2009
DOI: 10.1007/s00220-009-0974-2
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Non-Birational Twisted Derived Equivalences in Abelian GLSMs

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 under… Show more

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Cited by 92 publications
(191 citation statements)
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“…We will also describe a tentative proposal for understanding the mathematical relationship between non-birational phases: we propose that they should be understood in terms of Kuznetsov's homological projective duality [6,7,8]. In this paper we will only begin to outline the relevance of Kuznetsov's work -a much more thorough description, and further application to abelian GLSM's, will appear in [9].…”
Section: Non-birational Derived Equivalences In Nonabelian Glsmsmentioning
confidence: 99%
“…We will also describe a tentative proposal for understanding the mathematical relationship between non-birational phases: we propose that they should be understood in terms of Kuznetsov's homological projective duality [6,7,8]. In this paper we will only begin to outline the relevance of Kuznetsov's work -a much more thorough description, and further application to abelian GLSM's, will appear in [9].…”
Section: Non-birational Derived Equivalences In Nonabelian Glsmsmentioning
confidence: 99%
“…(Strictly speaking, because of the Z 2 orbifold along the fibers, they form a module over the sheaf of even parts of the Clifford algebra.) Mathematically, such matrix factorizations define what is known as a noncommutative resolution of the branched double cover [16,22]. Noncommutative resolutions, in the pertinent sense, are defined by their sheaves, and our claim is ultimately just an unraveling of definitions.…”
Section: Further Examples and Noncommutative Resolutionsmentioning
confidence: 98%
“…Perhaps the most important subtlety is that, away from the locus {det A = 0} where some of the φ i become massless, the only massless fields have nonminimal charges. Due to subtleties in two-dimensional quantum field theories [16,57,58,59], if the only massless fields have charges ±2, then physics sees a double cover, and so the correct interpretation of the r ≪ 0 limit is as a nonlinear sigma model on a branched double cover of CP 1 , branched along the locus {det A = 0}. Since A is a 4 × 4 matrix, det A is a degree four polynomial in p's, so the branch locus is degree four.…”
Section: Decomposition Conjecture and Corrected Analysismentioning
confidence: 99%
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