5d Field Theories and M Theory

TL;DR

This paper develops an M theory framework for 5d field theories using polynomial descriptions, resolving singularities and revealing small corrections related to instantons, and proposes a diagrammatic approach for these polynomials.

Contribution

It introduces a polynomial-based M theory description of 5d field theories that addresses singularities and connects to instanton corrections, offering a new diagrammatic perspective.

Findings

Resolved singularities at vertices in 5d theories

Identified exponentially small instanton corrections

Proposed a diagrammatic representation of polynomials in two variables

Abstract

5-brane configurations describing 5d field theories are promoted to an M theory description a la Witten in terms of polynomials in two complex variables. The coefficients of the polynomials are the Coulomb branch. This picture resolves apparent singularities at vertices and reveals exponentially small corrections. These corrections ask to be compared to world line instanton corrections. From a different perspective this procedure may be used to define a diagrammatic representation of polynomials in two variables.