Ali Davody
We study Weyl symmetry for non-relativistic conformal filed theories on curved spatial spaces, and calculate it's quantum anomaly. We show that there is no geometric anomaly, and the non-relativistic Weyl anomaly can appear only due to interaction. Also we study the anomaly by using the light-cone approach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Families of IIB duals for nonrelativistic CFTs
我们表明，最近的弦论嵌入的非相对论薛定谔对称性的时空可以推广到一个21维家庭的对称性的解决方案。我们的解决方案包括IIB背景，没有三种形式的通量打开，并出现在膜波时空的近视界极限。我们发现，有一个超曲面在这些理论的空间中出现的引力描述的不稳定性，表明在非相对论性场论对偶相变。我们还提出了简单的嵌入的非相对论临界点的动力学临界指数可以采取许多值z \neq 2。
The unitary Fermi gas, by virtue of its description as a nonrelativistic conformal field theory, has proven an interesting system by which the quantum properties of CFT can be held to experimental verification. Here, we examine the structure of conformal dimensions of charge-Q operators in nonrelativistic CFT, in the large-Q regime, from the non-linear sigma model perspective. We discuss in detail the renormalization of edge divergences using dimensional regularization, elucidating the presence of $\log(Q)$ terms in the large-charge expansion. Finally we use dimensional regularization to compu…
We study solutions of type IIB supergravity which are SL(2,R) x SU(2) x U(1)^2 invariant deformations of AdS_3 x S^3 x K3 and take the form of products of self-dual spacelike warped AdS_3 and a deformed three-sphere. One of these backgrounds has been recently argued to be relevant for a derivation of Kerr/CFT from string theory, whereas the remaining ones are holographic duals of two-dimensional dipole theories and their S-duals. We show that each of these backgrounds is holographically dual to a deformation of the DLCQ of the D1-D5 CFT by a specific supersymmetric (1,2) operator, which we wri…
We extend and clarify the large-charge expansion of the conformal dimension $Δ_Q$ of the lowest operator of charge $Q$ in nonrelativistic CFTs using the state-operator correspondence. The latter requires coupling the theory to an external harmonic trap that confines the particles to a spherical cloud, at the edge of which the effective theory breaks down and leads to divergences. Only recently has this issue been overcome by constructing appropriate counterterms at the edge of the cloud in arXiv:2010.07967. In this note, we extend these results by systematically analyzing the degree of diverge…
Weyl Anomaly Coefficients of Holographic Defect CFTs at Weak and Strong Coupling
研究了共维度二缺陷CFT的Weyl异常系数，通过强耦合和弱耦合方法计算，并发现系数b在参数空间有限区域为负，首次明确展示了相互作用的单位ary dCFT具有b<0的情况。
Induced p-wave superfluidity in two dimensions: Brane world in cold atoms and nonrelativistic defect CFTs
我们提出利用两种费米气体的种间s波费什巴赫共振实现二维p波超流性。通过将一种费米子限制在一个二维平面中，另一种费米子浸没在背景三维费米子海中，在二维费米子之间诱导出吸引相互作用。计算了弱耦合区的对能隙，并证明了对能隙具有px + ipy对称性。由于对能隙的大小向幺正极限增加，p_x+ip_y波超流性的临界温度可能在实验范围内。由此产生的系统有一个潜在的应用拓扑量子计算使用非阿贝尔统计涡旋。我们还讨论了我们的系统在幺正性极限方面作为一个“非相对论性缺陷共形场论（CFT）"。研究了约化薛定谔代数、算符-态对应、复合算符的标度维数和算子乘积展开。
For a general $λ$-deformation of current algebra CFTs we compute the exact Weyl anomaly coefficient and the corresponding metric in the couplings space geometry. By incorporating the exact $β$-function found in previous works we show that the Weyl anomaly is in fact the exact Zamolodchikov's $C$-function interpolating between exact CFTs occurring in the UV and in the IR. We provide explicit examples with the anisotropic $SU(2)$ case presented in detail. The anomalous dimension of the operator driving the deformation is also computed in general. Agreement is found with special cases existing al…
We develop a general approach to simplify the derivation of the holographic Weyl anomaly. As an application, we derive the holographic Weyl anomaly from general higher derivative gravity in asymptotically $AdS_{5}$ and $AdS_{7}$. Interestingly, to derive all the central charges of 4d and 6d CFTs, we make no use of equations of motion. Following Myers' idea, we propose a formula of holographic entanglement entropy for higher derivative gravity in asymptotically $AdS_5$. Applying this formula, we obtain the correct universal term of entanglement entropy for 4d CFTs. It turns out that our formula…
The large-charge expansion in nonrelativistic conformal field theories
本论文探讨非相对论共形场论中的大荷展开方法，通过态-算符对应将计算简化为有限密度系统的能级评估，揭示了具有全局对称性系统的普适特征，为凝聚态等实验相关系统提供预测工具。
