Subhroneel Chakrabarti, Madhusudhan Raman
We show that at the level of the equations of motion (i.e. classically), in the limit in which the $ \text{T}\overline{\text{T}} $ deformation parameter is sent to infinity, the left- and right-chiral sectors of $ \text{T}\overline{\text{T}} $-deformed free theories decouple.
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Recently we proposed a universal solvable irrelevant deformation of $AdS_3/CFT_2$ duality, which leads in the ultraviolet to a theory with a Hagedorn entropy [1]. In this note we provide a worldsheet description of this theory as a coset CFT, and compare its spectrum to the field theory predictions of [2,3].
In this paper we use the recently suggested conjecture about the integral representation for the flat coordinates on Frobenius manifolds, connected with the isolated singularities, to compute the flat coordinates and Saito primitive form on the space of the deformations of Gepner chiral ring $\widehat{SU}(3)_4$. We verify this conjecture comparing the expressions for the flat coordinates obtained from the conjecture with the one found by direct computation. The considered case is of a particular interest since together with the relevant and marginal deformations it has one irrelevant deformati…
We analyse the $T\bar{T}$ deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the $1/c$ contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ simultaneously. We comment on the implication…
We initiate the study of $T\bar T$-like irrelevant solvable deformations in quantum field theory with boundaries and defects. For this purpose, we employ a general formalism developed in the context of spin chains, which allows us to derive both, the deformed bulk and boundary/defect scattering matrices of integrable models. Using the deformed scattering matrices, we derive the flow equation for the deformed finite volume spectrum, as well as the cylinder partition function and the exact $g$-function.
I show that under certain conditions it is possible to define consistent irrelevant deformations of interacting conformal field theories. The deformations are finite or have a unique running scale ("quasi-finite"). They are made of an infinite number of lagrangian terms and a finite number of independent parameters that renormalize coherently. The coefficients of the irrelevant terms are determined imposing that the beta functions of the dimensionless combinations of couplings vanish ("quasi-finiteness equations"). The expansion in powers of the energy is meaningful for energies much smaller t…
Using Wilson-Polchinski renormalization group equations, we give a simple new proof of decoupling in a $ϕ^4$-type scalar field theory involving two real scalar fields (one is heavy with mass $M$ and the other light). Then, to all orders in perturbation theory, it is shown that effects of virtual heavy particles up to the order $1/M^{2N_0}$ can be systematically incorporated into light-particle theory via effective local vertices of canonical dimension at most $4+2N_0$. The couplings for vertices of dimension $4+2N$ are of order $1/M^{2N}$ and are systematically calculable. All this is achieved…
Recently it has been shown by Almheiri and Lin [1] that the reconstruction of black-hole interior is sensitive to knowing the exact coupling of the boundary theory even if the coupling is irrelevant. This motivates us to enlarge the set of the one-time and two-time toy models inspired from the SYK by deforming the same with \textit{irrelevant} coupling. We find that both half-wormholes as well as the wormholes persist in presence of the deformation, leading to a similar mechanism for curing the factorization problem. While for the one time case, the deformed partition function and its moments …
We discuss the systematics of obtaining the Callan-Symanzik equation within the framework of the gauge/gravity dualities. We present a completely general formula which in particular takes into account the new holographic renormalization results of arXiv:1102.2239. Non-trivial beta functions are obtained from new logarithmic terms in the radial expansion of the fields. The appearance of multi-trace counterterms is also discussed in detail and we show that mixing between single- and multi-trace operators leads to very specific non-linearities in the Callan-Symanzik equation. Additionally, we com…
