Built on

A. Giveon, “Comments on T T ¯ T\bar{T} , J T ¯ J\bar{T} and String Theory,” arXiv:1903.06883 [hep-th]
Original
1903
Earlier work this paper cites.
B. Le Floch and M. Mezei, “Solving a family of T T ¯ T\bar{T} -like theories,” arXiv:1903.07606 [hep-th]
Original
1903
Earlier work this paper cites.
Y. Jiang, “Lectures on solvable irrelevant deformations of 2d quantum field theory,” arXiv:1904.13376 [hep-th]
Original
1904
Earlier work this paper cites.
B. Le Floch and M. Mezei, “KdV charges in T T ¯ T\bar{T} theories and new models with super-Hagedorn behavior,” SciPost Phys
Original
1907
Earlier work this paper cites.
M. Borsi, B. Pozsgay, and L. Pristyák, “Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence,” arXiv e-prints
Original
1908
Earlier work this paper cites.
B. Pozsgay, “Current operators in integrable spin chains: lessons from long range deformations,” arXiv e-prints
Original
1910
Earlier work this paper cites.
A. J. Tolley, “ T T ¯ T\bar{T} Deformations, Massive Gravity and Non-Critical Strings,” arXiv:1911.06142 [hep-th]
Original
1911
Earlier work this paper cites.
T. Anous and M. Guica, “A general definition of J T a JT_{a} – deformed QFTs,” arXiv:1911.02031 [hep-th]
Original
1911
Earlier work this paper cites.
M. G. Tetelman Sovj. Phys. JETP
1981
Earlier work this paper cites.
K. Sogo and M. Wadati, “Boost Operator and Its Application to Quantum Gelfand-Levitan Equation for Heisenberg-Ising Chain with Spin One-Half,” Progress of Theoretical Physics
1983
Earlier work this paper cites.
H. B. Thacker, “Corner transfer matrices and Lorentz invariance on a lattice,” Physica D Nonlinear Phenomena
1986
Earlier work this paper cites.
Al. B. Zamolodchikov, “From tricritical Ising to critical Ising by thermodynamic Bethe ansatz,” Nucl. Phys
1991
Earlier work this paper cites.
Cambridge University Press, 1993
V. Korepin, N. Bogoliubov, and A. Izergin, Quantum inverse scattering method and correlation functions · 1993
Earlier work this paper cites.
M. Grabowski and P. Mathieu, “Structure of the conservation laws in integrable spin chains with short range interactions,” Annals Phys
1995
Earlier work this paper cites.
G. Mussardo and P. Simon, “Bosonic-type S-matrix, vacuum instability and CDD ambiguities,” Nuclear Physics B
2000
Earlier work this paper cites.

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Springer Netherlands, Dordrecht, 2006
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A. Rej, D. Serban, and M. Staudacher, “Planar N=4 gauge theory and the Hubbard model,” JHEP
2006
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J. Damerau, F. Göhmann, N. P. Hasenclever, and A. Klümper, “Density matrices for finite segments of Heisenberg chains of arbitrary length,” Journal of Physics A Mathematical General
2007
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T. Bargheer, N. Beisert, and F. Loebbert, “LETTER: Boosting nearest-neighbour to long-range integrable spin chains,” Journal of Statistical Mechanics: Theory and Experiment
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Then

E. Ilievski, M. Medenjak, and T. Prosen, “Quasilocal Conserved Operators in the Isotropic Heisenberg Spin-1 /2 Chain,” Physical Review Letters
Original
2015
Later among the works it cites.
A. Cavaglià, S. Negro, I. M. Szécsényi, and R. Tateo, “ T T ¯ T\bar{T} -deformed 2D Quantum Field Theories,” JHEP
Original
2016
Later among the works it cites.
O. A. Castro-Alvaredo, B. Doyon, and T. Yoshimura, “Emergent Hydrodynamics in Integrable Quantum Systems Out of Equilibrium,” Physical Review X
Original
2016
Later among the works it cites.
B. Bertini, M. Collura, J. De Nardis, and M. Fagotti, “Transport in Out-of-Equilibrium X X Z Chains: Exact Profiles of Charges and Currents,” Physical Review Letters
Original
2016
Later among the works it cites.
E. Ilievski, M. Medenjak, T. Prosen, and L. Zadnik, “Quasilocal charges in integrable lattice systems,” Journal of Statistical Mechanics: Theory and Experiment

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2019

$T\bar T$-deformation and long range spin chains

Pozsgay, Balázs, Jiang, Yunfeng, Takács, Gábor

Understand

We point out that two classes of deformations of integrable models, developed completely independently, have deep connections and share the same algebraic origin.

