Categorical 't Hooft Expansion and Twisted Holography

Abstract

This thesis studies ideas of Holography and 't Hooft expansions in the context of Twisted Holography.

The 1st part introduces a novel entry in the Twisted Holography dictionary, associating to certain boundary operators, bulk instantonic deformations of D1-D5 brane systems in SL(2,C). From the boundary operators, we are able to extract the data of both the shape and Chan-Paton bundle of the dual brane, encoding it in a derived coherent sheaf. We then apply this construction to chiral algebras with SO and Sp gauge groups, obtaining branes with Z2 identifications consistent with conjectures relating these chiral algebras to orientifolds of the bulk B-model theory.

The second part, extends the conjecture of Twisted Holography to a wide family of chiral algebras. In particular, we study boundary theories containing several βγ-systems with several U(N) gauge groups. Amongst these one has known chiral algebras arising from the twist of quiver-gauge theories, but also new chiral algebras whose dual B-model lives in non-commutative backgrounds. Using techniques from String Field Theory and Homological Algebra, we extract from these chiral algebras, algebraic properties of the conjectural dual worldsheet theories, and track how they deform under backreaction.