This is a pedagogical review on $\mathrm{T}\overline{\mathrm{T}}$ deformation of two dimensional quantum field theories. It is based on three lectures which the author gave at ITP-CAS in December 2018. This review consists of four parts. The first part is a general introduction to $\mathrm{T}\overline{\mathrm{T}}$ deformation. Special emphasises are put on the deformed classical Lagrangian and the exact solvability of the spectrum. The second part focuses on the torus partition sum of the $\mathrm{T}\overline{\mathrm{T}}$/$\mathrm{J}\overline{\mathrm{T}}$ deformed conformal field theories and …
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. …
We generalize our recent analysis [2006.13249] of probe string dynamics to the case of general single-trace $T\bar T$, $J\bar T$ and $T\bar J$ deformations. We show that in regions in coupling space where the bulk geometry is smooth, the classical trajectories of such strings are smooth and approach the linear dilaton boundary at either the far past or the far future. These trajectories give rise to quantum scattering states with arbitrarily high energies. When the bulk geometry has closed timelike curves (CTC's), the trajectories are singular for energies above a critical value $E_c$. This si…
From black holes to solvable irrelevant deformations and back
本文探讨了Kerr/CFT对应关系与二维量子场论中可解无关变形之间的联系，分析了T\ar T和J\ar T变形的对称性及其在黑洞微观结构研究中的应用。
In this paper we investigate the recently found $γ$-deformed Maldacena-Nunez background by studying the behavior of different semiclassical string configurations. This background is conjectured to be dual to dipole deformations of $\N=1$ SYM. We compare our results to those in the pure Maldacena-Nunez background and show that the energies of our string configurations are higher than in the undeformed background. Thinking in the lines of (hep-th/0505100) we argue that this is an evidence for better decoupling of the Kaluza-Klein modes from the pure SYM theory excitations. Moreover we are able t…
We study $ \text{T}\overline{\text{T}} $ deformations of chiral bosons using the formalism due to Sen. For arbitrary numbers of left- and right-chiral bosons, we find that the $ \text{T}\overline{\text{T}} $-deformed Lagrangian can be computed in closed form, giving rise to a novel non-local action in Sen's formalism. We establish that at the limit of infinite $ \text{T}\overline{\text{T}} $ coupling, the equations of motion of deformed theory exhibits chiral decoupling. We then turn to a discussion of $ \text{T}\overline{\text{T}} $-deformed chiral fermions, and point out that the stress tens…
Generalized $T\overline{T}$-like Deformations in Duality-Invariant Nonlinear Electrodynamic Theories
本研究提出高阶微扰方法，分类对偶不变非线性电动力学中的两类解，并确认无关与边缘算子引发的应力张量流的可交换性。
Double trace deformations, that is products of two local operators, define perturbations of conformal field theories that can be studied exactly in the large-N limit. Even when the double trace deformation is irrelevant in the infrared, it is believed to flow to an ultraviolet fixed point. In this note we define the Kallen-Lehmann representation of the two-point function of a local operator O in a theory perturbed by the square of such operator. We use such representation to discover potential pathologies at intermediate points in the flow that may prevent to reach the UV fixed point. We apply…
Classifying Causal Nonlinear Electrodynamics via $φ$-Parity and Irrelevant Deformations
本文通过分析自偶非线性电动力学理论的解析性性质，利用φ奇偶性不变性，分类了由能量动量张量标量的整数次幂构建的无关变形理论，以及涉及整数和半整数次幂的非解析理论。
We study decoupling in FRW spacetimes, emphasizing a Lagrangian description throughout. To account for the vacuum choice ambiguity in cosmological settings, we introduce an arbitrary boundary action representing the initial conditions. RG flow in these spacetimes naturally affects the boundary interactions. As a consequence the boundary conditions are sensitive to high-energy physics through irrelevant terms in the boundary action. Using scalar field theory as an example, we derive the leading dimension four irrelevant boundary operators. We discuss how the known vacuum choices, e.g. the Bunch…
Sequential Flows by Irrelevant Operators
该研究探究对已$T\overline{T}$形变的理论再次进行该形变的可行性，定义了含子系统信息的无关形变类，给出能谱与模不变性数值证据，研究了自由玻色、费米子经典拉格朗日量的连续形变流，部分序列流模型或有有趣全息意义。
In this note, we study the deformation of the topological string by $\barΩ$. Namely, adopting the perturbative string amplitudes approach, we identify the $\barΩ$-deformation in terms of a physical state in the sting spectrum. We calculate the topological amplitudes $F_g$ in heterotic string theory in the presence of the latter. In particular, we show that it is crucial to include quadratic terms in the effective action in order for $\barΩ$ to decouple. It turns out that this decoupling happens at the full string level, suggesting that this holds non-perturbatively.
