We show that the $T \overline{T}$ deformation of two-dimensional quantum field theory on $\mathrm{AdS}_2$ is well-defined and solvable at the quantum level. Flow equations for the energy spectrum and partition function are derived in analogy with the flat space case. As a non-trivial check, we perturbatively compute the deformed energy spectrum for the case of a free scalar field. We analyze the high energy density of states of the deformed theory and find a Hagedorn growth of states.
Quantum field theory in zero spatial dimensions has a rich infrared landscape and a universal ultraviolet, inverting the usual Wilsonian paradigm. For holographic theories this implies a rich landscape of asymptotically AdS$_2$ geometries. Isolating the interiors of these spacetimes suggests a study of the analog of the $T\overline{T}$ deformation in quantum mechanics, which we pursue here. An equivalent description of this deformation in terms of coupling to worldline gravity is proposed, and applications to quantum mechanical systems - including the Schwarzian theory - are studied.
The surface/state correspondence suggests that the bulk co-dimensional two surface could be dual to the quantum state in the holographic conformal field theory(CFT). Inspired by the cutoff-AdS/$T\overline{T}$-deformed-CFT correspondence, we propose that the quantum states of two-dimensional $T\overline{T}$-deformed holographic CFT are dual to some particular surfaces in the AdS$_3$ gravity. In particular, the time slice of the cut-off surface is dual to the ground state of the $T\overline{T}$-deformed CFT. We examine our proposal by studying the entanglement entropy and quantum information met…
We study the spectrum of certain two-particle operators in the supergravity regime of the D1-D5 system, focussing on the four-point correlators of tensor multiplets on $AdS_3\times S^3$ at tree level. In Mellin space, these are nicely determined by a single amplitude, which makes manifest the large $p$ limit, the connection with the flat space S-matrix, and the six dimensional conformal symmetry. We compute the $(1,1)\times \overline{(1,1)}$ superconformal blocks for the two-dimensional $\mathcal{N}=(4,4)$ conformal theory at the boundary, and then we obtain a formula for the anomalous dimensi…
According to the KKLT scenario, metastable dS vacua are formed as a result of uplifting of supersymmetric AdS vacua by $\overline {D3}$ branes. I describe an extended version of this scenario where metastable dS vacua appear after an uplift from a state where the potential of the volume modulus in the absence of $\overline {D3}$ branes would be unbounded below. This mechanism may considerably strengthen vacuum stabilization in the early universe.
In this paper, we study the entanglement entropy of a single interval on a cylinder in two-dimensional $T\overline{T}$-deformed conformal field theory. For such case, the (Rényi) entanglement entropy takes a universal form in a CFT. We compute the correction due to the deformation up to the leading order of the deformation parameter in the framework of the conformal perturbation theory. We find that the correction to the entanglement entropy is nonvanishing in the finite temperature case, while it is vanishing in the finite size case. For the deformed holographic large $c$ CFT, which is propos…
We study the $T\overline{T}$ deformation of two dimensional quantum field theories from a Hamiltonian point of view, focusing on aspects of the theory in Lorentzian signature. Our starting point is a simple rewriting of the spatial integral of the $T\overline{T}$ operator, which directly implies the deformed energy spectrum of the theory. Using this rewriting, we then derive flow equations for various quantities in the deformed theory, such as energy eigenstates, operators, and correlation functions. On the plane, we find that the deformation merely has the effect of implementing successive ca…
We study Big-Bang or -Crunch cosmological singularities in 2-dimensional dilaton-gravity-scalar theories, in general obtained by dimensional reduction of higher dimensional theories. The dilaton potential encodes information about the asymptotic data defining the theories, and encompasses various families such as flat space, $AdS$, conformally $AdS$ as arising from nonconformal branes, and more general nonrelativistic theories. We find a kind of universal near singularity behaviour independent of the dilaton potential, giving universal interrelations between the exponents defining the time beh…
The $T \overline{T}$ operator provides a universal irrelevant deformation of two-dimensional quantum field theories with remarkable properties, including connections to both string theory and holography beyond $\mathrm{AdS}$ spacetimes. In particular, it appears that a $T \overline{T}$-deformed theory is a kind of new structure, which is neither a local quantum field theory nor a full-fledged string theory, but which is nonetheless under some analytic control. On the other hand, supersymmetry is a beautiful extension of Poincaré symmetry which relates bosonic and fermionic degrees of freedom. …
