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| Paper IPM / Physic / 15087 |
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The NHEG algebra is an extension of Virasoro introduced in [arXiv:1503.07861]; it describes the symplectic symmetries of certain (n+4)-dimensional Near Horizon Extremal Geometries with SL(2,\mathbbR)×U(1)n+1 isometry. In this work we construct the NHEG group and classify the (coadjoint) orbits of its action on phase space. The group, as we show, consists of maps from an n-torus to the Virasoro group, so its orbits are bundles of standard Virasoro coadjoint orbits over Tn. We also describe the unitary representations that are expected to follow from the quantization of these orbits, and compute their characters. Along the way we show that the NHEG algebra can be built from u(1) currents using a twisted Sugawara construction. We briefly discuss the implications of our results for the microstates and entropy of extremal black holes.
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