Exotic theta terms in 2+1d fractonic field theory

TL;DR

This paper investigates exotic theta terms in 2+1d fractonic field theories, revealing new topological effects and generalized Witten effects involving vortex operators with subsystem charges.

Contribution

It introduces and analyzes bulk and foliated theta terms in fractonic field theories, showing their impact on vortex operator charges and classical equations of motion.

Findings

Foliated theta term allows spatially varying theta angles without classical effects.

Both theta terms induce vortex operators to carry subsystem charges.

Vortex operators can acquire quadrupolar momentum charges in the foliated case.

Abstract

In this work, we study exotic theta terms in the 2+1d $\phi$-theory, which provides a continuum description of the XY-plaquette model. The $\phi$-theory can be viewed as a fractonic analogue of the 1+1d compact boson and exhibits momentum and winding subsystem symmetries. In this theory, discontinuous field configurations play a crucial role. Although such configurations spoil the naive topology of the field, they induce nontrivial backreactions that give rise to new topological terms. We study two types of theta terms, which we call the bulk theta term and the foliated theta term. The foliated theta term is constructed by coupling winding currents on neighboring leaves of a foliation. Remarkably, the corresponding theta angle can vary spatially without affecting the classical equations of motion. Both theta terms lead to generalized Witten effects, in which vortex operators carrying winding subsystem charge acquire momentum subsystem charge. In the case of the foliated theta angle, the Witten effect exhibits a more intricate structure: vortex operators acquire a quadrupolar momentum charge. We demonstrate these features using lattice realizations based on the modified Villain formulation.