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3D Field Theories with Chern--Simons Term for Large $N$ in the Weyl Gauge | | Moshe Moshe
; Jean Zinn-Justin
; | | Date: |
2 Oct 2014 | | Abstract: | Three dimensional, $U(N)$ symmetric, field theory with fermion matter coupled
to a topological Chern--Simons term, in the large $N$ limit is analyzed in
details. We determine the conditions for the existence of a massless conformal
invariant ground state as well as the conditions for a massive phase. We
analyze the phase structure and calculate gauge invariant corelators comparing
them in several cases to existing results. In addition to the non-critical
explicitly broken scale invariance massive case we consider also a massive
ground state where the scale symmetry is spontaneously broken. We show that
such a phase appears only in the presence of a marginal deformation that is
introduced by adding a certain scalar auxiliary field. The ground state
contains in this case a massless $U(N)$ singlet bound state goldstone boson-
the dilaton whose properties are determined. We employ here the temporal gauge
which is at variance with respect to past calculations using the light-cone
gauge and thus, a check (though limited) of gauge independence is at hand. The
large $N$ properties are determined by using a field integral formalism and the
steepest descent method. The saddle point equations, which take here the form
of integral equations for non-local fields, determine the mass gap and the
dressed fermion propagator. Vertex functions are calculated at leading order in
$1/N$ as exact solutions of integral equations. From the vertex functions, we
infer gauge invariant two-point correlation functions for scalar operators and
a current. Indications about the consistency of the method are obtained by
verifying that gauge-invariant quantities have a natural $O(3)$ covariant form.
As a further verification, in several occasions, a few terms of the
perturbative expansion are calculated and compared with the exact results in
the appropriate order. | | Source: | arXiv, 1410.0558 | | Services: | Forum | Review | PDF | Favorites | |
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