Supersymmetry and the Atiyah-Singer Index Theorem I: Peierls Brackets, Green's Functions, and a Supersymmetric Proof of the Index Theorem

The Peierls bracket quantization scheme is applied to the supersymmetric system corresponding to the twisted spin index theorem. A detailed study of the quantum system is presented, and the Feynman propagator is exactly computed. The Green's function methods provide a direct derivation of the index formula. Note: This is essentially a new SUSY proof of the index theorem.Comment: 47 page

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.Comment: 6 page

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.Comment: Latex file, 19 pages, one figure, uses JHEP.cls. One reference added, final version as it appeared in JHE

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 $S=(A/4)(1-4\mu)$, where $\mu$ is the string tension.Comment: LaTeX, 9 pages, final version to appear in Phys.Lett.

Topological Symmetries

We introduce the notion of a topological symmetry as a quantum mechanical symmetry involving a certain topological invariant. We obtain the underlying algebraic structure of the Z_2-graded uniform topological symmetries of type (1,1) and (2,1). This leads to a novel derivation of the algebras of supersymmetry and $p=2$ parasupersummetry.Comment: Plain LaTeX Ref: Mod. Phys. Lett. A 15, 175-184 (2000

A systematic literature review on synchronous hybrid learning : gaps identified

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I Do Not Look Up Enough

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On the Opening of Branes

We relate, in 10 and 11 dimensional supergravities, configurations of intersecting closed branes with vanishing binding energy to configurations where one of the branes opens and has its boundaries attached to the other. These boundaries are charged with respect to fields living on the closed brane. The latter hosts electric and magnetic charges stemming from dual pairs of open branes terminating on it. We show that charge conservation, gauge invariance and supersymmetry entirely determine these charges and these fields, which can be seen as Goldstone fields of broken supersymmetry. Open brane boundary charges can annihilate, restoring the zero binding energy configuration. This suggests emission of closed branes by branes, a generalization of closed string emission by D-branes. We comment on the relation of the Goldstone fields to matrix models approaches to M-theory.Comment: 13 pages, LaTeX, no figure

Random walk in a random environment and 1f noise

A simple model showing a $\frac{1}{f}$ behavior is proposed. It is argued, on the basis of a scaling argument, that is has ${(\mathrm{ln}f)}^{k}$ corrections. Numerical simulations confirm this picture