Supersymmetric Chern-Simons Theories with Vector Matter

Abstract

In this paper we discuss SU(N) Chern-Simons theories at level k with both fermionic and bosonic vector matter. In particular we present an exact calculation of the free energy of the N=2 supersymmetric model (with one chiral field) for all values of the 't Hooft coupling in the large N limit. This is done by using a generalization of the standard Hubbard-Stratanovich method because the SUSY model contains higher order polynomial interactions.

Figures (6)

• Figure 1: In Fig.\ref{['sscw1']}, $\sqrt c$ and $\sqrt\sigma$ are shown as a function of $\lambda$ by undotted and dotted lines, respectively, when ${\cal N}=2$. They are degenerate and finite in all region of $\lambda$. In Fig.\ref{['freenw1']}, the free energy density normalized by $-NT^3$ is also finite in all region of $\lambda$.
• Figure 2: In Fig.\ref{['sscw0']}, we plot the $\sqrt c$ and $\sqrt\sigma$ as a function of $\lambda$ by undotted and dotted lines, respectively, when $w=0$. They are finite when $0\leq \lambda < 2$ and divergent at $\lambda=2$. In Fig.\ref{['freenw0']}, the free energy density divided by $-NT^3$ is shown as a function of $\lambda$ with $w=0$. $-F>0$ when $0\leq \lambda < 2$ and $F=0$ at $\lambda=2$.
• Figure 3: In Fig.\ref{['sscw0.5']}, $\sqrt c$ and $\sqrt\sigma$ are plotted as a function of $\lambda$ by undotted and dotted lines, respectively, when $w=0.5$. They are finite when $0\leq \lambda < 4$ and divergent at $\lambda=4$. In Fig.\ref{['freenw0.5']}, the free energy density divided by $-NT^3$ is shown. $-F>0$ when $0\leq \lambda < 4$ and $F=0$ at $\lambda=4$.
• Figure 4: The bosonic 1PI self energy diagram is drawn. The dotted, undotted and wavy lines respectively represent scalar, fermion and gauge field. The black and gray bubble respectively stand for the planar propagators of scalar and fermion.
• Figure 5: The fermionic 1PI self energy diagram is drawn.