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Determinants, torsion, and strings

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Abstract

We apply the results of [BF1, BF2] on determinants of Dirac operators to String Theory. For the bosonic string we recover the “holomorphic factorization” of Belavin and Knizhik. Witten's global anomaly formula is used to give sufficient conditions for anomaly cancellation in the heterotic string (for arbitrary background spacetimes). To prove the latter result we develop certain torsion invariants related to characteristic classes of vector bundles and to index theory.

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Communicated by A. Jaffe

Partially supported by an NSF Postdoctoral Research Fellowship

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Freed, D.S. Determinants, torsion, and strings. Commun.Math. Phys. 107, 483–513 (1986). https://doi.org/10.1007/BF01221001

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  • DOI: https://doi.org/10.1007/BF01221001

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