How glueball mass shapes the vacuum energy between boundaries

Non-abelian gauge theories occupy a peculiar middle ground: massless at high energies, massive at low energies, so their Casimir energy should shift from polynomial to exponential decay with boundary separation. Using lattice Monte Carlo methods, this thesis maps that crossover by measuring how vacuum energy depends on boundary conditions and separation distance. The central test is whether the lightest glueball mass sets the decay rate in the infrared regime. The results help connect the non-perturbative mass gap in pure gauge theory to a directly measurable geometric quantity.