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Febuary 2020 From the signature theorem to anomaly cancellation
Andreas Malmendier, Michael T. Schultz
Rocky Mountain J. Math. 50(1): 181-212 (Febuary 2020). DOI: 10.1216/rmj.2020.50.181

Abstract

We survey the Hirzebruch signature theorem as a special case of the Atiyah–Singer index theorem. The family version of the Atiyah–Singer index theorem in the form of the Riemann–Roch–Grothendieck–Quillen (RRGQ) formula is then applied to the complexified signature operators varying along the universal family of elliptic curves. The RRGQ formula allows us to determine a generalized cohomology class on the base of the elliptic fibration that is known in physics as (a measure of) the local and global anomaly. Combining several anomalous operators allows us to cancel the local anomaly on a Jacobian elliptic surface, a construction that is based on the construction of the Poincaré line bundle over an elliptic surface.

Citation

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Andreas Malmendier. Michael T. Schultz. "From the signature theorem to anomaly cancellation." Rocky Mountain J. Math. 50 (1) 181 - 212, Febuary 2020. https://doi.org/10.1216/rmj.2020.50.181

Information

Received: 24 July 2019; Accepted: 22 August 2019; Published: Febuary 2020
First available in Project Euclid: 30 April 2020

zbMATH: 07201562
MathSciNet: MR4092552
Digital Object Identifier: 10.1216/rmj.2020.50.181

Subjects:
Primary: 14J27, 14J28, 51P05, 58J20, 81T50

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 1 • Febuary 2020
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