Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model

Córdova, Lucía; Negro, Stefano; Massolo, Fidel I. Schaposnik

doi:10.1007/jhep01(2022)035

Cited by 15 publications

(7 citation statements)

References 61 publications

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“…Let us make an additional remark on fermionization of the S-matrix (3.22). A similar change of the sign is often discussed in the literature in the discussion of the so-called "bosonic TBA" [83,84]. In this context, one starts with a standard S-matrix of integrable theories and flips its sign.…”

Section: Fermionization Of Integrable Field Theoriesmentioning

confidence: 75%

“…The resulting S-matrix satisfies S(0) = +1, indicating that particles with the same mode number are now allowed to coexist. This leads to a substantial change of the TBA equation (for instance log(1 + Y ) changes to − log(1 − Y )), and it typically leads to a Hagedorn-like instability at finite volume [83,84].…”

Section: Fermionization Of Integrable Field Theoriesmentioning

confidence: 99%

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Crosscap States in Integrable Field Theories and Spin Chains

Caetano,

Komatsu

2021

Preprint

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We study crosscap states in integrable field theories and spin chains in 1 + 1 dimensions. We derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. We then compute the crosscap entropy, i.e. the overlap for the ground state, in some examples. In the examples we analyzed, the result turns out to decrease monotonically along the renormalization group flow except in cases where the discrete symmetry is spontaneously broken in the infrared. We next introduce crosscap states in integrable spin chains, and obtain determinant expressions for the overlaps with energy eigenstates. These states are long-range entangled and their entanglement entropy grows linearly until the size of the subregion reaches half the system size. This property is reminiscent of pure-state black holes in holography and makes them interesting for use as initial conditions of quantum quench. As side results, we propose a generalization of Zamolodchikov's staircase model to flows between D-series minimal models, and discuss the relation to fermionic minimal models and the GSO projection.

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Section: Fermionization Of Integrable Field Theoriesmentioning

confidence: 75%

Section: Fermionization Of Integrable Field Theoriesmentioning

confidence: 99%

Crosscap States in Integrable Field Theories and Spin Chains

Caetano,

Komatsu

2021

Preprint

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“…where the irrelevant operators [T T ] s depend on the cft IR and are defined in [5], as reviewed in the next section. These generalized T T deformations have been considered recently in a somewhat different context [22][23][24][25]; the main distinction from our work is that here the focus is on massless flows between CFT's which was not studied in these works. The problem we pose and study is to classify the possible tuned α s that have UV completions, i.e.…”

Section: Jhep08(2022)179mentioning

confidence: 95%

On the classification of UV completions of integrable $$ T\overline{T} $$ deformations of CFT

Ahn

LeClair

2022

J. High Energ. Phys.

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It is well understood that 2d conformal field theory (CFT) deformed by an irrelevant $$ T\overline{T} $$ T T ¯ perturbation of dimension 4 has universal properties. In particular, for the most interesting cases, the theory develops a singularity in the ultra-violet (UV), signifying a shortest possible distance, with a Hagedorn transition in applications to string theory. We show that by adding an infinite number of higher [$$ T\overline{T} $$ T T ¯ ]s>1 irrelevant operators of positive integer scaling dimension 2(s+1) with tuned couplings, this singularity can be resolved and the theory becomes UV complete with a Virasoro central charge cUV> cIR consistent with the c-theorem. We propose an approach to classifying the possible UV completions of a given CFT perturbed by [$$ T\overline{T} $$ T T ¯ ]s that are integrable. The main tool utilized is the thermodynamic Bethe ansatz. We study this classification for theories with scalar (diagonal) factorizable S-matrices. For the Ising model with cIR = $$ \frac{1}{2} $$ 1 2 we find 3 UV completions based on a single massless Majorana fermion description with cUV =$$ \frac{7}{10} $$ 7 10 and $$ \frac{3}{2} $$ 3 2 , which both have $$ \mathcal{N} $$ N = 1 SUSY and were previously known, and we argue that these are the only solutions to our classification problem based on this spectrum of particles. We find 3 additional ones with a spectrum of 8 massless particles related to the Lie group E8 appropriate to a magnetic perturbation with cUV = $$ \frac{21}{22},\frac{15}{12} $$ 21 22 , 15 12 , and $$ \frac{31}{2} $$ 31 2 . We argue that it is likely there are more cases for this E8 spectrum. We also study simpler cases based on su(3) and su(4) where we can propose complete classifications. For su(3) the infrared (IR) theory is the 3-state Potts model with cIR = $$ \frac{4}{5} $$ 4 5 and we find 3 completions with $$ \frac{4}{5} $$ 4 5 < cUV≤$$ \frac{16}{5} $$ 16 5 . For the su(4) case, which has 3 particles and cIR = 1, and we find 11 UV completions with 1 < cUV ≤ 5, most of which were previously unknown.

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“…It was shown by Wadati [22] that changing both the statistics and the interaction, one can obtain a different description of the same integrable model. Since bosonic S-matrices are known to describe interesting physical phenomena [23,24], both TBA statistics will be discussed here.…”

Section: Interacting Massive Integrable Qftmentioning

confidence: 99%

Two-dimensional massive integrable models on a torus

Kostov

2022

J. High Energ. Phys.

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The finite-volume thermodynamics of a massive integrable QFT is described in terms of a grand canonical ensemble of loops immersed in a torus and interacting through scattering factors associated with their intersections. The path integral of the loops is evaluated explicitly after decoupling the pairwise interactions by a Hubbard-Stratonovich transformation. The HS fields are holomorphic fields depending on the rapidity and can be expanded in elementary oscillators. The torus partition function is expressed as certain expectation value in the Fock space of these oscillators. In the limit where one of the periods of the torus becomes asymptotically large, the effective field theory becomes mean field type. The mean field describes the infinite-volume thermodynamics which is solved by the Thermodynamical Bethe Ansatz.

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Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model

Cited by 15 publications

References 61 publications

Crosscap States in Integrable Field Theories and Spin Chains

Crosscap States in Integrable Field Theories and Spin Chains

On the classification of UV completions of integrable $$ T\overline{T} $$ deformations of CFT

Two-dimensional massive integrable models on a torus

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