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Flopping and slicing: SO(4) and Spin(4)-models

Esole, Mboyo and Kang, Monica Jinwoo (2020) Flopping and slicing: SO(4) and Spin(4)-models. Advances in Theoretical and Mathematical Physics, 23 (4). pp. 1003-1066. ISSN 1095-0761. doi:10.4310/atmp.2019.v23.n4.a2.

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We study the geometric engineering of gauge theories with gauge group Spin(4) and SO(4) using crepant resolutions of Weierstrass models. The corresponding elliptic fibrations realize a collision of singularities corresponding to two fibers with dual graphs A₁. There are eight different ways to engineer such collisions using decorated Kodaira fibers. The Mordell–Weil group of the elliptic fibration is required to be trivial for Spin(4) and ℤ/2ℤ for SO(4). Each of these models has two possible crepant resolutions connected by a flop. We also compute a generating function for the Euler characteristic of such elliptic fibrations over a base of arbitrary dimensions. In the case of a threefold, we also compute the triple intersection numbers of the fibral divisors. In the case of Calabi–Yau threefolds, we also compute their Hodge numbers and check the cancellations of anomalies in a six-dimensional supergravity theory.

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Additional Information:© 2020 International Press. The authors are grateful to Lara Anderson, Richard Derryberry, Ravi Jagadeesan, Patrick Jefferson, Julian Salazar, and Shing-Tung Yau for useful discussions. This paper answers a question that was raised during the 2017 workshop on Singular Geometry and Higgs Bundles in String Theory organized by the American Institute of Mathematics (AIM). The authors would like to thank the support and hospitality of AIM and all the participants of the workshop. The authors are particularly thankful to those who attended the focus group on the mathematics of F-theory: Richard Derryberry, William Donovan, Olivia Dumitrescu, Matthew Woolf, and Laura Schaposnik. M.E. is supported in part by the National Science Foundation (NSF) grant DMS-1701635 "Elliptic Fibrations and String Theory". M.J.K. would like to acknowledge a partial support from NSF grant PHY-1352084.
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Issue or Number:4
Record Number:CaltechAUTHORS:20200131-112634260
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101033
Deposited By: Tony Diaz
Deposited On:31 Jan 2020 20:42
Last Modified:16 Nov 2021 17:58

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