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Register a new userThermal transport in $Tbar{T}$-deformed conformal field theories: from integrability to holography
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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.
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We consider the out-of-equilibrium transport in $Tbar{T}$-deformed (1+1)-dimension conformal field theories (CFTs). The theories admit two disparate approaches, integrability and holography, which we make full use of in order to compute the transport quantities, such as the the exact non-equilibrium steady state currents. We find perfect agreements between the results obtained from these two methods, which serve as the first checks of the $Tbar{T}$-deformed holographic correspondence from the dynamical standpoint. It turns out that integrability also allows us to compute the momentum diffusion, which is given by a universal formula. We also remark on an intriguing connection between the $Tbar{T}$-deformed CFTs and reversible cellular automata.
Classification of the non-equilibrium quantum many-body dynamics is a challenging problem in condensed matter physics and statistical mechanics. In this work, we study the basic question that whether a (1+1) dimensional conformal field theory (CFT) is stable or not under a periodic driving with $N$ non-commuting Hamiltonians. Previous works showed that a Floquet (or periodically driven) CFT driven by certain $SL_2$ deformed Hamiltonians exhibit both non-heating (stable) and heating (unstable) phases. In this work, we show that the phase diagram depends on the types of driving Hamiltonians. In general, the heating phase is generic, but the non-heating phase may be absent in the phase diagram. For the existence of the non-heating phases, we give sufficient and necessary conditions for $N=2$, and sufficient conditions for $N>2$. These conditions are composed of $N$ layers of data, with each layer determined by the types of driving Hamiltonians. Our results also apply to the single quantum quench problem with $N=1$.
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 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.
It is widely expected that at sufficiently high temperatures order is always lost, e.g. magnets loose their ferromagnetic properties. We pose the question of whether this is always the case in the context of quantum field theory in $d$ space dimensions. More concretely, one can ask whether there exist critical points (CFTs) which break some global symmetry at arbitrary finite temperature. The most familiar CFTs do not exhibit symmetry breaking at finite temperature, and moreover, in the context of the AdS/CFT correspondence, critical points at finite temperature are described by an uncharged black brane which obeys a no-hair theorem. Yet, we show that there exist CFTs which have some of their internal symmetries broken at arbitrary finite temperature. Our main example is a vector model which we study both in the epsilon expansion and arbitrary rank as well as the large rank limit (and arbitrary dimension). The large rank limit of the vector model displays a conformal manifold, a moduli space of vacua, and a deformed moduli space of vacua at finite temperature. The appropriate Nambu-Goldstone bosons including the dilaton-like particle are identified. Using these tools we establish symmetry breaking at finite temperature for finite small $epsilon$. We also prove that a large class of other fixed points, which describe some of the most common quantum magnets, indeed behave as expected and do not break any global symmetry at finite temperature. We discuss some of the consequences of finite temperature symmetry breaking for the spectrum of local operators. Finally, we propose a class of fixed points which appear to be possible candidates for finite temperature symmetry breaking in $d=2$.
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