A Vertex Superalgebra via Spin Factorization Algebras with Point Defects

Factorization algebras are one 'approximation'' to physicists' quantum field theories, and spin factorization algebras with point defects are a generalization of factorization algebras which allow us to take spin structures into account. In this thesis, we construct the spin factorization algebra with point defects of quantum observables for a particular free BV theory. Taking cohomology yields a spin prefactorization algebra with point defects. We investigate the structure maps of this cohomology prefactorization algebra and use them to give a geometric description of the free fermion vertex superalgebra and a geometric description of a twisted module over a vertex superalgebra.