Abstract
We analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in the context of generalized T overline{mathrm{T}} deformations. We focus on the sinh-Gordon model and its elliptic deformation in both its fermionic and bosonic realizations. We confirm that the determining factor for a turning point in the TBA, interpreted as a finite Hagedorn temperature, is the difference between the number of bound states and resonances in the theory. Implementing the numerical pseudo-arclength continuation method, we are able to follow the solutions to the TBA equations past the turning point all the way to the ultraviolet regime. We find that for any number k of resonances the pair of complex conjugate solutions below the turning point is such that the effective central charge is minimized. As k → ∞ the UV effective central charge goes to zero as in the elliptic sinh-Gordon model. Finally we uncover a new family of UV complete integrable theories defined by the bosonic counterparts of the S-matrices describing the Φ1,3 integrable deformation of non-unitary minimal models mathcal{M} 2,2n+3.
Highlights
Accumulation of UV divergences which necessarily require an infinite number of counterterms, destroying the predictive power of the theory
We focus on the sinh-Gordon model and its elliptic deformation in both its fermionic and bosonic realizations
Amongst the vast set of irrelevant deformations triggered by the operators TT (s,s ), a sub-family of Lorentz-breaking ones obtained by fixing s = 1 was introduced and studied in [26], while [27] and [28] initiated the analysis of integrable QFTs deformed by linear combinations of the operators TT (s) ≡ TT (s,s)
Summary
The main model of interest in the present work is an elliptic deformation of the sinh-Gordon model. The upper (lower) sign in (2.1) corresponds to the fermionic (bosonic) case This S-matrix has two periods, the usual one along the imaginary direction arising from crossing symmetry and unitarity S(θ) = S(θ + 2iπ) and an unusual one in the real direction S(θ) = S(θ + Tl). In order to ensure we have only zeros inside the physical strip — and, that the model possesses no bound-state — we need to limit the coupling constant a to take values in the interval [0, 1]. We will describe the different algorithms that can be used to numerically solve the TBA equation (2.5) These methods, the pseudoarclength continuation, were implemented to extract the results that will be presented in section 4 and section 5
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