Two-point Functions and Bootstrap Applications in Quantum Field Theories

TL;DR

This paper investigates two-point functions and spectral representations in UV complete quantum field theories, exploring their relation to central charges, c-theorems, and bootstrap problems across various dimensions.

Contribution

It provides new insights into the spectral structure of two-point functions, re-derives c-theorems in 2D, and formulates bootstrap problems for stress tensor form factors in generic dimensions.

Findings

Established connection between two-point functions and central charges.

Re-derived c-theorems in two dimensions.

Formulated bootstrap problems for stress tensor form factors.

Abstract

We study two-point functions of local operators and their spectral representation in UV complete quantum field theories in generic dimensions focusing on conserved currents and the stress-tensor. We establish the connection with the central charges of the UV and IR fixed points. We re-derive c-theorems in 2d and show the absence of their direct analogs in higher dimensions. We conclude by focusing on quantum field theories with a mass gap. We study the stress tensor two-particle form factor, derive implications of unitarity and define concrete bootstrap problems in generic dimensions.