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Non-Birational Twisted Derived Equivalences in Abelian GLSMs

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Abstract

In this paper we discuss some examples of abelian gauged linear sigma models realizing twisted derived equivalences between non-birational spaces, and realizing geometries in novel fashions. Examples of gauged linear sigma models with non-birational Kähler phases are a relatively new phenomenon. Most of our examples involve gauged linear sigma models for complete intersections of quadric hypersurfaces, though we also discuss some more general cases and their interpretation. We also propose a more general understanding of the relationship between Kähler phases of gauged linear sigma models, namely that they are related by (and realize) Kuznetsov’s ‘homological projective duality.’ Along the way, we shall see how ‘noncommutative spaces’ (in Kontsevich’s sense) are realized physically in gauged linear sigma models, providing examples of new types of conformal field theories. Throughout, the physical realization of stacks plays a key role in interpreting physical structures appearing in GLSMs, and we find that stacks are implicitly much more common in GLSMs than previously realized.

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Authors and Affiliations

  1. Mathematics Department, University of Wisconsin, Madison, WI, 53706-1388, USA

    Andrei Căldăraru

  2. Department of Physics, University of Texas, Austin, Austin, TX, 78712-0264, USA

    Jacques Distler

  3. Institute for Advanced Study, School of Natural Sciences, Princeton, NJ, 08540, USA

    Simeon Hellerman

  4. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104-6395, USA

    Tony Pantev

  5. Physics Department, Virginia Tech, Blacksburg, VA, 24061, USA

    Eric Sharpe

Authors
  1. Andrei Căldăraru
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  2. Jacques Distler
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  3. Simeon Hellerman
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  4. Tony Pantev
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  5. Eric Sharpe
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Correspondence to Eric Sharpe.

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Communicated by N.A. Nekrasov

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Căldăraru, A., Distler, J., Hellerman, S. et al. Non-Birational Twisted Derived Equivalences in Abelian GLSMs. Commun. Math. Phys. 294, 605–645 (2010). https://doi.org/10.1007/s00220-009-0974-2

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