A semiclassical formula for the topological susceptibility in a finite space-time volume

The volume dependence of the topological susceptibility (Q: topological charge, V: space-time volume in four-dimensional non-abelian gauge theories is studied. For small volumes, χ_t^V is shown to be dominated by the one-instanton contribution and is therefore analytically calculable. It turns out that χ_t^V increases monotonically with V. If this property continues to hold beyond the small volume range, a lower bound on χ_t = lim_V→∞χ_t^V can be obtained. For an SU(3) gauge group it reads χ_t?5Λ_MS⁴.