Non-abelian lattice gauge theory with a topological action

Abstract

SU (2) gauge theory is investigated with a lattice action which is insensitive to small perturbations of the lattice gauge fields. Bare perturbation theory can not be defined for such actions at all. We compare non-perturbative continuum results with that obtained by the usual Wilson plaquette action. The compared observables span a wide range of interesting phenomena: zero temperature large volume behavior (topological susceptibility), finite temperature phase transition (critical exponents and critical temperature) and also the small volume regime (discrete β-function or step-scaling function). In the continuum limit perfect agreement is found indicating that universality holds for these topological lattice actions as well.

Bulk-preventing actions for SU(N) gauge theories

“…For U(1) and SU(2), the actions in (12) have a similar effect as the topological actions discussed in [4][5][6]: the larger the inverse bare coupling 𝛾, the stronger the plaquette values are repelled from −1 resp. −1.…”

“…−1. For SU(𝑁) with 𝑁 > 2 the effect of (12) is different from the one of the topological action discussed in [6], as for 𝑁 > 2 the trace of the plaquette does no longer completely determine the plaquette eigenvalues. However, an action which can have a similar effect as our actions (12) has been given in [7].…”

Bulk-preventing actions for SU(N) gauge theories

“…For U(1) and SU(2), the actions in ( 12) have a similar effect as the topological actions discussed in [15,17,18]: the larger the inverse bare coupling γ, the stronger the plaquette values are repelled from −1 resp. −1.…”

“…−1. For SU(N ) with N > 2 the effect of ( 12) is different from the one of the topological action discussed in [18], as for N > 2 the trace of the plaquette does no-longer completely determine the plaquette eigenvalues. However, an action which can have a similar effect as our actions (12) has been given in [22].…”

“…Our approach is related to the "dislocation prevention" method by De-Grand et al [19]. For U (1) and SU (2) gauge groups also the topological gauge actions that restict the plaquette magnitude [15,17,18] or the gauge-topology preserving actions investigated in [16] are to some extent related. This is, however, no longer the case for SU(N ) gauge groups with N > 2.…”