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Small-instanton transitions in F-theory

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Abstract

We study the phase transition between G-instantons and D3-branes quantitatively. A G-instanton is a classical solution to the self-dual equation of the M/F-theory three-form tensor field C in the complex fourfold. This phase transition is dual to that between ‘vertical’ small instantons and 5-branes in the heterotic string. Using G as a background gauge flux, we may dynamically control the gauge symmetry breaking and connect between different vacua of F-theory. We may understand the amount of flux undergoing the phase transition and the resulting number of D3-branes in terms of group-theoretical quantities. We also discuss the resulting chirality change and preservation of anomaly freedom.

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Notes

  1. In the literature, sometimes G-instanton refers to an instanton with the structure group G [23].

  2. We may also have additional U(1) factors and the total gauge group can be enhanced. Non-perturbatively enhanced gauge groups are also possible [26, 40]. In this paper, we restrict our focus to the perturbative gauge group in ten dimensions.

  3. In this paper, we use the same notation for a line bundle, its dual divisor and its first Chern class, without confusion.

  4. A U(1) gauge group may also be preserved, unless its gauge boson acquires a Stückelberg mass. Its condition is topological: the dual divisor corresponding to U(1) should be trivial in the base threefold [31, 45]. Since it depends on the generous geometry of the Calabi–Yau fourfold in F-theory, this mechanism has no dual in the heterotic side. An explicit construction for such G-flux in native F-theory is given [69].

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Acknowledgements

This work is partly supported by the Grant NRF-2018R1A2B2007163 of National Research Foundation of Korea.

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Authors and Affiliations

  1. Institute of Mathematical Sciences, Ewha Womans University, Seoul, 03760, Korea

    Stephen Angus

  2. Scranton Honors Program, Ewha Womans University, Seoul, 03760, Korea

    Kang-Sin Choi

  3. Asia Pacific Center for Theoretical Physics, Postech, Pohang, 37673, Korea

    Stephen Angus

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Angus, S., Choi, KS. Small-instanton transitions in F-theory. Eur. Phys. J. Plus 137, 274 (2022). https://doi.org/10.1140/epjp/s13360-022-02456-6

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