Gravitational form factors and decoupling in 2D

TL;DR

This paper computes non-local gravitational form factors in 2D curved space for various quantum fields, revealing a generalized Polyakov action and a gravitational decoupling theorem in UV and IR limits.

Contribution

It provides a detailed analysis of gravitational form factors for different spins in 2D, including their UV and IR behaviors, and establishes a gravitational decoupling theorem.

Findings

Generalized running form of the Polyakov action in UV.

Standard Polyakov action in conformally invariant cases.

Gravitational decoupling theorem in IR.

Abstract

We calculate and analyse non-local gravitational form factors induced by quantum matter fields in curved two-dimensional space. The calculations are performed for scalars, spinors and massive vectors by means of the covariant heat kernel method up to the second order in the curvature and confirmed using Feynman diagrams. The analysis of the ultraviolet (UV) limit reveals a generalized "running" form of the Polyakov action for a nonminimal scalar field and the usual Polyakov action in the conformally invariant cases. In the infrared (IR) we establish the gravitational decoupling theorem, which can be seen directly from the form factors or from the physical beta function for fields of any spin.