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Making chiral fermion actions (almost) gauge invariant using Laplacian gauge fixing
Straight foreward lattice descriptions of chiral fermions lead to actions
that break gauge invariance. I describe a method to make such actions gauge
invariant (up to global gauge transformations) with the aid of gauge fixing. To
make this prescription unambiguous, Laplacian gauge fixing is used, which is
free from Gribov ambiguities.Comment: 3 p., Latex, (proc. Lattice '93, Dallas), 2 figs. appended, UCSD/PTH
93-4
The Standard Model from a New Phase Transition on the Lattice
Several years ago it was conjectured in the so-called Roma Approach, that
gauge fixing is an essential ingredient in the lattice formulation of chiral
gauge theories. In this paper we discuss in detail how the gauge-fixing
approach may be realized. As in the usual (gauge invariant) lattice
formulation, the continuum limit corresponds to a gaussian fixed point, that
now controls both the transversal and the longitudinal modes of the gauge
field. A key role is played by a new phase transition separating a conventional
Higgs or Higgs-confinement phase, from a phase with broken rotational
invariance. In the continuum limit we expect to find a scaling region, where
the lattice correlators reproduce the euclidean correlation functions of the
target (chiral) gauge theory, in the corresponding continuum gauge.Comment: 16 pages, revtex, one figure. Clarifications made, mainly in sections
3 and 6 that deal with the fermion action, to appear in Phys Rev
Four-Dimensional Yang-Mills Theory as a Deformation of Topological BF Theory
The classical action for pure Yang--Mills gauge theory can be formulated as a
deformation of the topological theory where, beside the two-form field
, one has to add one extra-field given by a one-form which transforms
as the difference of two connections. The ensuing action functional gives a
theory that is both classically and quantistically equivalent to the original
Yang--Mills theory. In order to prove such an equivalence, it is shown that the
dependency on the field can be gauged away completely. This gives rise
to a field theory that, for this reason, can be considered as semi-topological
or topological in some but not all the fields of the theory. The symmetry group
involved in this theory is an affine extension of the tangent gauge group
acting on the tangent bundle of the space of connections. A mathematical
analysis of this group action and of the relevant BRST complex is discussed in
details.Comment: 74 pages, LaTeX, minor corrections; to be published in Commun. Math.
Phy
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