On Factorizable S-matrices, Generalized TTbar, and the Hagedorn Transition
| Autor: | Alexander Zamolodchikov, Thiago Fleury, Stefano Negro, Giancarlo Camilo, Máté Lencsés |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
High Energy Physics - Theory Nuclear and High Energy Physics Integrable system Statistical Mechanics (cond-mat.stat-mech) Nonlinear Sciences - Exactly Solvable and Integrable Systems FOS: Physical sciences QC770-798 Mathematical Physics (math-ph) Renormalization group String (physics) Bethe ansatz Singularity High Energy Physics - Theory (hep-th) Nuclear and particle physics. Atomic energy. Radioactivity Renormalization Group Integrable Field Theories Limit (mathematics) Exactly Solvable and Integrable Systems (nlin.SI) Ultraviolet fixed point Condensed Matter - Statistical Mechanics Mathematical Physics Mathematical physics Boson |
| Zdroj: | Journal of High Energy Physics Journal of High Energy Physics, Vol 2021, Iss 10, Pp 1-37 (2021) |
| Popis: | 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. 42 pages, 10 figures; minor corrections and references added |
| Databáze: | OpenAIRE |
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