PUB - Publikationen an der Universität Bielefeld

Dirac operator eigenvalues split into two when subjected to two differentexternal vector sources. In a specific finite-volume scaling regime of gaugetheories with fermions, this problem can be mapped to a chiral RandomTwo-Matrix Theory. We derive analytical expressions to leading order in theassociated finite-volume expansion, showing how individual Dirac eigenvaluedistributions and their correlations equivalently can be computed directly fromthe effective chiral Lagrangian in the epsilon-regime. Because of itsequivalence to chiral Random Two-Matrix Theory, we use the latter for allexplicit computations. On the mathematical side, we define and determine gapprobabilities and individual eigenvalue distributions in that theory at finiteN, and also derive the relevant scaling limit as N is taken to infinity. Inparticular, the gap probability for one Dirac eigenvalue is given in terms of anew kernel that depends on the external vector source. This expression may givea new and simple way of determining the pion decay constant F_pi from latticegauge theory simulations.