Abstract
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.
Highlights
IR interesting continuation from its self-dual point to certain complex values of the coupling
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
In the present work we have shown how Zamolodchikov’s roaming flows can be analysed via the c-theorem, representing the c-function as a form factor spectral sum
Summary
The sinh-Gordon model is a theory of a single scalar field Φ, with a classical action depending on a mass scale M and coupling b: A=. The heights of these plateaux are the central charges of the unitary c < 1 minimal models, as illustrated in figure 4 These plots imply precisely the RG flows sketched in figure 1 above, with the increasing length of RG time spent on each plateau indicating that the corresponding RG trajectories get nearer and nearer to the RG fixed points as θ0 increases. To understand how this pattern emerges from the TBA equation (2.4), consider the form of the ‘kernel function’ φ(θ), which in terms of the parameter θ0 is φ(θ) =. The details are a little more intricate, but the basic idea of relocalisation of integrals, coupled with a form of double-scaling limit involving r and θ0 to expose the individual steps, is the same
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