Construction of 4d SYM compactified on open Riemann surfaces by the superfield formalism

TL;DR

This paper explores how to preserve supersymmetry when compactifying 4d N=4 super Yang-Mills theory on open Riemann surfaces with boundaries, using superfield formalism to include boundary degrees of freedom.

Contribution

It introduces a superfield formalism approach to incorporate boundary degrees of freedom in twisted compactifications of 4d SYM on Riemann surfaces with boundaries, maintaining supersymmetry.

Findings

Boundary degrees of freedom can be added while preserving supersymmetry.

Superfield formalism effectively describes boundary conditions and degrees of freedom.

The approach facilitates analysis of S-duality transformations involving boundaries.

Abstract

By compactifying gauge theories on a lower dimensional manifold, we often find many interesting relationships between a geometry and a supersymmetric quantum field theory. In this paper we consider conformal field theories obtained from twisted compactification on a Riemann surface with a boundary. Various kinds of supersymmetric boundary conditions are exchanged under S-duality. To consider these transformations one need to take into account boundary degrees of freedom. So we study how the degrees of freedom can be added at the boundary of the Riemann surface. In this paper I show that this introduction of the boundary fields can be done preserving supersymmetry by means of 2-dimensional superfields.