It has been recently discovered that the $\text{T}\bar{\text{T}}$ deformation is closely-related to Jackiw-Teitelboim gravity. At classical level, the introduction of this perturbation induces an interaction between the stress-energy tensor and space-time and the deformed EoMs can be mapped, through a field-dependent change of coordinates, onto the corresponding undeformed ones. The effect of this perturbation on the quantum spectrum is non-perturbatively described by an inhomogeneous Burgers equation. In this paper, we point out that there exist infinite families of models where the geometry …
We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in $d \geq 3$ dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model independent and do not require a Lagrangian description. Two unifying themes emerge: first, many theories admit deformations that reside in multiplets together with conserved currents. Such deformations can lead to modifications of the supersymmetry algebra by central and non-central charges. Second, many theories with a sufficient amount of supersymmetry do not…
It has been argued several times in the past that the structure of the entropy formula for general non-extremal asymptotically flat black holes in four dimensions can be understood in terms of an underlying conformal symmetry. A recent implementation of this idea, carried out by Cvetič and Larsen, involves the replacement of a conformal factor in the original geometry by an alternative conformal factor in such a way that the near-horizon behavior and thermodynamic properties of the black hole remain unchanged, while only the asymptotics or "environment" of the geometry are modified. The soluti…
The Triple $T\bar{T}$-Like Flow in Quantum Field Theories: Irrelevant, Marginal, and Relevant
本文引入一个单参数根-$T\bar{T}$-类流，通过应力张量形变组织成无关、边缘和相关分支，并在对偶不变电动力学和二维可积sigma模型中给出闭式解，表明根-$T\bar{T}$流是对偶不变和可变形变的统一组织原理。
On Entropy Bounds for Irrelevant Operators
基于黑洞热力学，研究红外共形场论中主导对称性保持的无关形变必须增加系统熵的猜想，并通过多种有效场论模型验证该熵正性猜想。
Irrelevant and marginal deformed BMS field theories
本文研究了BMSFT框架内的$T\overline{T}$、$JT_μ$和$\sqrt{T\overline{T}}$形变，利用BMS对称性Ward恒等式导出关联函数一阶修正，并以BMS自由标量与自由费米子为种子理论解析求解了形变作用量及二阶形变。
We investigate the non-perturbative stability of asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass near the Breitenlohner-Freedman bound. Such scalars are characterized by power-law radial decay near the AdS boundary, and typical boundary conditions are "Dirichlet" (fix the slower fall-off mode) or "Neumann" (fix the faster fall-off mode). More generally though, these "designer gravity" theories admit a large class of boundary conditions defined by a functional relation between the two modes. While previous stability proofs have considered boundary conditions t…
We consider the irrelevant flow of classical Liouville field theory driven by the $T\bar T$ operator. After discussing properties of its exact action and equation of motion we construct an infinite set of conserved currents. We also find its vacuum solutions.
