Phases of Antisymmetric Tensor Field Theories

TL;DR

This paper analyzes the different phases of antisymmetric tensor field theories in various dimensions, revealing dual descriptions and phase transitions including Coulomb, confinement, and Higgs phases, with applications to QED, string theory, and axion models.

Contribution

It develops a unified framework for understanding phase structures of antisymmetric tensor theories, extending previous work and providing explicit low-energy effective actions.

Findings

Identifies dual descriptions for each phase involving massless and massive tensors.

Demonstrates phase transitions in compact QED and related models.

Maintains T-duality in string-inspired models with instantons.

Abstract

We study the different phases of field theories of compact antisymmetric tensors of rank $h-1$ in arbitrary space-time dimensions $D=d+1$. Starting in a `Coulomb' phase, topological defects of dimension $d-h-1$ ($(d-h-1)$-branes) may condense leading to a generalized `confinement' phase. If the dual theory is also compact the model may also have a third, generalized `Higgs' phase, driven by the condensation of the dual $(h-2)$-branes. Developing on the work of Julia and Toulouse for ordered solid-state media, we obtain the low energy effective action for these phases. Each phase has two dual descriptions in terms of antisymmetric tensors of different ranks, which are massless for the Coulomb phase but massive for the Higgs and confinement phases. We illustrate our prescription in detail for compact QED in 4D. Compact QED and $O(2)$ models in 3D, as well as a periodic scalar field in 2D (strings on a circle), are also discussed. In this last case we show how $T$-duality is maintained if one considers both worldsheet instantons and their duals. We also unify various approaches to the problem of the axion mass in 4D string models. Finally we discuss possible implications of our results for non-perturbative issues in string theory.