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Dyson's Instability in Lattice Gauge Theory
Conference proceeding   Open access

Dyson's Instability in Lattice Gauge Theory

A Bazavov, A Denbleyker, Daping Du, Y Meurice, A Velytsky and Haiyuan Zou
The XXVII International Symposium on Lattice Field Theory (LAT2009) - Theoretical Developments
Proceedings of Science, v. 91
06/23/2010
DOI: 10.22323/1.091.0218
url
https://doi.org/10.22323/1.091.0218View
Published (Version of record) Open Access

Abstract

We discuss Dyson's argument that the vacuum is unstable under a change g^2 -> - g^2, in the context of lattice gauge theory. For compact gauge groups, the partition function is well defined at negative g^2, but the average plaquette P has a discontinuity when g^2 changes sign. This reflects a change of vacuum rather than a loss of vacuum. In addition, P has poles in the complex g^2 plane, located at the complex zeros of the partition function (Fisher's zeros). We discuss the relevance of these singularities for lattice perturbation theory. We present new methods to locate Fisher's zeros using numerical values for the density of state in SU(2) and U(1) pure gauge theory. We briefly discuss similar issues for O(N) nonlinear sigma models where the local integrals are also over compact spaces.
 Mathematical Models Perturbation Theory Gauge theory Partitions Partitions (mathematics) Singularities Stability

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