Quantum theories of (p,q)-forms

Abstract

We describe quantum theories for massless (p,q)-forms living on Kaehler spaces. In particular we consider four different types of quantum theories: two types involve gauge symmetries and two types are simpler theories without gauge invariances. The latter can be seen as building blocks of the former. Their equations of motion can be obtained in a natural way by first-quantizing a spinning particle with a U(2)-extended supersymmetry on the worldline. The particle system contains four supersymmetric charges, represented quantum mechanically by the Dolbeault operators and their hermitian conjugates. After studying how the (p,q)-form field theories emerge from the particle system, we investigate their one loop effective actions, identify corresponding heat kernel coefficients, and derive exact duality relations. The dualities are seen to include mismatches related to topological indices and analytic torsions, which are computed as Tr(-1)^F and Tr[(-1)^F F] in the first quantized supersymmetric nonlinear sigma model for a suitable fermion number operator F.

44 pages, 2 figures, a reference added

References in corpus (4)

• Real Forms of Complex Higher Spin Field Equations and New Exact Solutions
• Detours and Paths: BRST Complexes and Worldline Formalism
• U(N) spinning particles and higher spin equations on complex manifolds
• (p,q)-form Kaehler Electromagnetism

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• Cubic interactions of Maxwell-like higher spins
• Particles with non abelian charges
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• Quantum mechanical path integrals in the first quantised approach to quantum field theory
• One-loop quantum gravity from the N=4 spinning particle
• Mixed-symmetry multiplets and higher-spin curvatures
• Worldline description of a bi-adjoint scalar and the zeroth copy
• Mixed symmetry Wilson-loop interactions in the worldline formalism
• Six-dimensional one-loop divergences in quantum gravity from the $\mathcal{N}=4$ spinning particle
• Gauge-invariant coefficients in perturbative quantum gravity
• $U(N)$ Yang-Mills in non-commutative space time
• U(N) spinning particles and higher spin fields on Kaehler backgrounds