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A bstract We study solvable deformations of two-dimensional quantum field theories driven by a bilinear operator constructed from a pair of conserved U(1) currents J a . 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 J a 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. 

A bstract The 3d Ising model in the low temperature (ferromagnetic) phase describes dynamics of two-dimensional surfaces — domain walls between clusters of parallel spins. The Kramers-Wannier duality maps these surfaces into worldsheets of confining strings in the Wegner’s ℤ 2 gauge theory. We study the excitation spectrum of long Ising strings by simulating the ℤ 2 gauge theory on a lattice. We observe a strong mixing between string excitations and the lightest glueball state and do not find indications for light massive resonances on the string worldsheet. 

A bstract The ODE/IM correspondence is an exact link between classical and quantum integrable models. The primary purpose of this work is to show that it remains valid after $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ perturbation on both sides of the correspondence. In particular, we prove that the deformed Lax pair of the sinh-Gordon model, obtained from the unperturbed one through a dynamical change of coordinates, leads to the same Burgers-type equation governing the quantum spectral flow induced by $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ . Our main conclusions have general validity, as the analysis may be easily adapted to all the known ODE/IM examples involving integrable quantum field theories. 

A bstract Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (“Love”) SL(2 , ℝ) symmetry in the suitably defined near zone approximation. We present a detailed study of this symmetry and show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the SL(2 , ℝ) representation theory. In particular, static perturbations of four-dimensional black holes belong to highest weight SL(2 , ℝ) representations. It is this highest weight properety that forces the static Love numbers to vanish. We find that the Love symmetry is tightly connected to the enhanced isometries of extremal black holes. This relation is simplest for extremal charged spherically symmetric (Reissner-Nordström) solutions, where the Love symmetry exactly reduces to the isometry of the near horizon AdS 2 throat. For rotating (Kerr-Newman) black holes one is lead to consider an infinite-dimensional SL(2 , ℝ) ⋉ $$ \hat{\textrm{U}}{(1)}_{\mathcal{V}} $$ U ̂ 1 V extension of the Love symmetry. It contains three physically distinct subalgebras: the Love algebra, the Starobinsky near zone algebra, and the near horizon algebra that becomes the Bardeen-Horowitz isometry in the extremal limit. We also discuss other aspects of the Love symmetry, such as the geometric meaning of its generators for spin weighted fields, connection to the no-hair theorems, non-renormalization of Love numbers, its relation to (non-extremal) Kerr/CFT correspondence and prospects of its existence in modified theories of gravity.