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arXiv · hep-th/9910190

On Finite-Volume Gauge Theory Partition Functions

G. Akemann·P. H. Damgaard
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Abstract

We prove a Mahoux-Mehta--type theorem for finite-volume partition functions of SU(N_c\geq 3) gauge theories coupled to fermions in the fundamental representation. The large-volume limit is taken with the constraint V << 1/m_π^4. The theorem allows one to express any k-point correlation function of the microscopic Dirac operator spectrum entirely in terms of the 2-point function. The sum over topological charges of the gauge fields can be explicitly performed for these k-point correlation functions. A connection to an integrable KP hierarchy, for which the finite-volume partition function is a $τ$-function, is pointed out. Relations between the effective partition functions for these theories in 3 and 4 dimensions are derived. We also compute analytically, and entirely from finite-volume partition functions, the microscopic spectral density of the Dirac operator in SU(N_c) gauge theories coupled to quenched fermions in the adjoint representation. The result coincides exactly with earlier results based on Random Matrix Theory.

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G. Akemann, P. H. Damgaard. 2000-03-03. On Finite-Volume Gauge Theory Partition Functions. https://doi.org/10.1016/s0550-3213(00)00119-x

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