# On Finite-Volume Gauge Theory Partition Functions

Akemann G, Damgaard PH (2000)

Nucl.Phys. B 576(1-3): 597-626.

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Akemann, Gernot

^{UniBi}; Damgaard, P. H.Abstract

We prove a Mahoux-Mehta--type theorem for finite-volume partition functionsof SU(N_c\geq 3) gauge theories coupled to fermions in the fundamentalrepresentation. The large-volume limit is taken with the constraint V <<1/m_{\pi}^4. The theorem allows one to express any k-point correlation functionof the microscopic Dirac operator spectrum entirely in terms of the 2-pointfunction. The sum over topological charges of the gauge fields can beexplicitly performed for these k-point correlation functions. A connection toan integrable KP hierarchy, for which the finite-volume partition function is a$\tau$-function, is pointed out. Relations between the effective partitionfunctions for these theories in 3 and 4 dimensions are derived. We also computeanalytically, and entirely from finite-volume partition functions, themicroscopic spectral density of the Dirac operator in SU(N_c) gauge theoriescoupled to quenched fermions in the adjoint representation. The resultcoincides exactly with earlier results based on Random Matrix Theory.

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Akemann G, Damgaard PH. On Finite-Volume Gauge Theory Partition Functions.

*Nucl.Phys. B*. 2000;576(1-3):597-626.Akemann, G., & Damgaard, P. H. (2000). On Finite-Volume Gauge Theory Partition Functions.

*Nucl.Phys. B*,*576*(1-3), 597-626. doi:10.1016/S0550-3213(00)00119-XAkemann, G., and Damgaard, P. H. (2000). On Finite-Volume Gauge Theory Partition Functions.

*Nucl.Phys. B*576, 597-626.Akemann, G., & Damgaard, P.H., 2000. On Finite-Volume Gauge Theory Partition Functions.

*Nucl.Phys. B*, 576(1-3), p 597-626. G. Akemann and P.H. Damgaard, “On Finite-Volume Gauge Theory Partition Functions”,

*Nucl.Phys. B*, vol. 576, 2000, pp. 597-626. Akemann, G., Damgaard, P.H.: On Finite-Volume Gauge Theory Partition Functions. Nucl.Phys. B. 576, 597-626 (2000).

Akemann, Gernot, and Damgaard, P. H. “On Finite-Volume Gauge Theory Partition Functions”.

*Nucl.Phys. B*576.1-3 (2000): 597-626.
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arXiv hep-th/9910190