-
[show abstract]
[hide abstract]
ABSTRACT: In an earlier work we used a path integral analysis to propose a higher genus
generalization of the elliptic genus. We found a cobordism invariant
parametrized by Teichmuller space. Here we simplify the formula and study the
behavior of our invariant under the action of the mapping class group of the
Riemann surface. We find that our invariant is a modular function with
multiplier just as in genus one.
04/2011;
-
[show abstract]
[hide abstract]
ABSTRACT: We derive a cohomological formula for the analytic index of a family of Dirac-Ramond operators and exhibit its modular properties.
Proceedings of the National Academy of Sciences 03/2010; 107(11):4845-50. · 9.68 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: Given a Riemann surface and a riemannian manifold M with certain restrictions, we construct a cobordism invariant of M. This invariant is a generalization of the elliptic genus and it shares some similar properties. Comment: 42 pages, LaTeX
04/2001;
-
[show abstract]
[hide abstract]
ABSTRACT: 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-K\v{a}c character formula which we compute explicitly by the steepest descent approximation. Comment: 40 pages
09/1991;
-
[show abstract]
[hide abstract]
ABSTRACT: The index of the Direc-Ramond operator is computed and analyzed. It is
shown to be the extension of the Atiyah-Singer index theorem for loop
space. It can also be seen as a generating function for the
Atiyah-Singer index for the states of the string. Its existence depends
on the Green-Schwarz anomaly cancellation condition, p1 (M) =
0, which defines an analog of a spin structure for the loop space. One
also finds topological invariants for the loop space which correspond to
different twistings of the Dirac-Ramond operator. All of them can be
expressed in terms of Jacobi elliptic functions.
Address after October 87: LPTHE, Université Pierre et Marie
Curie, Tour 16, 1er étage, Paris VI, 4 pl. Jussieu, F-753200
Paris CEDEX 05, FRANCE
Nuclear Physics B - Proceedings Supplements 08/1987; 1:189-215. · 0.88 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: General field theoretic methods are developed which will allow a path integral derivation of the character formula for loop groups. The methods are introduced in the classical Weyl character case. The irreducible representations of a compact semi-simple Lie group G are realized as the ground states of a supersymmetric quantum mechanical system. The Hilbert space for the quantum mechanical system is the space of sections of a holomorphic line bundle L over the complex manifold G/T, where T is the maximal torus of G. The Weyl character formula is derived by an explicit path integral computation of the index of the Dolbeault operator .
Nuclear Physics B.
-
[show abstract]
[hide abstract]
ABSTRACT: We present a new definition of the continuum limit in the random triangulation formulation of two-dimensional quantum gravity. This method uses a diffusion equation describing random walks in the space of orthogonal polynomials as the defining equation of the theory. This leads to a simple proof for universality of any potential and a direct connection of the KdV hierarchy.
Nuclear Physics B. 348(3):490-506.
-
[show abstract]
[hide abstract]
ABSTRACT: Given a Riemann surface Σ and a Riemannian manifold M with certain restrictions, we construct a cobordism invariant of M. This invariant is a generalization of the elliptic genus and it shares some similar properties.
Nuclear Physics B.
-
[show abstract]
[hide abstract]
ABSTRACT: Field theoretic and geometric ideas are used to construct a chiral supersymmetric field theory for which the 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-Kač character formula which we compute explicitly by the steepest-descent approximation.
Nuclear Physics B.
-
-
