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A bstract We analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in the context of generalized T $$ \overline{\mathrm{T}} $$ 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 Φ 1 , 3 integrable deformation of non-unitary minimal models $$ \mathcal{M} $$ M 2 , 2 n +3 .
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On factorizable S-matrices, generalized TTbar, and the Hagedorn transition
A bstract We study solutions of the Thermodynamic Bethe Ansatz equations for relativistic theories defined by the factorizable S -matrix of an integrable QFT deformed by CDD factors. Such S -matrices appear under generalized TTbar deformations of integrable QFT by special irrelevant operators. The TBA equations, of course, determine the ground state energy E ( R ) of the finite-size system, with the spatial coordinate compactified on a circle of circumference R . We limit attention to theories involving just one kind of stable particles, and consider deformations of the trivial (free fermion or boson) S -matrix by CDD factors with two elementary poles and regular high energy asymptotics — the “2CDD model”. We find that for all values of the parameters (positions of the CDD poles) the TBA equations exhibit two real solutions at R greater than a certain parameter-dependent value R * , which we refer to as the primary and secondary branches. The primary branch is identified with the standard iterative solution, while the secondary one is unstable against iterations and needs to be accessed through an alternative numerical method known as pseudo-arc-length continuation. The two branches merge at the “turning point” R * (a square-root branching point). The singularity signals a Hagedorn behavior of the density of high energy states of the deformed theories, a feature incompatible with the Wilsonian notion of a local QFT originating from a UV fixed point, but typical for string theories. This behavior of E ( R ) is qualitatively the same as the one for standard TTbar deformations of local QFT.
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- PAR ID:
- 10371692
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2021
- Issue:
- 10
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP10(2021)062
