Super symmetric vertex algebras and supercurves

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

Supersymmetry of the Chiral de Rham Complex

We present a superfield formulation of the chiral de Rham complex (CDR) of Malikov-Schechtman-Vaintrob in the setting of a general smooth manifold, and use it to endow CDR with superconformal structures of geometric origin. Given a Riemannian metric, we construct an N=1 structure on CDR (action of the N=1 super--Virasoro, or Neveu--Schwarz, algebra). If the metric is K"ahler, and the manifold Ricci-flat, this is augmented to an N=2 structure. Finally, if the manifold is hyperk"ahler, we obtain an N=4 structure. The superconformal structures are constructed directly from the Levi-Civita connection. These structures provide an analog for CDR of the extended supersymmetries of nonlinear sigma-models.Comment: References adde