The quantum Hilbert space of a chiral two-form in d = 5 + 1 dimensions

Abstract

We consider the quantum theory of a two-form gauge field on a space-time which is a direct product of time and a spatial manifold, taken to be a compact five-manifold with no torsion in its cohomology. We show that the Hilbert space of this non-chiral theory is a certain subspace of a tensor product of two spaces, that are naturally interpreted as the Hilbert spaces of a chiral and anti-chiral two-form theory respectively. We also study the observable operators in the non-chiral theory that correspond to the electric and magnetic field strengths, the Hamiltonian, and the exponentiated holonomy of the gauge-field around a spatial two-cycle. All these operators can be decomposed into contributions pertaining to the chiral and anti-chiral sectors of the theory.

15 pages

References in corpus (5)

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• Duality Relations Among Topological Effects In String Theory
• Weyl anomaly for Wilson surfaces
• Holomorphic factorization of correlation functions in (4k+2)-dimensional (2k)-form gauge theory
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• Superconformal Field Theory In Six Dimensions And Supertwistor
• Projective unitary representations of smooth Deligne cohomology groups
• Partition Functions for Maxwell Theory on the Five-torus and for the Fivebrane on S1XT5
• Electric-magnetic Duality of Abelian Gauge Theory on the Four-torus, from the Fivebrane on T2 x T4, via their Partition Functions