TY - JOUR

T1 - SU(3) lattice gauge theory in 4 dimensions with a modified Wilson action

AU - Bhanot, Gyan

N1 - Funding Information:
I wish to thank BNL for this and also for their hospitality and support during my stay there. I am greatly indebted to Michael Creutz and Claudio Rebbi for their constant encouragement and guidance and the entire Theory Group at BNL for their friendship. Work supported in part by the Department of Energy Contract No. DE AC02-76ER02220.

PY - 1982/1/28

Y1 - 1982/1/28

N2 - The Wilson action for the 4-d gauge theory involves the trace in the fundamental representation of the product of link variables on lattice plaquettes. By computer simulation, we study an extension of this action with an additional term involving the plaquette trace in the adjoint representation. The gauge group is SU(3). We find a phase structure similar to that found recently for SU(2) with such an action. In particular, we find a first order transition in the SU(3)/Z(3) gauge theory and a critical endpoint close to the so-called crossover region for the Wilson action. We also study a 648 element subgroup of SU(3) to see whether it might be sufficient to simulate the continuum limit of the SU(3) theory. We find that, even with the extended action, the freezing transition from the discreteness of this subgroup precludes this possibility. Using an abalogy with the Potts model, we approximate the phase diagram for an even bigger subgroup of SU(3), one with 1080 elements. We find that this group is also not dense enough to describe the SU(3) continuum limit with the extended action.

AB - The Wilson action for the 4-d gauge theory involves the trace in the fundamental representation of the product of link variables on lattice plaquettes. By computer simulation, we study an extension of this action with an additional term involving the plaquette trace in the adjoint representation. The gauge group is SU(3). We find a phase structure similar to that found recently for SU(2) with such an action. In particular, we find a first order transition in the SU(3)/Z(3) gauge theory and a critical endpoint close to the so-called crossover region for the Wilson action. We also study a 648 element subgroup of SU(3) to see whether it might be sufficient to simulate the continuum limit of the SU(3) theory. We find that, even with the extended action, the freezing transition from the discreteness of this subgroup precludes this possibility. Using an abalogy with the Potts model, we approximate the phase diagram for an even bigger subgroup of SU(3), one with 1080 elements. We find that this group is also not dense enough to describe the SU(3) continuum limit with the extended action.

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U2 - 10.1016/0370-2693(82)91207-2

DO - 10.1016/0370-2693(82)91207-2

M3 - Article

AN - SCOPUS:0000973837

VL - 108

SP - 337

EP - 340

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 4-5

ER -