Quantum theory of massless (p,0)-forms

Abstract

We describe the quantum theory of massless (p,0)-forms that satisfy a suitable holomorphic generalization of the free Maxwell equations on Kaehler spaces. These equations arise by first-quantizing a spinning particle with a U(1)-extended local supersymmetry on the worldline. Dirac quantization of the spinning particle produces a physical Hilbert space made up of (p,0)-forms that satisfy holomorphic Maxwell equations coupled to the background Kaehler geometry, containing in particular a charge that measures the amount of coupling to the U(1) part of the U(d) holonomy group of the d-dimensional Kaehler space. The relevant differential operators appearing in these equations are a twisted exterior holomorphic derivative and its hermitian conjugate (twisted Dolbeault operators with charge q). The particle model is used to obtain a worldline representation of the one-loop effective action of the (p,0)-forms. This representation allows to compute the first few heat kernel coefficients contained in the local expansion of the effective action and to derive duality relations between (p,0) and (d-p-2,0)-forms that include a topological mismatch appearing at one-loop.

32 pages, 3 figures

References in corpus (4)

• Dirac Operator on Complex Manifolds and Supersymmetric Quantum Mechanics
• U(N) spinning particles and higher spin equations on complex manifolds
• Extended SUSY quantum mechanics: transition amplitudes and path integrals
• Dolbeault Complex on S^4\{.} and S^6\{.} through Supersymmetric Glasses

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• U(N) spinning particles and higher spin fields on Kaehler backgrounds