The classically perfect fixed-point action for SU(3) gauge theory

doi:10.1016/0550-3213(95)00458-5

Nuclear Physics B

Volume 454, Issue 3, 13 November 1995, Pages 587-614

https://doi.org/10.1016/0550-3213(95)00458-5 Get rights and content

Abstract

In this paper (the first of a series) we describe the construction of fixed-point actions for lattice SU(3) pure gauge theory. Fixed-point actions have scale-invariant instanton solutions and the spectrum of their quadratic part is exact (they are classical perfect actions). We argue that the fixed-point action is even one-loop quantum perfect, i.e. in its physical predictions there are no g²aⁿ cut-off effects for any n. We discuss the construction of fixed-point operators and present examples. The lowest-order $q q$ potential $V(r)$ obtained from the fixed-point Polyakov loop correlator is free of any cut-off effects which go to zero as an inverse power of the distance r.

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Citation Excerpt :
More detailed discussions of the fermionic methods and Monte Carlo results can be found in Refs. [223,228,232,497] (using ultralocal fermion actions), and Refs. [1,90,131,139,142,178,185,191,198,223,225,227,231,233,253,271,274–279,306,307,412,418,428,432,433,508,556] (using Ginsparg–Wilson fermions). Topological structures, such as instanton-like configurations, have been investigated on the lattice in Refs. [104,110,111,144,164,178,179,182,183,225,229,244,262,268,300,303,320,324–327,332,379,402,405,504,529]. In particular, Refs. [104,110,111,179,225,228,320,324–327] investigated topological structures beyond instanton-like configurations.
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We discuss issues related to $θ$ dependence in full QCD: the neutron electric dipole moment, the dependence of the topological susceptibility on the quark masses, the $U {(1)}_{A}$ symmetry breaking at finite temperature.
We also review results in the 2D $C P^{N - 1}$ model, which is an interesting theoretical laboratory to study issues related to topology.
Finally, we discuss the main features of the two-point correlation function of the topological charge density.
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^☆: Work supported in part by Schweizerischer Nationalfonds, NSF Grant PHY-9023257 and U.S. Department of Energy grant DE-FG02-92ER-40672.

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The classically perfect fixed-point action for SU(3) gauge theory☆

Abstract

Nucl. Phys. B

Phys. Rep.

Rev. Mod. Phys.

Rev. Mod. Phys.

Nucl. Phys. B

Nucl. Phys. B

preprint DESY 94-226

Phys. Rev. B