Duality Defects

Abstract

We propose a unified approach to a general class of codimension-2 defects in field theories with non-trivial duality symmetries and discuss various constructions of such "duality defects" in diverse dimensions. In particular, in d=4 we propose a new interpretation of the Seiberg-Witten u-plane by "embedding" it in the physical space-time: we argue that it describes a BPS configuration of two duality defects (at the monopole/dyon points) and propose its vast generalization based on Lefschetz fibrations of 4-manifolds.

Figures (3)

• Figure 1: Identifying $D \cong {\mathbb R}^2$ with a cigar offers another perspective on a codimension-2 duality defect: it corresponds to a boundary condition in $(d-1)$-dimensional theory obtained by a compactification on $S^1$ with a duality twist by $\gamma \in \Gamma$.
• Figure 2: The simplest holomorphic map $D \to {\mathcal{M}}_C$ is given by identifying the space-time $(x^2,x^3)$ plane with the $u$-plane.
• Figure 3: Lefschetz fibration defines a $\frac{1}{4}$-BPS configuration of duality defects at the locations of singular fibers.