Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 5

Ramond–Ramond fields and twisted differential K-theory

Pages: 1097 – 1155



Daniel Grady (Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas, U.S.A.)

Hisham Sati (Mathematics, Division of Science; and Center for Quantum and Topological Systems, NYUAD Research Institute, New York University, Abu Dhabi, United Arab Emirates)


We provide a systematic approach to describing the Ramond–Ramond (RR) fields as elements in twisted differential K-theory. This builds on a series of constructions by the authors on geometric and computational aspects of twisted differential K-theory, which to a large extent were originally motivated by this problem. In addition to providing a new conceptual framework and a mathematically solid setting, this allows us to uncover interesting and novel effects. Explicitly, we use our recently constructed Atiyah–Hirzebruch spectral sequence (AHSS) for twisted differential K-theory to characterize the RR fields and their quantization, which involves interesting interplay between geometric and topological data. We illustrate this with the examples of spheres, tori, and Calabi-Yau threefolds.

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Published 30 March 2023