Abstract
Non-abelian Chern-Simons theories coupled to fermions are known to provide an interesting class of non-supersymmetric conformal fixed points [1]. These theories, particularly those based on bifundamental matter, are important because they may provide simple non-supersymmetric examples of the AdS/CFT correspondence. For instance, it seems natural to conjecture that O(N)−k × O(N) k Chern-Simons theory coupled to Majorana fermions transforming in a bi-vector representation may be dual to pure Einstein gravity with a small negative cosmological constant in the “M-theory” limit where k = 1 and N is large. While it is extremely difficult to directly study such bifundamental theories when k = 1 or even at strong ’t Hooft coupling \( \lambda =\frac{N}{k} \), it is possible to calculate physical quantities to all orders in λ in a \( \mathrm{U}{(M)}_{k_M}\times \mathrm{U}{(N)}_{k_N} \) theory, in the limit M ≪ N, in an M/N expansion. To illustrate this, we calculate the anomalous dimension of the primary operator tr \( \overline{\psi}\psi \), to first order in M/N, to all orders in \( {\lambda}_M=\frac{N}{k_M} \), but with \( {\lambda}_N=\frac{N}{k_N} = 0 \). We also comment on possible bosonization dualities for bifundamental Chern-Simons theories.
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09 November 2017
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ArXiv ePrint: 1404.7849
An erratum to this article is available at https://doi.org/10.1007/JHEP11(2017)045.
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Gurucharan, V., Prakash, S. Anomalous dimensions in non-supersymmetric bifundamental Chern-Simons theories. J. High Energ. Phys. 2014, 9 (2014). https://doi.org/10.1007/JHEP09(2014)009
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DOI: https://doi.org/10.1007/JHEP09(2014)009