Aspects of Higher Spin Theories, Conformal Field Theories and Holography

This dissertation consists of three parts. The first part of the thesis is devoted to the study of gravity and higher spin gauge theories in 2+1 dimensions. The first part deals with cosmological solutions of spin-3 gravity and their thermodynamics, flat space limit of AdS$_3$ gravity and higher spins using Grassmann approach and chiral higher spin solutions with the most general AdS$_3$ boundary condition. The second part is devoted to the problem of Neumann boundary condition in Einstein's gravity. We present an explicit boundary term that makes the Neumann variational problem well posed and explore its consequences for holography in various dimensions. In the third part of the dissertation, we use the CFT techniques of Rychkov and Tan to compute anomalous dimensions in the O(N) Gross-Neveu model in $d=2+\epsilon$ dimensions. To do this, we extend the "cow-pie contraction" algorithm of Basu and Krishnan to theories with fermions.