指出了D维共形场论与D'维对偶共振模型之间的精确对应，其中D'可能不同于D。由Veneziano开创的对偶共振模型是弦论的先驱。类似的散射振幅称为梅林振幅;它们依赖于复变量，复变量代替了散射振幅依赖的曼德尔维变量。梅林振幅满足精确的对偶性--即单变量中具有简单极点的亚纯性和交叉对称性--以及算子乘积展开（OPE）所隐含的适当形式的因式分解。对偶性是D-独立的性质。主导极点的位置由OPE中的场的维数给出;它们的留数依赖于D并确定卫星。讨论了D到D-1和D+1的降维和诱导。降维导致Anti de Sitter空间的出现。
英文摘要：
An exact correspondence is pointed out between conformal field theories in D dimensions and dual resonance models in D' dimensions, where D' may differ from D. Dual resonance models, pioneered by Veneziano, were forerunners of string theory. The analog of scattering amplitudes are called Mellin amplitudes; they depend on complex variables which substitute for the Mandelstam variables on which scattering amplitudes depend. The Mellin amplitudes satisfy exact duality - i.e. meromorphy with simple poles in single variables, and crossing symmetry - and an appropriate form of factorization which is implied by operator product expansions (OPE). Duality is a D-independent property. The positions of the leading poles are given by the dimensions of fields in the OPE; their residues depend on D and determine satellites. Dimensional reduction and induction D goes to D-1 and D+1 are discussed. Dimensional reduction leads to the appearence of Anti de Sitter space.
In this paper we study classical limit of conformal field theories realized by large N gauge theories using the generalized coherent states. For generic large N gauge theories with conformal symmetry, we show that the classical limit of them is described by the classical Einstein gravity. This may be regarded as a kind of derivation of the AdS/CFT correspondence.
We construct Euclidean Liouville conformal field theories in odd number of dimensions. The theories are nonlocal and non-unitary with a log-correlated Liouville field, a ${\cal Q}$-curvature background, and an exponential Liouville-type potential. We study the classical and quantum properties of these theories including the finite entanglement entropy part of the sphere partition function $F$, the boundary conformal anomaly and vertex operators' correlation functions. We derive the analogue of the even-dimensional DOZZ formula and its semi-classical approximation.
We argue that conformal invariance is a common thread linking several scalar effective field theories that appear in the double copy and scattering equations. For a derivatively coupled scalar with a quartic ${\cal O}(p^4)$ vertex, classical conformal invariance dictates an infinite tower of additional interactions that coincide exactly with Dirac-Born-Infeld theory analytically continued to spacetime dimension $D=0$. For the case of a quartic ${\cal O}(p^6)$ vertex, classical conformal invariance constrains the theory to be the special Galileon in $D=-2$ dimensions. We also verify the conform…
We construct five-dimensional non-Lorentzian Lagrangian gauge field theories with an SU(1,3) conformal symmetry and 12 (conformal) supersymmetries. Such theories are interesting in their own right but can arise from six-dimensional (1,0) superconformal field theories on a conformally compactified Minkowski spacetime. In the limit that the conformal compactification is removed the Lagrangians we find give field theory formulations of DLCQ constructions of six-dimensional (1,0) conformal field theories.
Using a uniformization map we determine the holographic entanglement entropy for states of a Warped Conformal Field Theory dual to a generic vacuum metric in AdS$_3$ gravity with Compère--Song--Strominger boundary conditions. We point out how that expression could lead to inequalities that can be interpreted as quantum energy conditions for Warped Conformal Field Theories.
In boundary conformal field theories, global symmetries can be broken by boundary conditions, generating a homogeneous conformal manifold. We investigate these geometries, showing they have a coset structure, and give fully worked out examples in the case of free fields of spin zero and one-half. These results give a simple illustration of the salient features of conformal manifolds while generalising to interacting and more intricate setups. Our work was inspired by [2203.17157]
Supersymmetric three dimensional conformal sigma models
我们构造了三维超对称共形西格玛模型。三维非线性西格玛模型在微扰理论中是不可重正化的。我们使用非微扰方法中的Wilson重整化群方程方法来寻找不动点。不动点的存在性在这种方法中是非常重要的，以显示重正化。共形西格玛模型被定义为Wilson重整化群方程的不动点理论。具有反常维数的Wilson重整化群方程与修正的Ricci流方程一致。共形西格玛模型的特征在于一个参数，该参数对应于标量场的反常维数。当反常维数为$γ=-1/2$时，任何爱因斯坦-凯勒流形都对应于共形场论。在二维情形下，我们进一步研究了目标空间的性质，发现不动点理论的目标空间是紧的还是非紧的取决于反常维数的大小.这是根据E. I.
