thermodynamic Bethe Ansatz. This turns out to be a consequence of a nontrivial underlying mechanism, which leads to an interesting localisation pattern for the spectral integrals giving the multi-particle contributions. We demonstrate several aspects of this form factor relocalisation, which suggests a novel approach to the construction of form factors and spectral sums in integrable renormalisation group flows with non-diagonal scattering.

Jan 1, 20156 citations

Patrick Dorey, Guy Siviour, Gábor Takács

arXiv:1412.8442Journal of High Energy PhysicsMar 1, 20156 citations

Integrable Boundary Flows and the g-function

Ruth Margaret Wilbourne

This thesis explores renormalisation group flows in integrable quantum field theories with boundaries, as described by the g-function. The main focus is on the g-function in the staircase model, the renormalisation group flow of which passes close to the unitary minimal models. This g-function is used to identify flows between boundary conditions both within and between the minimal models. In certain limits the $\\mathcal{M}A_m^{(+)}$ theories which interpolate between pairs of minimal models emerge from the staircase model, and exact expressions for the g-function in these models are extracted from the staircase g-function. Perturbative tests on the $\\mathcal{M}A_4^{(+)}$ g-function are discussed, as is initial work on the g-function for the $\\mathcal{M}A_4^{(-)}$ theory, which describes flows that emerge when the bulk coupling is taken to have the opposite sign to that in $\\mathcal{M}A_4^{(+)}$ . Expressions are also found for excited state versions of the $\\mathcal{M}A_m^{(+)}$ g-function, and these allow the unique identification of certain boundary flows.This thesis explores renormalisation group flows in integrable quantum field theories with boundaries, as described by the g-function. The main focus is on the g-function in the staircase model, the renormalisation group flow of which passes close to the unitary minimal models. This g-function is used to identify flows between boundary conditions both within and between the minimal models. In certain limits the $\\mathcal{M}A_m^{(+)}$ theories which interpolate between pairs of minimal models emerge from the staircase model, and exact expressions for the g-function in these models are extracted from the staircase g-function. Perturbative tests on the $\\mathcal{M}A_4^{(+)}$ g-function are discussed, as is initial work on the g-function for the $\\mathcal{M}A_4^{(-)}$ theory, which describes flows that emerge when the bulk coupling is taken to have the opposite sign to that in $\\mathcal{M}A_4^{(+)}$. Expressions are also found for excited state versions of the $\\mathcal{M}A_m^{(+)}$ g-function, and these allow the unique identification of certain boundary flows.

Jan 1, 20120 citations

\\mathcal{M}A_m^{(+)}

theories which interpolate between pairs of minimal models emerge from the staircase model, and exact expressions for the g-function in these models are extracted from the staircase g-function. Perturbative tests on the

\\mathcal{M}A_4^{(+)}

g-function are discussed, as is initial work on the g-function for the

\\mathcal{M}A_4^{(-)}

theory, which describes flows that emerge when the bulk coupling is taken to have the opposite sign to that in

\\mathcal{M}A_4^{(+)}

. Expressions are also found for excited state versions of the

\\mathcal{M}A_m^{(+)}

g-function, and these allow the unique identification of certain boundary flows.