# Poster presented by Tilo Wettig

Poster Session

Topic: Theoretical Developments

### Random matrix theory, chiral perturbation theory, and lattice data

Abstract: The distribution and the correlations of the small eigenvalues of the Dirac operator are desribed by random matrix theory (RMT) up to an energy $\propto 1/\sqrt{V}$, where $V$ is the physical volume. For somewhat larger energies, the same quantities can be described by chiral perturbation theory (chPT). There is an intermediate energy regime, roughly $1/V\ll E \ll 1/\sqrt{V}$, where the results of RMT and chPT are predicted to agree with each other. We test these predictions by constructing the connected and disconnected chiral susceptibilities from Dirac spectra obtained in quenched SU(2) and SU(3) simulations with staggered fermions for a variety of lattice sizes and coupling constants. In deriving the predictions of chPT, it is important to take into account the symmetries of staggered fermions which are different in SU(2) and SU(3), as are the RMT ensembles describing these two cases.

Massimo Campostrini,   campo@mailbox.difi.unipi.it