TitleChiral algebras of (0,2) models
NameYagi, Junya (author), Moore, Gregory (chair), Friedan, Daniel (internal member), Strassler, Matthew (internal member), Jha, Saurabh (internal member), Witten, Edward (outside member), Rutgers University, Graduate School - New Brunswick,
SubjectPhysics and Astronomy,
Field theory (Physics),
DescriptionSigma models with (0,2) supersymmetry in two dimensions possess quasi-topological sectors characterized by chiral algebras. In this thesis, we study these chiral algebras and explore their
The chiral algebras of (0,2) models emerge when one considers the cohomology of local operators with respect to one of the supercharges, and provide infinite-dimensional generalizations of the chiral rings of (2,2) models. Perturbatively, they enjoy rich mathematical structures described by sheaves of chiral differential operators.
Nonperturbatively, however, they vanish completely for certain (0,2) models with no left-moving fermions. Examples include the models in which the target spaces are the complete flag manifolds of compact
semisimple Lie groups.
The vanishing of the chiral algebra of a (0,2) model implies that supersymmetry is spontaneously broken in the model, which in turn suggests that no harmonic spinors exist on the loop space of the target space. We analyze this supersymmetry breaking using holomorphic Morse theory on the loop space in the case where the target space is CP(1). As expected, we find that instantons interpolate between pairs of perturbative supersymmetric states, thereby lifting them out of the supersymmetric spectrum.
This thesis is based on the work of the author with Meng-Chwan Tan, reported in the papers arXiv:0801.4782 [hep-th], arXiv:0805.1410 [hep-th], and the Letter Lett. Math. Phys. 84, 257 (2008)
NoteIncludes bibliographical references (p. 74-76)
Noteby Junya Yagi
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work