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Register a new userCanonical maps and integrability in $Tbar T$ deformed 2d CFTs
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We study $Tbar T$ deformations of 2d CFTs with periodic boundary conditions. We relate these systems to string models on $mathbb{R}times {S}^1times{cal M}$, where $cal M$ is the target space of a 2d CFT. The string model in the light cone gauge is identified with the corresponding 2d CFT and in the static gauge it reproduces its $Tbar T$ deformed system. This relates the deformed system and the initial one by a worldsheet coordinate transformation, which becomes a time dependent canonical map in the Hamiltonian treatment. The deformed Hamiltonian defines the string energy and we express it in terms of the chiral Hamiltonians of the initial 2d CFT. This allows exact quantization of the deformed system, if the spectrum of the initial 2d CFT is known. The generalization to non-conformal 2d field theories is also discussed.
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We study perturbative renormalization of the composite operators in the $Tbar T$-deformed two-dimensional free field theories. The pattern of renormalization for the stress-energy tensor is different in the massive and massless cases. While in the latter case the canonical stress tensor is not renormalized up to high order in the perturbative expansion, in the massive theory there are induced counterterms at linear order. For a massless theory our results match the general formula derived recently in [1].
In this work, we try to construct the Lax connections of $Tbar{T}$-deformed integrable field theories in two different ways. With reasonable assumptions, we make ansatz and find the Lax pairs in the $Tbar{T}$-deformed affine Toda theories and the principal chiral model by solving the Lax equations directly. This way is straightforward but maybe hard to apply for general models. We then make use of the dynamical coordinate transformation to read the Lax connection in the deformed theory from the undeformed one. We find that once the inverse of the transformation is available, the Lax connection can be read easily. We show the construction explicitly for a few classes of scalar models, and find consistency with the ones in the first way.
We propose a symmetry of $Tbar T$ deformed 2D CFT, which preserves the trace relation. The deformed conformal killing equation is obtained. Once we consider the background metric runs with the deformation parameter $mu$, the deformation contributes an additional term in conformal killing equation, which plays the role of renormalization group flow of metric. The conformal symmetry coincides with the fixed point. On the gravity side, this deformed conformal killing equation can be described by a new boundary condition of AdS$_3$. In addition, based on the deformed conformal killing equation, we derive that the stress tensor of the deformed CFT equals to Brown-Yorks quasilocal stress tensor on a finite boundary with a counterterm. For a specific example, BTZ black hole, we get $Tbar T$ deformed conformal killing vectors and the associated conserved charges are also studied.
In this paper we consider the energy and momentum transport in (1+1)-dimension conformal field theories (CFTs) that are deformed by an irrelevant operator $Tbar{T}$, using the integrability based generalized hydrodynamics, and holography. The two complementary methods allow us to study the energy and momentum transport after the in-homogeneous quench, derive the exact non-equilibrium steady states (NESS) and calculate the Drude weights and the diffusion constants. Our analysis reveals that all of these quantities satisfy universal formulae regardless of the underlying CFT, thereby generalizing the universal formulae for these quantities in pure CFTs. As a sanity check, we also confirm that the exact momentum diffusion constant agrees with the conformal perturbation. These fundamental physical insights have important consequences for our understanding of the $Tbar{T}$-deformed CFTs. First of all, they provide the first check of the $Tbar{T}$-deformed $mathrm{AdS}_3$/$mathrm{CFT}_2$ correspondence from the dynamical standpoint. And secondly, we are able to identify a remarkable connection between the $Tbar{T}$-deformed CFTs and reversible cellular automata.
We use the quantum null energy condition in strongly coupled two-dimensional field theories (QNEC2) as diagnostic tool to study a variety of phase structures, including crossover, second and first order phase transitions. We find a universal QNEC2 constraint for first order phase transitions with kinked entanglement entropy and discuss in general the relation between the QNEC2-inequality and monotonicity of the Casini-Huerta c-function. We then focus on a specific example, the holographic dual of which is modelled by three-dimensional Einstein gravity plus a massive scalar field with one free parameter in the self-interaction potential. We study translation invariant stationary states dual to domain walls and black branes. Depending on the value of the free parameter we find crossover, second and first order phase transitions between such states, and the c-function either flows to zero or to a finite value in the infrared. Strikingly, evaluating QNEC2 for ground state solutions allows to predict the existence of phase transitions at finite temperature.
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