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The Physical Mirror Equivalence for the Local \({\mathbb{P}^2}\)

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Abstract

In this paper we consider the total space of the canonical bundle of \({\mathbb{P}^2}\) and we use a proposal by Hosono, together with results of Seidel and Auroux–Katzarkov–Orlov, to deduce the physical mirror equivalence between \({D^b_{\mathbb{P}^2}(K_{\mathbb{P}2})}\) and the derived Fukaya category of its mirror which assigns the expected central charge to BPS states. By construction, our equivalence is compatible with the mirror map relating the complex and the Kähler moduli spaces and with the computation of Gromov–Witten invariants.

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Authors and Affiliations

  1. Dipartimento di Scienza ed Alta Tecnologia, Università degli Studi dell’Insubria, Via Valleggio 11, 22100, Como, Italy

    Sergio Luigi Cacciatori

  2. INFN, via Celoria 16, 20133, Milan, Italy

    Sergio Luigi Cacciatori

  3. Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133, Milan, Italy

    Marco Compagnoni

  4. Department of Mathematics, Oregon State University, Corvallis, OR, USA

    Stefano Guerra

Authors
  1. Sergio Luigi Cacciatori
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  2. Marco Compagnoni
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  3. Stefano Guerra
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Correspondence to Marco Compagnoni.

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Communicated by A. Klemm

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Cacciatori, S.L., Compagnoni, M. & Guerra, S. The Physical Mirror Equivalence for the Local \({\mathbb{P}^2}\) . Commun. Math. Phys. 333, 367–388 (2015). https://doi.org/10.1007/s00220-014-2214-7

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  • DOI: https://doi.org/10.1007/s00220-014-2214-7

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