Twisted Holography in B-model

Abstract

Supersymmetric quantum field theories contain protected subsectors which can be obtained by the procedure known as twisting. The idea of twisted holography is to study holographic duals of such twists. The main example of twisted holography in this thesis is the duality between the chiral algebra subsector of N = 4 super Yang-Mills and the B-model topological string theory on the complex manifold SL(2,C). In this thesis, we study two aspects of the duality: the correspondence between determinant operators in the chiral algebra and “Giant Graviton” branes in the dual geometry, and the extension to non-conformal vacua of the chiral algebra.

The second BPS subsector studied in this thesis is the holomorphic twist of 4d N = 1 super Yang-Mills. The holomorphic twist is defined as the cohomology of one supercharge and captures the quarter-BPS operators that are counted by the supersymmetric index. The twisted theory is endowed with extra structures and symmetries which are a 4d analogue of a 2d chiral algebra. We observe that the differential in the holomorphic twist receives loop corrections which make the theory topological and can be interpreted as a sign of confinement of the original theory. Finally, we present a holographic realization of the holomorphic theory in the B-model topological string theory.