Higher-form anomalies and state-operator correspondence beyond conformal invariance

TL;DR

This paper develops a state-operator correspondence for non-conformal quantum field theories with higher-form symmetries and anomalies, revealing a rich algebraic structure and explicit examples beyond conformal invariance.

Contribution

It introduces a novel state-operator correspondence for non-conformal theories with higher-form symmetries, generalizing conformal results and explicitly constructing the associated algebra.

Findings

Constructs an infinite tower of conserved charges satisfying a higher-dimensional current algebra.

Demonstrates the correspondence explicitly in free theories via Euclidean path integrals and canonical quantization.

Shows that the vacuum state in non-conformal theories is a squeezed vacuum, not the true ground state.

Abstract

We establish a state-operator correspondence for a class of non-conformal quantum field theories with continuous higher-form symmetries and a mixed anomaly. Such systems can always be realised as a relativistic superfluid. The symmetry structure induces an infinite tower of conserved charges, which we construct explicitly. These charges satisfy an abelian current algebra with a central extension, generalising the familiar Kac-Moody algebras to higher dimensions. States and operators are organised into representations of this algebra, enabling a direct correspondence. We demonstrate the correspondence explicitly in free examples by performing the Euclidean path integral on a $d$-dimensional ball, with local operators inserted in the origin, and matching to energy eigenstates on $S^{d-1}$ obtained by canonical quantisation. Interestingly, in the absence of conformal invariance, the empty path integral prepares a squeezed vacuum rather than the true ground state.