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Quantum theories of (p, q)-forms

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Abstract

We describe quantum theories for massless (p, q)-forms living on Kähler 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 ∂, \( \overline \partial \), and their hermitian conjugates ∂†, \( {\overline \partial^{\dag }} \). 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 .

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Bologna and INFN, Sezione di Bologna, via Irnerio 46, I-40126, Bologna, Italy

    Fiorenzo Bastianelli, Roberto Bonezzi & Carlo Iazeolla

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  1. Fiorenzo Bastianelli
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  2. Roberto Bonezzi
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  3. Carlo Iazeolla
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Correspondence to Roberto Bonezzi.

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ArXiv ePrint: 1204.5954

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Bastianelli, F., Bonezzi, R. & Iazeolla, C. Quantum theories of (p, q)-forms. J. High Energ. Phys. 2012, 45 (2012). https://doi.org/10.1007/JHEP08(2012)045

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