Shell formulas for instantons and gauge origami

TL;DR

The paper introduces the shell formula framework that unifies and simplifies the computation of various partition functions in gauge theories and related physical systems.

Contribution

It provides explicit closed-form expressions and recursion relations for instanton partition functions and gauge origami configurations across multiple dimensions.

Findings

Unified description of partition functions via shell formulas

Explicit formulas and recursion relations for diverse gauge theories

Application to Donaldson-Thomas invariants in complex spaces

Abstract

We introduce the shell formula-a framework that unifies the description of partition functions whose pole structures are classified by Young diagrams of arbitrary dimension. The formalism yields explicit closed-form expressions and recursion relations for a wide range of physical systems, including instanton partition functions of 5d pure super Yang-Mills theory with classical gauge groups, as well as gauge origami configurations such as the magnificent four, tetrahedron instantons, spiked instantons, and Donaldson-Thomas invariants in $\mathbb{C}^3$ and $\mathbb{C}^4$.