Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2009-10-30
PoS LAT2009:218,2009
Physics
High Energy Physics
High Energy Physics - Lattice
7 pages, 8 figures, talk given by Y. Meurice at Lattice 2009, PoS(LAT2009)218
Scientific paper
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.
Bazavov Alexei
Denbleyker Alan
Du Daping
Meurice Yannick
Velytsky Alexander
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