We study whether the relations between the Weyl anomaly, entanglement entropy (EE), and thermal entropy of a two-dimensional (2D) conformal field theory (CFT) extend to 2D boundaries of 3D CFTs, or 2D defects of $D \geq 3$ CFTs. The Weyl anomaly of a 2D boundary or defect defines two or three central charges, respectively. One of these, $b$, obeys a c-theorem, as in 2D CFT. For a 2D defect, we show that another, $d_2$, interpreted as the defect's `conformal dimension,' must be non-negative by the Averaged Null Energy Condition (ANEC). We show that the EE of a sphere centered on a planar defect…
We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special …
The role played by the Euler anomaly in the dictionary relating sphere partition functions of four dimensional theories of class $\mathcal{S}$ and two dimensional nonrational CFTs is clarified. On the two dimensional side, this involves a careful treatment of scale factors in Liouville/Toda correlators. Using ideas from tinkertoy constructions for Gaiotto duality, a framework is proposed for evaluating these scale factors. The representation theory of Weyl groups plays a critical role in this framework.
We use modular invariance to derive constraints on the spectrum of warped conformal field theories (WCFTs) --- nonrelativistic quantum field theories described by a chiral Virasoro and $U(1)$ Kac-Moody algebra. We focus on holographic WCFTs and interpret our results in the simplest holographic set up: three dimensional gravity with Compere-Song-Strominger boundary conditions. Holographic WCFTs feature a negative $U(1)$ level that is responsible for negative norm descendant states. Despite the violation of unitarity we show that the modular bootstrap is still viable provided the (Virasoro-Kac-M…
Auxiliary-Field Formalism for Higher-Derivative Boundary CFTs
本文通过引入辅助场方法，研究高导数边界CFTs的共形场理论，计算热核、Seeley-DeWitt系数及边界电荷，揭示其与曲率背景下的共形边界条件关系。
Nonrelativistic Dirac fermions on the torus
本文研究环面上由质量项和化学势变形的狄拉克费米子理论，利用扭曲边界条件的傅里叶变换得到环面自由能的对偶表示，并推导出高能态密度的类Cardy公式。
Unitary conformal field theories (CFTs) are believed to have positive (non-negative) energy correlators. Energy correlators are universal observables in higher-dimensional CFTs built out of integrated Wightman functions of the stress-energy tensor. We analyze energy correlators in parity invariant four-dimensional CFTs. The goal is to use the positivity of energy correlators to further constrain unitary CFTs. It is known that the positivity of the simplest one-point energy correlator implies that 1/3 <= a/c <= 31/18 where a and c are the Weyl anomaly coefficients. We use the positivity of high…
Motivated by questions about quantum information and classification of quantum field theories, we consider Conformal Field Theories (CFTs) in spacetime dimension $d\geq 5$ with a conformally-invariant spatial boundary (BCFTs) or $4$-dimensional conformal defect (DCFTs). We determine the boundary or defect contribution to the Weyl anomaly using the standard algorithm, which includes imposing Wess-Zumino consistency and fixing finite counterterms. These boundary/defect contributions are built from the intrinsic and extrinsic curvatures, as well as the pullback of the ambient CFT's Weyl tensor. F…
There is a widely held belief that conformal field theories (CFTs) require zero beta functions. Nevertheless, the work of Jack and Osborn implies that the beta functions are not actually the quantites that decide conformality, but until recently no such behavior had been exhibited. Our recent work has led to the discovery of CFTs with nonzero beta functions, more precisely CFTs that live on recurrent trajectories, e.g., limit cycles, of the beta-function vector field. To demonstrate this we study the S function of Jack and Osborn. We use Weyl consistency conditions to show that it vanishes at …
We compute the full asymptotic symmetry group of black holes belonging to the same equivalence class of solutions within the Conformal Weyl Gravity formalism. We do this within an $AdS_2/CFT_1$ correspondence and by performing a Robinson-Wilczek two dimensional reduction, thus enabling the construction of an effective quantum theory of the remaining field content. The resulting energy momentum tensors generate asymptotic Virasoro algebras, to $s$-wave, with calculable central extensions. These centers in conjunction with their proper regularized lowest Virasoro eigen-modes yield the Bekenstein…
