The analytic index for a family of Dirac-Ramond operators
We derive a cohomological formula for the analytic index of the Dirac-Ramond operator and we exhibit its modular properties.
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arXiv subjects
Paul Windey
Publications and source records attributed to Paul Windey.
Orientifolds of the 3-sphere
We study the geometry of orientifolds in the SU(2) WZW model. They correspond to the two inequivalent, orientation-reversing involutions of $S^3$, whose fixed-point sets are: the north and south poles (O0), or the equator two-sphere (O2). We show how the geometric action of these involutions leads unambiguously to the previously obtained algebraic results for the Klein bottle and Moebius amplitudes. We give a semiclassical derivation of the selection rules and signs in the crosscap couplings, paying particular attention to discrete B-fluxes. A novel observation, which does not follow from consistency of the one-loop vacuum diagrams, is that in the case of the O0 orientifolds only integer- or only half-integer-spin Cardy states may coexist.
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Thermodynamics of Black Holes in Presence of String Instantons
The coupling of a Nambu-Goto string to gravity allows for Schwarzschild black holes whose entropy to area relation is $S=(A/4)(1-4μ)$, where $μ$ is the string tension. The departure from $A/4$ universality results from a string instanton which leads to a materialisation of the horizon at the quantum level.
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The Black Hole Entropy Can Be Smaller than A/4
The coupling of a Nambu-Goto string to gravity allows for Schwarzschild black holes whose entropy to area relation is $S=(A/4)(1-4μ)$, where $μ$ is the string tension.
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Black Hole Entropy and String Instantons
The coupling of a string to gravity allows for Schwarzschild black holes whose entropy to area relation is $S=(A/4)(1-4μ)$, where $μ$ is the string tension. This departure from the A/4 universality results from a string instanton generating a black hole with smaller entropy at a temperature exceeding the Hawking value. The temperature is sensitive to the presence of classical matter outside the black hole horizon but the entropy is not. The horizon materializes at the quantum level. It is conjectured that such a macroscopic non local effect may be operative in retrieving information from incipient black holes.
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The supersymmetric sigma model and the geometry of the Weyl-Kac character formula
Field theoretic and geometric ideas are used to construct a chiral supersymmetric field theory whose ground state is a specified irreducible representation of a centrally extended loop group. The character index of the associated supercharge (an appropriate Dirac operator on $LG/T$) is the Weyl-Kǎc character formula which we compute explicitly by the steepest descent approximation.
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