# MS Seminar (Mathematics - String Theory)

Speaker: V. Guru Charan (Dayalbagh Educational Institute, Agra) M/N and 1/N Anomalous Dimensions in Chern-Simons theory Thu, Jun 21, 2018, 13:00 - 14:00 Seminar Room B 2101.pdf Non-abelian Chern-Simons theories coupled to fermions are known to provide an interesting class of non-supersymmetric conformal fixed points. 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 $O(N)_{-k}\times O(N)_k$ 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 $\lambda$ in a $U(M)_{k_M} \times U(N)_{k_N}$ theory, in the limit $M \ll N$, in an $M/N$ expansion. To illustrate this, we calculate the anomalous dimension of the primary operator $\tr \bar{\psi}{\psi}$, 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 will also discuss the higher spin spectrum of $U(M)_k$ Chern-Simons theory coupled to $N$ flavours of fundamental fermions, in the limit $N\gg M$ with the 't Hooft coupling $\lambda_M =\frac{N}{k_m}$ held fixed, to order $M/N$. This theory possesses a slightly broken higher spin symmetry, and may be of interest from the perspective of higher-spin and non-supersymmetric holography.