When conformal field theories (CFTs) are perturbed by marginally relevant deformations, renormalization group (RG) flows ensue that can be studied with perturbative methods, at least as long as they remain close to the original CFT. In this work we study such RG flows in the vicinity of six-dimensional unitary CFTs. Neglecting effects of scalar operators of dimension two and four, we use Weyl consistency conditions to prove the $a$-theorem in perturbation theory, and establish that scale implies conformal invariance. We identify a quantity that monotonically decreases in the flow to the infrar…
We formulate the chiral vortical effect (CVE) and its generalization called generalized vortical effect using the semiclassical theory of wave packet dynamics. We take the spin-vorticity coupling into account and calculate the transport charge current by subtracting the magnetization one from the Noether local one. We find that the transport charge current in the CVE always vanishes in relativistic chiral fermions. This result implies that it cannot be observed in transport experiments in condensed matter systems such as Dirac/Weyl semimetals with the pseudo-Lorentz symmetry. We also demonstra…
AdS$_3$ Einstein Gravity and Boundary Description: Pedagogical Review
本文综述了带有负宇宙学常数的AdS$_3$ Einstein引力理论，指出其边界自由度可由2D Schwarzian理论描述，并探讨了模对称性破缺、配分函数一圈精确性及全息原理等特性。
We initiate a systematic study of `t Hooft anomalies in Galilean field theories, focusing on two questions therein. In the first, we consider the non-relativistic theories obtained from a discrete light-cone quantization (DLCQ) of a relativistic theory with flavor or gravitational anomalies. We find that these anomalies survive the DLCQ, becoming mixed flavor/boost or gravitational/boost anomalies. We also classify the pure Weyl anomalies of Schrödinger theories, which are Galilean conformal field theories (CFTs) with $z=2$. There are no pure Weyl anomalies in even spacetime dimension, and the…
The Ambient Space Formalism
本文提出环境空间形式体系，通过构造外尔协变几何对象求解CFT运动学约束，应用于热态和挤压球面，计算2点函数并与热OPE及全息结果精确一致，且给出双扭曲系数计算方法。
In this thesis we analyse three aspects of Conformal Field Theories (CFTs). First, we consider correlation functions of descendant states in two-dimensional CFTs. We discuss a recursive formula to calculate them and provide a computer implementation of it. This allows us to obtain any correlation function of vacuum descendants, and for non-vacuum descendants to express the correlator as a differential operator acting on the respective primary correlator. With this code, we study some entanglement and distinguishability measures between descendant states, i.e. the Rényi entropy, trace square di…
The tensors which may be defined on the conformal manifold for six dimensional CFTs with exactly marginal operators are analysed by considering the response to a Weyl rescaling of the metric in the presence of local couplings. It is shown that there are three symmetric two index tensors only one of which satisfies any positivity conditions. The general results are specialised to the six dimensional conformal theory defined by free two-forms and also to the interacting scalar $ϕ^3$ theory at two loops which preserves conformal invariance to this order. All three two index tensor contributions a…
It was found by Hung, Myers and Smolkin that there is entropy discrepancy for the CFTs in 6-dimensional space-time, between the field theoretical and the holographic analysis. Recently, two different resolutions to this puzzle have been proposed. One of them suggests to utilize the anomaly-like entropy and the generalized Wald entropy to resolve the HMS puzzle, while the other one initiates to use the entanglement entropy which arises from total derivative terms in the Weyl anomaly to explain the HMS mismatch. We investigate these two proposals carefully in this note. By studying the CFTs dual…
We make a detailed study of the infinite dimensional Galilean Conformal Algebra (GCA) in the case of two spacetime dimensions. Classically, this algebra is precisely obtained from a contraction of the generators of the relativistic conformal symmetry in 2d. Here we find quantum mechanical realisations of the (centrally extended) GCA by considering scaling limits of certain 2d CFTs. These parent CFTs are non-unitary and have their left and right central charges become large in magnitude and opposite in sign. We therefore develop, in parallel to the usual machinery for 2d CFT, many of the tools …
