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Register a new userThe a-function for N=2 supersymmetric gauge theories in three dimensions
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Recently, the existence of a candidate a-function for renormalisable theories in three dimensions was demonstrated for a general theory at leading order and for a scalar-fermion theory at next-to-leading order. Here we extend this work by constructing the a-function at next-to-leading order for an N=2 supersymmetric Chern-Simons theory. This increase in precision for the a-function necessitated the evaluation of the underlying renormalization-group functions at four loops.
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We consider general aspects of N=2 gauge theories in three dimensions, including their multiplet structure, anomalies and non-renormalization theorems. For U(1) gauge theories, we discuss the quantum corrections to the moduli space, and their relation to ``mirror symmetries of 3d N=4 theories. Mirror symmetry is given an interpretation in terms of vortices. For SU(N_c) gauge groups with N_f fundamental flavors, we show that, depending on the number of flavors, there are quantum moduli spaces of vacua with various phenomena near the origin.
A solution to the infinite coupling problem for N=2 conformal supersymmetric gauge theories in four dimensions is presented. The infinitely-coupled theories are argued to be interacting superconformal field theories (SCFTs) with weakly gauged flavor groups. Consistency checks of this proposal are found by examining some low-rank examples. As part of these checks, we show how to compute new exact quantities in these SCFTs: the central charges of their flavor current algebras. Also, the isolated rank 1 E_6 and E_7 SCFTs are found as limits of Lagrangian field theories.
The four dimensional Godel spacetime is known to have the structure M_3 x R. It is also known that the three-dimensional factor M_3 is an exact solution of three-dimensional gravity coupled to a Maxwell-Chern-Simons theory. We build in this paper a N=2 supergravity extension for this action and prove that the Godel background preserves half of all supersymmetries.
Using the off-shell formulation for ${mathcal N}=2$ conformal supergravity in four dimensions, we propose superconformal higher-spin multiplets of conserved currents and their associated unconstrained gauge prepotentials. The latter are used to construct locally superconformal chiral actions, which are demonstrated to be gauge invariant in arbitrary conformally flat backgrounds.
We investigate in which sense, at the linearized level, one can extend the 3D topologically massive gravity theory beyond three dimensions. We show that, for each k=1,2,3... a free topologically massive gauge theory in 4k-1 dimensions can be defined describing a massive spin-2 particle provided one uses a non-standard representation of the massive spin-2 state which makes use of a two-column Young tableau where each column is of height 2k-1. We work out the case of k=2, i.e. 7D, and show, by canonical analysis, that the model describes, unitarily, 35 massive spin-2 degrees of freedom. The issue of interactions is discussed and compared with the three-dimensional situation.
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