Absence of stress energy tensor in CFT_2 models

Generalized free fields and the AdS-CFT correspondence

Motivated by structural issues in the AdS-CFT correspondence, the theory of generalized free fields is reconsidered. A stress-energy tensor for the generalized free field is constructed as a limit of Wightman fields. Although this limit is singular, it fulfils the requirements of a conserved local density for the Poincar'e generators. An explicit "holographic" formula relating the Klein-Gordon field on AdS to generalized free fields on Minkowski space-time is provided, and contrasted with the "algebraic" notion of holography. A simple relation between the singular stress-energy tensor and the …

The Cocycle of the Quantum HJ Equation and the Stress Tensor of CFT

We consider two theorems formulated in the derivation of the Quantum Hamilton-Jacobi Equation from the EP. The first one concerns the proof that the cocycle condition uniquely defines the Schwarzian derivative. This is equivalent to show that the infinitesimal variation of the stress tensor "exponentiates" to the Schwarzian derivative. The cocycle condition naturally defines the higher dimensional version of the Schwarzian derivative suggesting a role in the transformation properties of the stress tensor in higher dimensional CFT. The other theorem shows that energy quantization is a direct co…

Calculus on manifolds of conformal maps and CFT

In conformal field theory (CFT) on simply connected domains of the Riemann sphere, the natural conformal symmetries under self-maps are extended, in a certain way, to local symmetries under general conformal maps, and this is at the basis of the powerful techniques of CFT. Conformal maps of simply connected domains naturally have the structure of an infinite-dimensional groupoid, which generalizes the finite-dimensional group of self-maps. We put a topological structure on the space of conformal maps on simply connected domains, which makes it into a topological groupoid. Further, we (almost) …

高亏格黎曼面上的全息应力张量关联函数

Holographic stress tensor correlators on higher genus Riemann surfaces

本文利用Schottky单值化技术在AdS₃/CFT₂框架下研究高亏格黎曼面上的全息应力张量关联函数，推导四点关联函数及更高点递推关系，并揭示截断AdS₃空间中T\bar{T}变形理论低点关联函数的新性质。

Conformal loop ensembles and the stress-energy tensor. II. Construction of the stress-energy tensor

This is the second part of a work aimed at constructing the stress-energy tensor of conformal field theory (CFT) as a local "object" in conformal loop ensembles (CLE). This work lies in the wider context of re-constructing quantum field theory from mathematically well-defined ensembles of random objects. In the present paper, based on results of the first part, we identify the stress-energy tensor in the dilute regime of CLE. This is done by deriving both its conformal Ward identities for single insertion in CLE probability functions, and its properties under conformal transformations involvin…

从AdS视角探讨非局域缺陷CFT中的保护算符

Protected operators in non-local defect CFTs from AdS

研究非局域缺陷CFT中保护算符的存在机制，通过AdS空间中的对称性破缺解释保护量子数的来源，涵盖缺陷RG流、长程Landau-Ginzburg模型等案例。