We study the free energy of four-dimensional CFTs on deformed spheres. For generic nonsupersymmetric CFTs only the coefficient of the logarithmic divergence in the free energy is physical, which is an extremum for the round sphere. We then specialize to $\mathcal{N}=2$ SCFTs where one can preserve some supersymmetry on a compact manifold by turning on appropriate background fields. For deformations of the round sphere the $c$ anomaly receives corrections proportional to the supersymmetric completion of the (Weyl)$^2$ term, which we determine up to one constant by analyzing the scale dependence…
The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important \qo{Pauli Exclusion Principle} but by the adoption of the complex standard relativistic quantum field theory. In a recent paper (Ref. [1]) we presented a proof of the spin-statistics problem in the nonrelativistic approximation on the basis of the \qo{Conformal Quantum Geometrodynamics}. In the present paper, by the same theory the proof of the Spin-Statistics Theorem is extended to the relativistic domain in the general scenario of curved spacetime. The re…
We explore the consequences of conformal symmetry for the operator product expansions in nonrelativistic field theories. Similar to the relativistic case, the OPE coefficients of descendants are related to that of the primary. However, unlike relativistic CFTs the 3-point function of primaries is not completely specified by conformal symmetry. Here, we show that the 3-point function between operators with nonzero particle number, where (at least) one operator has the lowest dimension allowed by unitarity, is determined up to a numerical coefficient. We also look at the structure of the family …
Integral quantization based on the Heisenberg-Weyl group
本文提出一种基于 Heisenberg-Weyl 群相干态的相对论性积分量子化框架，利用正定算符值测度处理 Minkowski 时空中的无自旋粒子运动，并证明其在一维谐振子量子化中能恢复标准 Hamiltonian。
We study deformations of three-dimensional large N CFTs by double-trace operators constructed from spin s single-trace operators of dimension Δ. These theories possess UV fixed points, and we calculate the change of the 3-sphere free energy δF= F_{UV}- F_{IR}. To describe the UV fixed point using the dual AdS_4 space we modify the boundary conditions on the spin s field in the bulk; this approach produces δF in agreement with the field theory calculations. If the spin s operator is a conserved current, then the fixed point is described by an induced parity invariant conformal spin s gauge theo…
Conformal Carroll Scalars with Boosts
针对弯曲背景上共形Carroll理论缺少局域boost对称性的问题，本文构造任意维度下两类无迹、boost与Weyl不变的标量作用量，并表明空间型可约化为低维Euclidean CFT。
In this work we elaborate on an extension of the AdS/CFT framework to a subclass of gravitational theories with vanishing cosmological constant. By building on earlier ideas, we construct a correspondence between Ricci-flat spacetimes admitting asymptotically hyperbolic hypersurfaces and a family of conformal field theories on a codimension two manifold at null infinity. By truncating the gravity theory to the pure gravitational sector, we find the most general spacetime asymptotics, renormalize the gravitational action, reproduce the holographic stress tensors and Ward identities of the famil…
Gaplessness protected by bulk-edge correspondence
本文证明由非幺正共形场论构造的 Gaffnian 和 Haldane-Rezayi 分数量子霍尔态在保持体-边对应时难以打开能隙，指出其根源在于单值荷与简单荷不匹配及 Galois shuffle 等非局域结构，并提出判断拓扑有序态是否有能隙及局域性的新判据。
After a brief outline of general aspects of conformal field theories in coordinate space, in a first part we review the solution of the conformal constraints of three- and four-point functions in momentum space in dimensions $d\geq 2$, in the form of conformal Ward identities (CWI's). We center our discussion on the analysis of correlators containing stress-energy tensors $(T)$, conserved currents $(J)$, and scalar operators $(O)$. For scalar four-point functions, we briefly discuss our method for determining the dual conformal solutions of such equations, identified only by the CWI's, and rel…
In the first part of the thesis we focus on local symmetries. We review a self-consistent framework that we employed in order to discuss the dynamics of the theories of interest. Its merit lies in that we can make the symmetry group act internally and thus be effectively separated from coordinate transformations. We investigate under which conditions it is not needed to introduce extra compensating fields to make relativistic as well as nonrelativistic theories invariant under local symmetries and more precisely under scale transformations. We clarify the role that torsion plays in this contex…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。