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Supersymmetry and the Atiyah-Singer index theorem

- L. Alvarez-Gaumé
- Mathematics
- 1 March 1984

Using a recently introduced index for supersymmetric theories, we present a simple derivation of the Atiyah-Singer index theorem for classical complexes and itsG-index generalization using elementary… Expand

Theta functions, modular invariance, and strings

- L. Alvarez-Gaumé, G. Moore, C. Vafa
- Mathematics
- 1 March 1986

We use Quillen's theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory. In particular, we show that the spin structure… Expand

Supersymmetry and the Atiyah-Singer index theorem

- L. Alvarez-Gaumé
- Physics
- 1 June 1983

Using a recently introduced index for supersymmetric theories, we present a simple derivation of the Atiyah-Singer index theorem for classical complexes and itsG-index generalization using elementary… Expand

Potentials for the supersymmetric nonlinear σ-model

- L. Alvarez-Gaumé, D. Freedman
- Mathematics
- 1 March 1983

The most general structure for potential terms compatible withN=1,N=2, andN=4 supersymmetry in the nonlinear σ-model in two space-time dimensions is determined. The differential geometry of the… Expand

An O(16) × O(16) heterotic string

- L. Alvarez-Gaumé, P. Ginsparg, G. Moore, C. Vafa
- Physics
- 24 April 1986

By modifying the definition of the fermion number projection in the E 8 × E 8 heterotic superstring theory in a manner consistent with modular invariance and factorization, a tachyon-free string… Expand

The Structure of Gauge and Gravitational Anomalies

- L. Alvarez-Gaumé, P. Ginsparg
- Physics
- 1 May 1985

It is shown how the form of the gauge and gravitational anomalies in quantum field theories may be derived from classical index theorems. The gravitational anomaly in both Einstein and Lorentz form… Expand

General Properties of Noncommutative Field Theories

- L. Alvarez-Gaumé, M. A. Vazquez-Mozo
- Physics
- 12 May 2003

In this paper we study general properties of noncommutative field theories obtained from the Seiberg-Witten limit of string theories in the presence of an external B-field. We analyze the extension… Expand

Bosonization on higher genus Riemann surfaces

- L. Alvarez-Gaumé, J. Bost, G. Moore, P. Nelson, C. Vafa
- Mathematics
- 1 September 1987

We prove the equivalence between certain fermionic and bosonic theories in two spacetime dimensions. The theories have fields of arbitrary spin on compact surfaces with any number of handles. Global… Expand

Anomalies and odd dimensions

- L. Alvarez-Gaumé, S. D. Pietra, G. Moore
- Physics
- 1 September 1985

The parity-violating effective action for theories of fermions coupled to external gauge and gravitational fields in odd dimensions is computed exactly. This action is then used to compute gauge and… Expand

Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model

- L. Alvarez-Gaumé, D. Freedman
- Physics
- 1981

A complete geometrical classification of supersymmetric σ-models is given. Extended supersymmetry requires covariantly constant complex structures, and Kahler and hyperkahler manifolds play a special… Expand

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