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String Theory on Elliptic Curve Orientifolds and KR-Theory

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Abstract

We analyze the brane content and charges in all of the orientifold string theories on space-times of the form \({E \times \mathbb{R}^8}\), where E is an elliptic curve with holomorphic or anti-holomorphic involution. Many of these theories involve “twistings” coming from the B-field and/or sign choices on the orientifold planes. A description of these theories from the point of view of algebraic geometry, using the Legendre normal form, naturally divides them into three groupings. The physical theories within each grouping are related to one another via sequences of T-dualities. Our approach agrees with both previous topological calculations of twisted KR-theory and known physics arguments, and explains how the twistings originate from both a mathematical and a physical perspective.

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Charles Doran & Stefan Méndez-Diez

  2. Department of Mathematics and Statistics, Utah State University, Logan, UT, 84322-3900, USA

    Stefan Méndez-Diez

  3. Department of Mathematics, University of Maryland, College Park, MD, 20742-4015, USA

    Jonathan Rosenberg

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  1. Charles Doran
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  2. Stefan Méndez-Diez
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  3. Jonathan Rosenberg
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Correspondence to Jonathan Rosenberg.

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Communicated by H. Ooguri

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Doran, C., Méndez-Diez, S. & Rosenberg, J. String Theory on Elliptic Curve Orientifolds and KR-Theory. Commun. Math. Phys. 335, 955–1001 (2015). https://doi.org/10.1007/s00220-014-2200-0

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