Celebratio Mathematica — Schwarz

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Works connected to David Robert Morrison

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A. Schwarz, V. Vologodsky, and J. Walcher: “Framing the di-logarithm (over \( \mathbb{Z} \)),” pp. 113–128 in String-Math 2012 (Bonn, Germany, 16–21 July 2012). Edited by R. Donagi, S. Katz, A. Klemm, and D. R. Morrison. Proceedings of Symposia in Pure Mathematics 90. American Mathematical Society (Providence, RI), 2015. MR 3409790 Zbl 1356.81196 ArXiv 1306.4298 incollection

Motivated by their role for integrality and integrability in topological string theory, we introduce the general mathematical notion of “\( s \)-functions” as integral linear combinations of poly-logarithms. 2-functions arise as disk amplitudes in Calabi–Yau D-brane backgrounds and form the simplest and most important special class. We describe \( s \)-functions in terms of the action of the Frobenius endomorphism on formal power series and use this description to characterize 2-functions in terms of algebraic K-theory of the completed power series ring. This characterization leads to a general proof of integrality of the framing transformation, via a certain orthogonality relation in K-theory. We comment on a variety of possible applications. We here consider only power series with rational coefficients; the general situation when the coefficients belong to an arbitrary algebraic number field is treated in a companion paper.

David Robert Morrison	Related
Sheldon H. Katz	Related
Vadim Aleksandrovich Vologodsky	Related
Albrecht Klemm	Related
Johannes Walcher	Related
Ron Yehuda Donagi	Related

M. V. Movshev and A. Schwarz: “Generalized Chern–Simons action and maximally supersymmetric gauge theories,” pp. 327–340 in String-Math 2012 (Bonn, Germany, 16–21 July 2012). Edited by R. Donagi, S. Katz, A. Klemm, and D. R. Morrison. Proceedings of Symposia in Pure Mathematics 90. American Mathematical Society (Providence, RI), 2015. MR 3409803 Zbl 1356.81200 ArXiv 1304.7500 incollection

Michael V. Movshev	Related
David Robert Morrison	Related
Sheldon H. Katz	Related
Albrecht Klemm	Related
Ron Yehuda Donagi	Related