Abstract
We study the theory of a single fundamental fermion and boson coupled to Chern-Simons theory at leading order in the large N limit. Utilizing recent progress in understanding the Higgsed phase in Chern-Simons-Matter theories, we compute the quantum effective potential that is exact to all orders in the ’t Hooft coupling for the lightest scalar operator of this theory at finite temperature. Specializing to the zero temperature limit we use this potential to determine the phase diagram of the large N mathcal{N} = 2 supersymmetric theory with this field content. This intricate two dimensional phase diagram has four topological phases that are separated by lines of first and second order phase transitions and includes special conformal points at which the infrared dynamics is governed by Chern-Simons theory coupled respectively to free bosons, Gross-Neveu fermions, and to a theory of Wilson-Fisher bosons plus free fermions. We also describe the vacuum structure of the most general mathcal{N} = 1 supersymmetric theory with one fundamental boson and one fundamental fermion coupled to an SU(N ) Chern-Simons gauge field, at arbitrary values of the ’t Hooft coupling.
Highlights
In this paper we continue the study, initiated in [1,2,3], of U(N ) (or SU(N )) Chern-Simons theories coupled to a single fundamental boson φ and a single fundamental fermion ψ in the large N limit
At this transition point the theory reduces to the conformal or the conformal. Note that in both cases there is a point on the phase diagram at which the four second order phase transition lines meet. At this point the dynamics is governed by Chern-Simons gauged Wilson-Fisher bosons and regular fermions
The dynamics on the second order transition line L in figure 8 is governed by the conformal critical boson theory CB+ and terminates at the point RB+ which is governed by a theory of conformal regular bosons i.e. free bosons
Summary
In this paper we continue the study, initiated in [1,2,3], of U(N ) (or SU(N )) Chern-Simons theories coupled to a single fundamental boson φ and a single fundamental fermion ψ in the large N limit. At any finite N , no matter how large, this fixed hyperplane presumably breaks up into a set of isolated fixed points connected by a presumably intricate pattern of RG flows Each of these fixed points defines a new conformal field theory; the phase diagram of this theory is obtained by studying its relevant deformations. Note that in both cases there is a point on the phase diagram at which the four second order phase transition lines meet At this point the dynamics is governed by Chern-Simons gauged Wilson-Fisher bosons and regular fermions (the CB-RF theory). This theory was first encountered (in the same context) in [1], and has recently been intensively studied in their own right at finite values of N in [4, 5]. The more important in-principle advantage of the approach of this paper is that the quantum effective potential allows us to access the (+, −) and (−, −) phases (the analysis of [1] was blind to these phases) and allows us to compute the complete phase diagram schematically depicted in figure 1, a task that could not have been accomplished using only the analysis of [1]
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