The quantization of pure 3D gravity with Dirichlet boundary conditions on a finite boundary is of interest both as a model of quantum gravity in which one can compute quantities which are "more local" than S-matrices or asymptotic boundary correlators, and for its proposed holographic duality to $T \overline{T}$-deformed CFTs. In this work we apply covariant phase space methods to deduce the Poisson bracket algebra of boundary observables. The result is a one-parameter nonlinear deformation of the usual Virasoro algebra of asymptotically AdS$_3$ gravity. This algebra should be obeyed by the st…
Recently proposed double trace deformations of large $N$ holographic CFTs in four dimensions define a one parameter family of quantum field theories, which are interpreted in the bulk dual as living on successive finite radius hypersurfaces. The transformation of variables that turns the equation defining the deformation of a four dimensional large $N$ CFT by such operators into the expression for the radial ADM Hamiltonian in the bulk is found. This prescription clarifies the role of various functions of background fields that appear in the flow equation defining the deformed holographic CFT,…
We consider sphere partition functions of TT deformed large N conformal field theories in d=2,3,4,5 and 6 dimensions, computed using the flow equation. These are shown to non-perturbatively match with bulk computations of $AdS_{d+1}$ with a finite radial cut-off. We then demonstrate how the flow equation can be independently derived from a regularization procedure in defining TT operators through a local Callan-Symanzik equation. Finally, we show that the sphere partition functions, modulo bulk-counterterm contributions, can be reproduced from Wheeler-DeWitt wave functions.
$\mathrm{T}\overline{\mathrm{T}}$ deformation was originally proposed as an irrelevant solvable deformation for 2d relativistic quantum field theories (QFTs). The same family of deformations can also be defined for integrable quantum spin chains which was first studied in the context of integrability in AdS/CFT. In this paper, we construct such deformations for yet another type of models, which describe a collection of particles moving in 1d and interacting in an integrable manner. The prototype of such models is the Lieb-Liniger model. This shows that such deformations can be defined for a ve…
We generalize the $T\overline{T}$ deformation of CFT$_2$ to higher-dimensional large-$N$ CFTs, and show that in holographic theories, the resulting effective field theory matches semiclassical gravity in AdS with a finite radial cutoff. We also derive the deformation dual to arbitrary bulk matter theories. Generally, the deformations involve background fields as well as CFT operators. By keeping track of these background fields along the flow, we demonstrate how to match correlation functions on the two sides in some simple examples, as well as other observables.
psu（2，2）的代数曲线|4）量子自旋链由代数Bethe不等式的热力学极限确定。该自旋链的哈密顿量与N=4 SYM的平面单圈伸缩算符一致。在对偶AdS_5 x S^5弦论中，定义规范理论曲线的数据的各种性质与从半经典自旋弦组态得到的数据进行了比较，特别是对于AdS_5 x S^1上的弦的情况，并且曲线的su（2，2）自旋链一致性被显示出来。
Dipartimento di Fisica, Università di Trieste（的里雅斯特大学物理系）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学卡弗里理论科学研究所）；Laboratory for Theoretical Fundamental Physics, Institute of Physics, Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院物理研究所基础物理实验室）；CERN, Theoretical Physics Department（欧洲核子研究中心理论物理部）
In this paper, we demonstrate the emergence of nonlinear gravitational equations directly from the physics of a broad class of conformal field theories. We consider CFT excited states defined by adding sources for scalar primary or stress tensor operators to the Euclidean path integral defining the vacuum state. For these states, we show that up to second order in the sources, the entanglement entropy for all ball-shaped regions can always be represented geometrically (via the Ryu-Takayanagi formula) by an asymptotically AdS geometry. We show that such a geometry necessarily satisfies Einstein…
On Supersymmetric D-brane probes in 4d $\mathcal{N}=2$ $\text{AdS}_2\times\mathbf{S}^2$ Attractors
Enrico Fermi Institute & Leinweber Institute for Theoretical Physics, University of Chicago（恩里科·费米研究所与莱因韦伯理论物理研究所，芝加哥大学）；Kavli Institute for Cosmological Physics, University of Chicago（卡弗里宇宙物理学研究所，芝加哥大学）；Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)（马克斯·普朗克物理学研究所（维尔纳·海森堡研究所））
Supersymmetric Holomorphic Masses in AdS/CFT with Flavour
University of Southampton（南安普顿大学）；Tsinghua University（清华大学）；SUNY Old Westbury（纽约州立大学奥尔德韦斯利分校）；Stockholm University（斯德哥尔摩大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）
