Lattice gluodynamics at negative g^2
arXiv:hep-lat/0410029 · doi:10.1103/PhysRevD.71.016008
Abstract
We consider Wilson's SU(N) lattice gauge theory (without fermions) at negative values of beta= 2N/g^2 and for N=2 or 3. We show that in the limit beta -> -infinity, the path integral is dominated by configurations where links variables are set to a nontrivial element of the center on selected non intersecting lines. For N=2, these configurations can be characterized by a unique gauge invariant set of variables, while for N=3 a multiplicity growing with the volume as the number of configurations of an Ising model is observed. In general, there is a discontinuity in the average plaquette when g^2 changes its sign which prevents us from having a convergent series in g^2 for this quantity. For N=2, a change of variables relates the gauge invariant observables at positive and negative values of beta. For N=3, we derive an identity relating the observables at beta with those at beta rotated by +- 2pi/3 in the complex plane and show numerical evidence for a Ising like first order phase transition near beta=-22. We discuss the possibility of having lines of first order phase transitions ending at a second order phase transition in an extended bare parameter space.
arXiv comment7 pages, 7 figures, uses revtex, Eqs. 15-17 corrected, minor changes
References in corpus (11)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Complex Extension of Quantum Mechanics
- Scalar Quantum Field Theory with Cubic Interaction
- The Three-Loop Lattice Free Energy
- RENORMALONS FROM EIGHT LOOP EXPANSION OF THE GLUON CONDENSATE IN LATTICE GAUGE THEORY,
- A Simple Method to Make Asymptotic Series of Feynman Diagrams Converge
- Separating perturbative and non-perturbative contributions to the plaquette
- Numerical Simulations of PT-Symmetric Quantum Field Theories
- On the Divergence of Perturbation Theory. Steps Towards a Convergent Series
- A consistency check for Renormalons in Lattice Gauge Theory: beta^(-10) contributions to the SU(3) plaquette
- New Optimization Methods for Converging Perturbative Series with a Field Cutoff
Cited by in corpus (18)
- UV and IR Zeros of Gauge Theories at The Four Loop Order and Beyond
- Quantum simulation of scattering in the quantum Ising model
- Fisher's zeros as boundary of renormalization group flows in complex coupling spaces
- Theoretical methods to design and test quantum simulators for the compact Abelian Higgs model
- Density of states and Fisher's zeros in compact U(1) pure gauge theory
- Searching for continuous phase transitions in 5D SU(2) lattice gauge theory
- The non-perturbative part of the plaquette in quenched QCD
- Kurt Symanzik - a stable fixed point beyond triviality
- An example of optimal field cut in lattice gauge perturbation theory
- About a possible 3rd order phase transition at T=0 in 4D gluodynamics
- Series expansions of the density of states in SU(2) lattice gauge theory
- A Tractable Example of Perturbation Theory with a Field Cutoff: the Anharmonic Oscillator
- Dyson instability for 2D nonlinear O(N) sigma models
- Dyson's Instability in Lattice Gauge Theory
- Is there a third-order phase transition in quenched QCD?
- Volume dependence of Fisher's zeros
- Definition and parametrization of non-perturbative effects in quenched QCD
- Fisher's Zeros and Perturbative Series in Gluodynamics