Dilaton shifts, probability measures, and decomposition

TL;DR

This paper explores dilaton shifts in 2D quantum field theories with higher-form symmetries, providing a universal formula and discussing their relation to decomposition and ensembles.

Contribution

It introduces a general formula for dilaton shifts in theories with higher-form symmetries and analyzes their connection to decomposition phenomena.

Findings

Dilaton shifts have a universal form reflecting noninvertible symmetries

Derived a general formula for dilaton shifts in 2D QFTs

Discussed the relation between decomposition and ensemble interpretations

Abstract

In this paper we discuss dilaton shifts (Euler counterterms) arising in decomposition of two-dimensional quantum field theories with higher-form symmetries. These take a universal form, reflecting underlying (noninvertible, quantum) symmetries. The first part of this paper constructs a general formula for such dilaton shifts, and discusses related computations. In the second part of this paper, we comment on the relation between decomposition and ensembles.