Abstract We study solvable deformations of two-dimensional quantum field theories driven by a bilinear operator constructed from a pair of conserved U(1) currents Ja. We propose a quantum formulation of these deformations, based on the gauging of the corresponding symmetries in a path integral. This formalism leads to an exact dressing of the S-matrix of the system, similarly as what happens in the case of a $\textrm{T}\overline{\textrm{T}}$ T T ¯ deformation. For conformal theories the deformations under study are expected to be exactly marginal. Still, a peculiar situation might arise when the conserved currents Ja are not well-defined local operators in the original theory. A simple example of this kind of system is provided by rotation currents in a theory of multiple free, massless, non-compact bosons. We verify that, somewhat unexpectedly, such a theory is indeed still conformal after deformation and that it coincides with a TsT transformation of the original system. We then extend our formalism to the case in which the conserved currents are non-Abelian and point out its connection with Deformed T-dual Models and homogeneous Yang-Baxter deformations. In this case as well the deformation is based on a gauging of the symmetries involved and it turns out to be non-trivial only if the symmetry group admits a non-trivial central extension. Finally we apply what we learned by relating the $\textrm{T}\overline{\textrm{T}}$ T T ¯ deformation to the central extension of the two-dimensional Poincaré algebra.Abstract We study solvable deformations of two-dimensional quantum field theories driven by a bilinear operator constructed from a pair of conserved U(1) currents Ja. We propose a quantum formulation of these deformations, based on the gauging of the corresponding symmetries in a path integral. This formalism leads to an exact dressing of the S-matrix of the system, similarly as what happens in the case of a $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ deformation. For conformal theories the deformations under study are expected to be exactly marginal. Still, a peculiar situation might arise when the conserved currents Ja are not well-defined local operators in the original theory. A simple example of this kind of system is provided by rotation currents in a theory of multiple free, massless, non-compact bosons. We verify that, somewhat unexpectedly, such a theory is indeed still conformal after deformation and that it coincides with a TsT transformation of the original system. We then extend our formalism to the case in which the conserved currents are non-Abelian and point out its connection with Deformed T-dual Models and homogeneous Yang-Baxter deformations. In this case as well the deformation is based on a gauging of the symmetries involved and it turns out to be non-trivial only if the symmetry group admits a non-trivial central extension. Finally we apply what we learned by relating the $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ deformation to the central extension of the two-dimensional Poincaré algebra.

arXiv:2302.01654Journal of High Energy PhysicsMay 31, 202318 citations

Yang-Baxter Relations in Terms ofn-jSymbols ofsuq(2) Algebra

Masao Nomura

A trigonometric function parametrization of Yang-Baxter (Y-B) relations is described in terms of n - j symbols of su q (2), a deformation of su (2). The formalism starts with deduction of the Y-B relation for the IRF (interaction round a face) model of su q (2) from a general operator relation for the vertex model. The relation obtained for the IRF model is transformed into the Y-B relation for the vertex model using the property that the 3- j symbol is an asymptotic limit of the 6- j symbol. A class of very general solutions to Y-B equations is also presented. This solution of the IRF model with infinite rapidity parameters is linked to a symmetry of the 12- j symbol of the second kind.A trigonometric function parametrization of Yang-Baxter (Y-B) relations is described in terms of n - j symbols of su q (2), a deformation of su (2). The formalism starts with deduction of the Y-B relation for the IRF (interaction round a face) model of su q (2) from a general operator relation for the vertex model. The relation obtained for the IRF model is transformed into the Y-B relation for the vertex model using the property that the 3- j symbol is an asymptotic limit of the 6- j symbol. A class of very general solutions to Y-B equations is also presented. This solution of the IRF model with infinite rapidity parameters is linked to a symmetry of the 12- j symbol of the second kind.

Journal of the Physical Society of JapanAug 15, 198918 citations

Baxter operators for arbitrary spin

Dmitry Chicherin, Sergey E. Derkachov, David Roudolph Karakhanyan +1 more

arXiv:1106.4991Nuclear Physics BSep 10, 201116 citations

Baxters's Q-operators for the simplest q-deformed model

A. E. Kovalsky, G. P. Pronko

In the present paper we describe the procedure of the Q-operators construction for the q-deformed model, described by the Lax operator, which is important to formulate the Bethe ansatz for the Sin-Gordon model. This Lax operator can also be considered as some massless limit of the Lax operator of SG model. We constructed two R-operators which are the universal intertwiners for the Lax operators. The traces of its monodromies over the auxiliary space are Baxter operators i.e. the operator solutions of T-Q equation. We also found the intertwining relations which imply the mutual commutativity of the corresponding Q-operators.In the present paper we describe the procedure of the Q-operators construction for the q-deformed model, described by the Lax operator, which is important to formulate the Bethe ansatz for the Sin-Gordon model. This Lax operator can also be considered as some massless limit of the Lax operator of SG model. We constructed two R-operators which are the universal intertwiners for the Lax operators. The traces of its monodromies over the auxiliary space are Baxter operators i.e. the operator solutions of T-Q equation. We also found the intertwining relations which imply the mutual commutativity of the corresponding Q-operators.

arXiv:nlin/0307040Jul 22, 20034 citations

\textrm{T}\overline{\textrm{T}}

T T ¯ deformation. For conformal theories the deformations under study are expected to be exactly marginal. Still, a peculiar situation might arise when the conserved currents Ja are not well-defined local operators in the original theory. A simple example of this kind of system is provided by rotation currents in a theory of multiple free, massless, non-compact bosons. We verify that, somewhat unexpectedly, such a theory is indeed still conformal after deformation and that it coincides with a TsT transformation of the original system. We then extend our formalism to the case in which the conserved currents are non-Abelian and point out its connection with Deformed T-dual Models and homogeneous Yang-Baxter deformations. In this case as well the deformation is based on a gauging of the symmetries involved and it turns out to be non-trivial only if the symmetry group admits a non-trivial central extension. Finally we apply what we learned by relating the

\textrm{T}\overline{\textrm{T}}

T T ¯ deformation to the central extension of the two-dimensional Poincaré algebra.