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Elliptic Genus of Phases of N = 2 Theories

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Abstract

We discuss an algebro-geometric description of Witten’s phases of N = 2 theories and propose a definition of their elliptic genus provided some conditions on singularities of the phases are met. For Landau–Ginzburg phase one recovers elliptic genus of LG models proposed in physics literature in early 1990s. For certain transitions between phases we derive invariance of elliptic genus from an equivariant form of McKay correspondence for elliptic genus. As special cases one obtains Landau–Giznburg/Calabi–Yau correspondence for elliptic genus of weighted homogeneous potentials as well as certain hybrid/CY correspondences.

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  1. Department of Mathematics, University of Illinois, Chicago, IL, 60607, USA

    Anatoly Libgober

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  1. Anatoly Libgober
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Correspondence to Anatoly Libgober.

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Communicated by H. Ooguri

Author supported by a grant from Simons Foundation.

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Libgober, A. Elliptic Genus of Phases of N = 2 Theories. Commun. Math. Phys. 340, 939–958 (2015). https://doi.org/10.1007/s00220-015-2465-y

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