We study thermodynamic and transport observables of quantum critical states that arise in the infra-red limit of holographic renormalisation group flows. Although these observables are expected to exhibit quantum critical scaling, there are a number of cases in which their frequency and temperature dependences are in apparent contradiction with scaling theories. We study two different classes of examples, and show in both cases that the apparent breakdown of scaling is a consequence of the dependence of observables on an irrelevant deformation of the quantum critical state. By assigning scalin…
Geometric realization via irrelevant deformations induced by the stress-energy tensor
本文推广了由能动张量驱动的形变，发展了将形变作用量与任意时空维度度规流方程关联的形式体系，并在特定形变下获得了闭式精确解，探讨了其与引力模型的关系及标量场理论应用。
Krylov Complexity of Supersymmetric SYK Models
通过研究N=2 SYK模型在无关和质量变形下的Krylov复杂度，发现超对称破缺机制在量子复杂度上留下印记，无关变形使饱和复杂度达到Krylov维数的一半，而质量变形在中间强度范围内降低饱和复杂度。
We consider a general (beyond $T\bar T$) deformation of the 2D $O(N+1)$ $σ$-model by the irrelevant dimension-four operators. The theory deformed in this most general way is not integrable, and the $S$-matrix loses its factorization properties. We perform the all-order summation of the leading infrared logs for the $2 \to 2$ scattering amplitude and provide the exact result for the $2 \to 2$ $S$-matrix in the leading logarithmic approximation. These results can provide us with new insights into the properties of the theories deformed by irrelevant operators more general than the $T\bar T$ defo…
We construct a solvable deformation of two-dimensional theories with $(2,2)$ supersymmetry using an irrelevant operator which is a bilinear in the supercurrents. This supercurrent-squared operator is manifestly supersymmetric, and equivalent to $T\bar{T}$ after using conservation laws. As illustrative examples, we deform theories involving a single $(2,2)$ chiral superfield. We show that the deformed free theory is on-shell equivalent to the $(2,2)$ Nambu-Goto action. At the classical level, models with a superpotential exhibit more surprising behavior: the deformed theory exhibits poles in th…
We analyze the effective field equations of the Randall-Sundrum braneworld coupled with a Klein-Gordon scalar field through the minimal geometric deformation decoupling method (MGD-decoupling). We introduce two different ways to apply the MGD-decoupling method to obtain new solutions for this enlarged system. We also compare the behavior of the new solutions with those obtained directly from the Randall-Sumdrum braneworld without coupling to the scalar field.
We study the addition of an irrelevant operator to the N=4 supersymmetric large n SU(n) gauge theory, in the presence of finite temperature, T. In the supergravity dual, the effect of the operator is known to correspond to a deformation of the AdS_5 x S^5 ``throat'' which restores the asymptotic ten dimensional Minkowski region of spacetime, completing the full D3-brane solution. The system at non-zero T is interesting, since at the extremes of some of the geometrical parameters the geometry interpolates between a seven dimensional spherical Minkowskian Schwarzschild black hole (times R^3) and…
Matrix Theory Reloaded: A BPS Road to Holography
本文通过BPS退耦极限统一矩阵理论与全息，提出DLCQ^n/DLCQ^m对应，将AdS/CFT视为特例，并关联T\ar{T}形变。
Higgs-like (pseudo)Scalars in AdS$_4$, Marginal and Irrelevant Deformations in CFT_3 and Instantons on S^3
该研究在 AdS4 超引力截断中研究类希格斯标量，通过 Adomian 分解求解呼吸模式，实现 ABJM 模型中的边界对偶，并构造 SO(4) 不变瞬子解，对应坍缩气泡与大挤压奇点。
Entanglement in $\text{T}\bar{\text{T}}$ and root-$\text{T}\bar{\text{T}}$ deformed AdS$_3$/CFT$_2$
本文研究了T̄T和根T̄T变形对AdS₃/CFT₂中纠缠结构的影响，探讨了混合边界条件下纠缠熵的变化及意义。
A solvable irrelevant deformation of AdS$_3$/CFT$_2$ correspondence leading to a theory with Hagedorn spectrum at high energy has been recently proposed. It consists of a single trace deformation of the boundary theory, which is inspired by the recent work on solvable $T\bar{T}$ deformations of two-dimensional CFTs. Thought of as a worldsheet $σ$-model, the interpretation of the deformed theory from the bulk viewpoint is that of string theory on a background that interpolates between AdS$_3$ in the IR and a linear dilaton vacuum of little string theory in the UV. The insertion of the operator …
Zoo of flows in a 3d gauged supergravity with periodic potential
本文研究了三维规范超引力中带有周期势的流体结构，通过分析发现其可解释为CFT的变形，并展示了$T\overline{T}$算子的因子分解特性。
