Classical sphaleron rate on fine lattices

Journal of High Energy Physics, 2014

We find that using open boundary condition in the temporal direction can yield the expected value of the topological susceptibility in lattice SU(3) Yang-Mills theory. As a further check, we show that the result agrees with numerical simulations employing the periodic boundary condition. Our results support the preferability of the open boundary condition over the periodic boundary condition as the former allows for computation at smaller lattice spacings needed for continuum extrapolation at a lower computational cost.

Physics Letters B, 1998

3D electroweak sphalerons on the lattice are used as test configurations for definitions of various topological defects. In the maximally Abelian gauge they are shown to contain a symmetric array of Abelian monopoles and anti-monopoles connected by two kinds of Abelian vortex strings. Gauge-invariant lattice definitions of the Nambu monopole and the Z-vortex string are formulated which correspond to Abelian projection from the unitary gauge. The sphalerons contain in their core just one (non-Abelian) Nambu monopole-anti-monopole pair (connected by a Z-string) in an unstable saddle point bound state. This provides an example for the monopole-pair unbinding mechanism expected to work at the electroweak phase transition. The definitions of defects developed here will be used in future studies of topological aspects of this transition.

2000

We investigate the high temperature limit of SU(2) and SO(3) lattice gauge theory, respectively. In particular, we study the Stefan-Boltzmann constant in both cases. As is well known, the Stefan-Boltzmann constant extracted from SU(2) lattice gauge theory by incorporating finite size effects is smaller than the continuum value which assumes three gluon degrees of freedom. On the other hand, the extrapolation of our SO(3) lattice data comes much closer to the continuum value. This rises the question whether SU(2) and SO(3) lattice gauge theories represent different quantum theories in the continuum limit.

Physics Letters B, 1991

The slope of the topological susceptibility at q2= 0 is determined by Monte Carlo simulation for an SU (2) quenched gauge theory. Both the sign and the magnitude agree with the sum rule phenomenological determinations

Physics Letters B, 1982

Monte Carlo methods are used to investigate finite volume effects in an SU(2) gauge theory formulated on a hypercubical lattice. As a consequence of the finite volume of the lattice, a deconf'ming phase transition analogous to the finite temperature phase transition is observed. The critical temperature is consistent with the value obtained by similar studies on asymmetric lattices. The importance of using large lattices in Monte Carlo simulations is emphasized.

Physics Letters B, 1992

We investigate multiplicative renormalization of euclidean Yang-Mills theory in lattice regularization. We argue that asymptotic freedom implies the occurrence of the scale anomaly and a fiat measure for the gauge fields, which is in agreement with numerical simulations of lattice gauge theory. The renormalized theory exhibits the same structure as the recently proposed field strength approach to Yang-Mills theory, which in this way is put on a firmer basis.

2012

We investigate the infrared behaviour of the gluon propagator in Landau gauge on a lattice with twisted boundary conditions. Analytic calculations using Dyson-Schwinger equations, exact renormalization group and stochastic quantization show that the gluon propagator in Landau gauge approaches zero for small momentum. On the other hand lattice calculations and calculations on a four-torus seem to give rise to a non-zero limit. One possible reason for this difference is the existence of zero-momentum fluctuation modes which potentially give a massive contribution to the gluon propagator. Our simulations show that with twisted boundary conditions these zero-momentum modes are suppressed and the gluon propagator becomes smaller than in a periodic ensemble. PoS(LAT2005)334

2005

We determine effective lattice actions for the Polyakov loop using inverse Monte Carlo techniques.

Communications in Mathematical Physics, 1988

In this paper I analyse lattice Yang-Mills theories with continuous time. After a short discussion of more conceptual questions, such as the existence of a Hamilton operator in the infinite volume limit, I study the phase diagram. The existence of a strong coupling/low temperature confinement phase (which was not proven up to now) is established for arbitrary compact groups, continuous or discrete. For discrete compact groups the deconfinement region decomposes into (at least) two phases, which are distinguished by the behaviour of spatial Wilson loops: a deconfinement phase where spatial Wilson loops still show area law behaviour, and a “freezing” phase with perimeter law behaviour for spatial Wilson loops. The methods to prove these results rely on cluster expansion methods, combined with renormalisation ideas.

Nuclear Physics B, 1998

We consider the lattice regularization of N = 1 supersymmetric Yang-Mills theory with Wilson fermions. This formulation breaks supersymmetry at any finite lattice spacing; we discuss how Ward identities can be used to define a supersymmetric continuum limit, which coincides with the point where the gluino becomes massless. As a first step towards the understanding of the zero gluino-mass limit, we present results on the quenched low-lying spectrum of SU(2) N = 1 Super-Yang-Mills, at β = 2.6 on a V = 16 3 × 32 lattice, in the OZI approximation. Our results, in spite of the quenched and OZI approximations, are in remarkable agreement with theoretical predictions in the supersymmetric theory, for the states with masses which are not expected to get a large contribution from fermion loops.