Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 3D Field Theories with Chern--Simons Term for Large $N$ in the Weyl
  Gauge   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 and discuss the
fermion-boson dual mapping. 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.

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The categories of this paper are: eess
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math