We consider the massless charge-$N$ Schwinger model and its deformation with two four-fermion operators. Without the deformations, this model exhibits chiral symmetry breaking without confinement. It is usually asserted that the massless Schwinger model is always deconfined and a string tension emerges only when a mass for the fermion field is turned on. We show that in the presence of these four-fermion operators, the massless theory can in fact confine. One of the four-fermion deformations is chirally neutral, and is a marginal deformation. The other operator can be relevant or irrelevant, a…
Complete Minimal Form Factors for Irrelevant Deformations of Integrable Quantum Field Theory
本文针对受广义$T\ar{T}$微扰的对角可积场论，提出无自由参数的最小形状因子计算方法，发现原有形状因子方程不变的假设过强，需修改相关核心假设。
We consider holographic renormalization for the decoupling limit of coincident Dp-branes. We truncate the theory to the supergravity sector which is homogeneous on the (8-p)-sphere and carries only RR electric (p+2)-flux, leaving a graviton and two scalar degrees of freedom associated to the dilaton and the sphere radius. We non-linearly construct the asymptotic graviton and dilaton deformations - the analog of the Graham-Fefferman expansion for AdS/CFT - and compute counterterms to give a finite renormalized bulk action and dual one point functions. Restricting to linear deformations we find …
We consider QCD-like theories with one massless fermion in various representations of the gauge group SU$(N)$. The theories are formulated on $R_3\times S_1$. In the decompactification limit of large $r(S_1)$ all these theories are characterized by confinement, mass gap and spontaneous breaking of a (discrete) chiral symmetry ($χ$SB). At small $r(S_1)$, in order to stabilize the vacua of these theories at a center-symmetric point, we suggest to perform a double trace deformation. With these deformation, the theories at hand are at weak coupling at small $r(S_1)$ and yet exhibit basic features …
Role of Complexity on the Minimal Deformation of Black Holes
本文在引力解耦框架下，利用最小几何形变和最小复杂性因子方案研究自引力流体分布，发现零复杂性条件下各向异性物质可转化为完美流体，为构建物理真实的各向同性恒星模型提供了新途径。
A Note on $T\bar{T}$ Deformations and Boundaries
本文针对存在边界与缺陷时$T\ar{T}$形变理论行为研究不足的问题，回顾相关解析结果，在热力学贝特ansatz框架下研究$T\ar{T}$形变精确g函数，验证其与Burgers型流方程解的一致性，并指出潜在重要开放问题。
We study ${\cal N}=1$ supergravity with $N>1$ chiral superfields in which one of the fields has a Kähler potential of exact no-scale type. Such systems admit de Sitter (dS) solutions in which supersymmetry is predominantly broken by the no-scale field, with only a small contribution to the breaking coming from the other fields. Metastable dS vacua of this type were recently shown to be achievable by the finetuning of an $N\times N$ sub-matrix of the Hessian matrix at the critical point. We show that perturbatively small deformations of the no-scale Minkowski vacuum into dS are only possible wh…
Physical Features of Geometrically Deformed Anisotropic Charged Three-dimensional BTZ Black Holes
本文通过最小几何变形解耦方案，研究了三维带电BTZ黑洞的物理特性，探讨了变形参数和电荷对热力学量的影响，并分析了低维量子效应。
Traversable Wormholes in Minimally Geometrical Deformed Trace-Free Gravity using Gravitational Decoupling
本研究在无迹引力框架下用最小几何形变方法结合引力解耦，研究不同物态参数、引力源下的Morris-Thorne可穿越虫洞，发现零能量条件破缺并算出弱偏转角。
We calculate the D-brane superpotentials for two Calabi-Yau manifolds with three deformations by the generalized hypergeometric GKZ systems, which give rise to the flux superpotentials $\mathcal{W}_{GVW}$ of the dual F-theory compactification on the relevant Calabi-Yau fourfolds in the weak decoupling limit. We also compute the Ooguri-Vafa invariants from A-model expansion with mirror symmetry, which are related to the open Gromov-Witten invariants.
Quantum gravity in a finite region of spacetime is conjectured to be dual to a conformal field theory deformed by the irrelevant operator $T \overline{T}$. We test this conjecture with entanglement entropy, which is sensitive to ultraviolet physics on the boundary while also probing the bulk geometry. We find that the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere is finite and precisely matches the Ryu-Takayanagi formula applied to a finite region consistent with the conjecture of McGough, Mezei and Verlinde. We also consider a one-parameter fami…
$T\overline{T}$ Deformation: Introduction and Some Recent Advances
本文综述 $T\bar{T}$ 形变的经典几何解释、量子特征及其与全息和弦论的联系，并梳理未来研究方向。
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