# Glueballs on the three-sphere

## TL;DR

This paper investigates non-perturbative effects in SU(2) gauge theory on a three-sphere by deriving an effective low-energy Hamiltonian, incorporating theta dependence, and computing the glueball spectrum.

## Contribution

It introduces a method to derive an effective Hamiltonian for low-energy modes of SU(2) gauge theory on a three-sphere, including non-perturbative theta effects, and calculates the glueball spectrum.

## Key findings

- Derived one-loop corrected effective Hamiltonian.
- Incorporated theta dependence via boundary conditions.
- Computed the glueball spectrum using a variational approach.

## Abstract

We study the non-perturbative effects of the global features of the configuration space for SU(2) gauge theory on the three-sphere. The strategy is to reduce the full problem to an effective theory for the dynamics of the low-energy modes. By explicitly integrating out the high-energy modes, the one-loop correction to the effective hamiltonian is obtained. Imposing the $\theta$ dependence through boundary conditions in configuration space incorporates the non-perturbative effects of the non-contractable loops in the full configuration space. After this we obtain the glueball spectrum of the effective theory with a variational method.