The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations

Abstract

We introduce an extension of the generalised $T\bar{T}$-deformation described by Smirnov-Zamolodchikov, to include the complete set of extensive charges. We show that this gives deformations of S-matrices beyond CDD factors, generating arbitrary functional dependence on momenta. We further derive from basic principles of statistical mechanics the flow equations for the free energy and all free energy fluxes. From this follows, without invoking the microscopic Bethe ansatz or other methods from integrability, that the thermodynamics of the deformed models are described by the integral equations of the thermodynamic Bethe-Ansatz, and that the exact average currents take the form expected from generalised hydrodynamics, both in the classical and quantum realms.

arXiv commentv1:6+10 pages. v2: 23 pages, references added. v3: 23 pages, minor corrections. v4: minor clarifications. v5: 29 pages, rearrangement of sections and appendices made, clarifications on quasi-local charges and the properties of the S-matrix of deformed theories added

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Cited by in corpus (10)

• Weak integrability breaking perturbations of integrable models
• Gravity and $T\bar{T}$ flows in higher dimensions
• New classical integrable systems from generalized $T\bar{T}$-deformations
• Adiabatic gauge potential and integrability breaking with free fermions
• Hamiltonian formulation and aspects of integrability of generalised hydrodynamics
• Duality defect in a deformed transverse-field Ising model
• Simulating generalised fluids via interacting wave packets evolution
• Locality and Conserved Charges in $T\overline{T}$-Deformed CFTs
• Quasiconservation Laws and Suppressed Transport in Weakly Interacting Localized Models
• Complete Minimal Form Factors for Irrelevant Deformations of Integrable Quantum Field Theory