Lightcone Commutator and Stress-Tensor Exchange in $d>2$ CFTs

Stress-Tensor Commutator in CFT near the Lightcone

Starting with the general stress-tensor commutation relations consistent with the Poincaré algebra in local quantum field theory, we impose the tracelessness condition and focus on the dominating contributions in the lightcone limit. It is shown that, under a certain assumption on the Schwinger term, a Virasoro-algebra-like structure emerges near the lightcone in $d>2$ conformal field theories.

Lightcone Effective Hamiltonians and RG Flows

We present a prescription for an effective lightcone (LC) Hamiltonian that includes the effects of zero modes, focusing on the case of Conformal Field Theories (CFTs) deformed by relevant operators. We show how the prescription resolves a number of issues with LC quantization, including i) the apparent non-renormalization of the vacuum, ii) discrepancies in critical values of bare parameters in equal-time vs LC quantization, and iii) an inconsistency at large N in CFTs with simple AdS duals. We describe how LC quantization can drastically simplify Hamiltonian truncation methods applied to some…

On Local and Integrated Stress-Tensor Commutators

We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and th…

Near Lightcone Thermal Conformal Correlators and Holography

Heavy-heavy-light-light (HHLL) correlators of pairwise identical scalars in CFTs with a large central charge in any number of dimensions admit a double scaling limit where the ratio of the heavy conformal dimension to the central charge becomes large as the separation between the light operators becomes null. In this limit the stress tensor sector of a generic HHLL correlator receives contributions from the multi stress tensor operators with any number of stress tensors, as long as their twist is not increased by index contractions. We show how one can compute this leading twist stress tensor …

Dispersion Formulas in QFTs, CFTs, and Holography

We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At $n$-points, the QF…

高维中多重应力张量的重求和

Resummation of Multi-Stress Tensors in Higher Dimensions

本文研究了全息共形场论中多重应力张量偏微分方程的精确解，通过重求和发现 d=2 下关联子可用 Bessel 函数表示并得到 Virasoro 真空块，而 d=4 下重求和会导致本质奇点，并证明了关联子可通过特定模式重建。