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dc.contributor.authorWard, Brandonen_US
dc.date.accessioned2016-01-27T18:47:18Z
dc.date.available2016-01-27T18:47:18Z
dc.date.issued2013
dc.identifier.urihttps://hdl.handle.net/2144/14108
dc.description.abstractThis paper will examine observables in the bc system, a two-dimensional free conformal field theory. We begin by encoding the bc system into the BV formalism following procedures of Costello and Gwilliam. This will allow us to construct the factorization algebra of observables for the bc system. The cohomology of the factorization algebra recovers the observables themselves. In cohomology, we will compute the commutation relations and factorization algebra structure maps for observables supported on disks and annuli. These structure maps will be used to prove the equivalence of the factorization algebra and vertex algebra structures for the bc system. This proof provides a rigorous derivation of the free fermionic vertex algebra starting from the action functional of the bc system. Using this equivalence, we will provide a dictionary to translate the action of the Virasoro algebra to the language of factorization algebras. Also in this paper, we examine the bc system in four-dimensions. We construct its factorization algebra and show that its observables are anti-commutative. Lastly, we prove that the global observables of the bc system are one-dimensional on a compact manifold of complex dimension one or two.en_US
dc.language.isoen_US
dc.subjectMathematicsen_US
dc.subjectbc systemen_US
dc.subjectFactorization algebraen_US
dc.subjectGlobal observablesen_US
dc.subjectVertex algebraen_US
dc.subjectVirasoro algebraen_US
dc.titleObservables in the bc systemen_US
dc.typeThesis/Dissertationen_US
dc.date.updated2016-01-22T18:53:52Z
etd.degree.nameDoctor of Philosophyen_US
etd.degree.leveldoctoralen_US
etd.degree.disciplineMathematics & Statisticsen_US
etd.degree.grantorBoston Universityen_US


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