Abstract
We compute R-charges of the BPS-monopole operators in mathcal{N} = 3 hat{ADE} Chern-Simons quiver gauge theories, along the lines of the work of Benna, Klebanov and Klose in [1]. These theories have a weakly coupled UV completion in terms of mathcal{N} = 3 supersymmetric Chern-Simons Yang-Mills theories. In the UV limit the monopole operators are well approximated by classical solutions. We construct classical BPS and anti-BPS monopole solutions to these theories which preserve frac{1}{3} supersymmetry all along the RG flow. We compute the SU(2)R charges in these backgrounds and show that the smallest possible value of quantised SU(2)R charge is zero in each quiver theory.
Highlights
Study of AdS4/CFT3 correspondence [2] received a lot of interest after the discovery of an N = 6 superconformal Chern-Simons (CS) matter theory which describes the world volume theory of multiple M2 branes [16]( see [3]–[7]) in the low energy limit
The field content in the brane construction is similar to ABJM theory but the gauge fields and their superpartners become dynamical in the high energy regime
Since ABJM theory is strongly coupled for small values of k, which is the only coupling in the theory, it is difficult to compute the conformal dimension of the monopole operators
Summary
Study of AdS4/CFT3 correspondence [2] received a lot of interest after the discovery of an N = 6 superconformal Chern-Simons (CS) matter theory which describes the world volume theory of multiple M2 branes [16]( see [3]–[7]) in the low energy limit This theory, widely known as ABJM theory, has gauge group U(N )k × U(N )−k where k is the CS level. Since ABJM theory is strongly coupled for small values of k, which is the only coupling in the theory, it is difficult to compute the conformal dimension of the monopole operators To overcome this difficulty BKK introduces a method which goes as follows:. Keeping in mind that in three dimension the R-symmetry group of N = 3 theory is SO(3), which is isomorphic to SU(2) at the algebra level, the on-shell component fields in the superfield expansion are arranged in R-symmetry representations in BKK as follows. The component action and the supersymmetry variations will be written in terms of the above R-symmetry representations
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