One class includes the $T\bar T$-deformation of 1+1 dimensional integrable quantum field theory and related solvable irrelevant deformations proposed recently.
The other class is a specific type of long range integrable deformation of quantum spin chains introduced a decade ago, in the context of $\mathcal{N} = 4$ super-Yang-Mills theory.
We show that the detailed structures of the two deformations are formally identical and therefore share many features.

Built on

A. Giveon, “Comments on T T ¯ T\bar{T} , J T ¯ J\bar{T} and String Theory,” arXiv:1903.06883 [hep-th]
Original
1903
Earlier work this paper cites.
B. Le Floch and M. Mezei, “Solving a family of T T ¯ T\bar{T} -like theories,” arXiv:1903.07606 [hep-th]
Original
1903
Earlier work this paper cites.
Y. Jiang, “Lectures on solvable irrelevant deformations of 2d quantum field theory,” arXiv:1904.13376 [hep-th]
Original
1904
Earlier work this paper cites.
B. Le Floch and M. Mezei, “KdV charges in T T ¯ T\bar{T} theories and new models with super-Hagedorn behavior,” SciPost Phys
Original
1907
Earlier work this paper cites.
M. Borsi, B. Pozsgay, and L. Pristyák, “Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence,” arXiv e-prints
Original
1908
Earlier work this paper cites.
B. Pozsgay, “Current operators in integrable spin chains: lessons from long range deformations,” arXiv e-prints
Original
1910
Earlier work this paper cites.
A. J. Tolley, “ T T ¯ T\bar{T} Deformations, Massive Gravity and Non-Critical Strings,” arXiv:1911.06142 [hep-th]
Original
1911
Earlier work this paper cites.
T. Anous and M. Guica, “A general definition of J T a JT_{a} – deformed QFTs,” arXiv:1911.02031 [hep-th]
Original
1911
Earlier work this paper cites.
M. G. Tetelman Sovj. Phys. JETP
1981
Earlier work this paper cites.
K. Sogo and M. Wadati, “Boost Operator and Its Application to Quantum Gelfand-Levitan Equation for Heisenberg-Ising Chain with Spin One-Half,” Progress of Theoretical Physics
1983
Earlier work this paper cites.
H. B. Thacker, “Corner transfer matrices and Lorentz invariance on a lattice,” Physica D Nonlinear Phenomena
1986
Earlier work this paper cites.
Al. B. Zamolodchikov, “From tricritical Ising to critical Ising by thermodynamic Bethe ansatz,” Nucl. Phys
1991
Earlier work this paper cites.
Cambridge University Press, 1993
V. Korepin, N. Bogoliubov, and A. Izergin, Quantum inverse scattering method and correlation functions · 1993
Earlier work this paper cites.
M. Grabowski and P. Mathieu, “Structure of the conservation laws in integrable spin chains with short range interactions,” Annals Phys
1995
Earlier work this paper cites.
G. Mussardo and P. Simon, “Bosonic-type S-matrix, vacuum instability and CDD ambiguities,” Nuclear Physics B
2000
Earlier work this paper cites.

Similar

Springer Netherlands, Dordrecht, 2006
A. Pogrebkov, “Hierarchy Of Quantum Explicitly Solvable And Integrable Models,” in Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete · 2006
Cited alongside, same era.
H. Boos, M. Jimbo, T. Miwa, F. Smirnov, and Y. Takeyama, “Algebraic Representation of Correlation Functions in Integrable Spin Chains,” Annales Henri Poincaré
2006
Cited alongside, same era.
A. Rej, D. Serban, and M. Staudacher, “Planar N=4 gauge theory and the Hubbard model,” JHEP
2006
Cited alongside, same era.
J. Damerau, F. Göhmann, N. P. Hasenclever, and A. Klümper, “Density matrices for finite segments of Heisenberg chains of arbitrary length,” Journal of Physics A Mathematical General
2007
Cited alongside, same era.
T. Bargheer, N. Beisert, and F. Loebbert, “LETTER: Boosting nearest-neighbour to long-range integrable spin chains,” Journal of Statistical Mechanics: Theory and Experiment
Original