| Summary: | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006. === Includes bibliographical references (p. 149-151). === We define and study the structure of SUSY Lie conformal and vertex algebras. This leads to effective rules for computations with superfields. Given a strongly conformal SUSY vertex algebra V and a supercurve X, we construct a vector bundle [ ... ] on X, the fiber of which, is isomorphic to V. Moreover, the state-field correspondence of V canonically gives rise to (local) sections of these vector bundles. We also define chiral algebras on any supercurve X, and show that the vector bundle [ ... ] corresponding to a SUSY vertex algebra, carries the structure of a chiral algebra. === by Reimundo Heluani. === Ph.D.
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