<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-form Kähler electromagnetism

We study the extended supersymmetric quantum mechanics, with supercharges transforming in the fundamental representation of U (N |M ), as realized in certain onedimensional nonlinear sigma models with Kähler manifolds as target space. We discuss the symmetry algebra characterizing these models and, using operatorial methods, compute the heat kernel in the limit of short propagation time. These models are relevant for studying the quantum properties of a certain class of higher spin field equations in first quantization.

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U(N|M) quantum mechanics on Kähler manifolds

Bastianelli

Bonezzi

2010

J. High Energ. Phys.

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Quantum theories of (p, q)-forms

Bastianelli

Bonezzi

Iazeolla

2012

J. High Energ. Phys.

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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 ∂,∂, 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 .

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Quaternionic Kähler Detour Complexes and $${\mathcal{N} = 2}$$ Supersymmetric Black Holes

Cherney

Latini

Waldron

2011

Commun. Math. Phys.

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We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional N = 2 supergravities. By virtue of the cmap, these spinning particles move in quaternionic Kähler manifolds. Their spinning degrees of freedom describe mini-superspace-reduced supergravity fermions. We quantize these models using BRST detour complex technology. The construction of a nilpotent BRST charge is achieved by using local (worldline) supersymmetry ghosts to generating special holonomy transformations. (An interesting byproduct of the construction is a novel Dirac operator on the superghost extended Hilbert space.) The resulting quantized models are gauge invariant field theories with fields equaling sections of special quaternionic vector bundles. They underly and generalize the quaternionic version of Dolbeault cohomology discovered by Baston. In fact, Baston's complex is related to the BPS sector of the models we write down. Our results rely on a calculus of operators on quaternionic Kähler manifolds that follows from BRST machinery, and although directly motivated by black hole physics, can be broadly applied to any model relying on quaternionic geometry.

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(p,q)-form Kähler electromagnetism

Cited by 5 publications

References 19 publications

U(N|M) quantum mechanics on Kähler manifolds

U(N|M) quantum mechanics on Kähler manifolds

Quantum theories of (p, q)-forms

Quaternionic Kähler Detour Complexes and $${\mathcal{N} = 2}$$ Supersymmetric Black Holes

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