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Supersymmetry and the Atiyah-Singer index theorem
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 elementaryExpand
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Theta functions, modular invariance, and strings
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 structureExpand
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Potentials for the supersymmetric nonlinear σ-model
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 theExpand
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The Structure of Gauge and Gravitational Anomalies
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 formExpand
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An O(16) × O(16) heterotic string
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 stringExpand
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General Properties of Noncommutative Field Theories
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 extensionExpand
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Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model
A complete geometrical classification of supersymmetric σ-models is given. Extended supersymmetry requires covariantly constant complex structures, and Kahler and hyperkahler manifolds play a specialExpand
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Bosonization on higher genus Riemann surfaces
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. GlobalExpand
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Anomalies and odd dimensions
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 andExpand
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Some global aspects of duality in String Theory
Abstract We explore some of the global aspects of duality transformations in String Theory and Field Theory. We analyze in some detail the equivalence of dual models corresponding to differentExpand
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