D-brane probes, branched double covers, and noncommutative resolutions

Addington, Nicolas; Segal, Edward Paul; Sharpe, Eric

doi:10.4310/atmp.2014.v18.n6.a5

Cited by 30 publications

(42 citation statements)

References 70 publications

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“…This results in a geometric interpretation as a branched double cover. This trick has been utilized since in for example [16][17][18][19][20], and see also [21] for a recent summary.…”

Section: Introductionmentioning

confidence: 99%

Undoing decomposition

Sharpe

2019

Int. J. Mod. Phys. A

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In this paper we discuss gauging one-form symmetries in two-dimensional theories. The existence of a global one-form symmetry in two dimensions typically signals a violation of cluster decomposition -an issue resolved by the observation that such theories decompose into disjoint unions, a result that has been applied to, for example, Gromov-Witten theory and gauged linear sigma model phases. In this paper we describe how gauging one-form symmetries in two-dimensional theories can be used to select particular elements of that disjoint union, effectively undoing decomposition. We examine such gaugings explicitly in examples involving orbifolds, nonsupersymmetric pure Yang-Mills theories, and supersymmetric gauge theories in two dimensions. Along the way, we learn explicit concrete details of the topological configurations that path integrals sum over when gauging a one-form symmetry, and we also uncover 'hidden' one-form symmetries.

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“…This results in a geometric interpretation as a branched double cover. This trick has been utilized since in for example [16][17][18][19][20], and see also [21] for a recent summary.…”

Section: Introductionmentioning

confidence: 99%

Undoing decomposition

Sharpe

2019

Int. J. Mod. Phys. A

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“…See e.g. [70,71] for further information on the U(1) R action for matrix factorizations.) Now, in a (bulk) nonlinear sigma model without superpotential, the U(1) R acts only on the fermions, not the bosons, so we are requiring that the bundles E 0,1 be equivariant with respect to a group that acts trivially on the space over which they are defined.…”

Section: Derived Categoriesmentioning

confidence: 99%

Categorical Equivalence and the Renormalization Group

Sharpe

2019

Fortschritte der Physik

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In this article we review how categorical equivalences are realized by renormalization group flow in physical realizations of stacks, derived categories, and derived schemes. We begin by reviewing the physical realization of sigma models on stacks, as (universality classes of) gauged sigma models, and look in particular at properties of sigma models on gerbes (equivalently, sigma models with restrictions on nonperturbative sectors), and ‘decomposition,’ in which two‐dimensional sigma models on gerbes decompose into disjoint unions of ordinary theories. We also discuss stack structures on examples of moduli spaces of SCFTs, focusing on elliptic curves, and implications of subtleties there for string dualities in other dimensions. In the second part of this article, we review the physical realization of derived categories in terms of renormalization group flow (time evolution) of combinations of D‐branes, antibranes, and tachyons. In the third part of this article, we review how Landau–Ginzburg models provide a physical realization of derived schemes, and also outline an example of a derived structure on a moduli spaces of SCFTs.

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“…Noncommutative resolutions, in the pertinent sense, are defined by their sheaves, and our claim is ultimately just an unraveling of definitions. See [43] for a computation of Gromov-Witten invariants in such a noncommutative resolution, and [25] for an orthogonal analysis involving D-brane probes.…”

Section: Further Examples and Noncommutative Resolutionsmentioning

confidence: 99%

“…More recent work such as [53,54] has studied dualities and dynamical supersymmetry breaking in (0,2) GLSM's. (Our own work, including [12,16,25,26,43], has spanned a number of the areas above.) Nor has this progress been confined to the physics community, as for example, work in progress on mathematics of gauged linear sigma models by T. Jarvis, Y. Ruan, and their collaborators was reported at a conference on the subject in Michigan this past March.…”

Section: Introductionsmentioning

confidence: 99%

“…[2,3,4,5,6,7,8,9,10] and references therein) to new developments in Calabi-Yau compactifications, including realizations of non-complete-intersection target spaces [11,12,13,14,15], non-birational phases [11,12,15,16,17,18,19,20] (leading to modern conjectures that all phases of GLSM's are related by a new notion known as "homological projective duality" [17,18,19,20,21,22,23]), nonperturbative realizations of geometry [11,12,15,16,24,25,26], realizations of noncommutative resolutions [12,16,25,26], and localization techniques [27,28]. Those localization techniques have been applied to deduce new methods for computing Gromov-Witten invariants [24,29], computations of elliptic genera directly in GLSM's [30,31,…”

Section: Introductionsmentioning

confidence: 99%

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Some recent advances in gauged linear sigma models

Sharpe¹

2014

Proceedings of Third International Satellite Conference on Mathematical Methods in Physics — PoS(ICMP 2013)

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Gauged linear sigma models (GLSM's) are simple generalizations of the supersymmetric CP n model which have played a surprisingly important role in string compactifications over the last twenty years. The last six years have seen a resurgence of interest in GLSM's and some new technologies that have significantly advanced our understanding of these tools. In this talk, we will first review the basic properties of GLSM's, and then briefly discuss a few of the recent advances in their understanding.

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D-brane probes, branched double covers, and noncommutative resolutions

Abstract: 16.04.15 KB. Ok to add accepted version to spira

Cited by 30 publications

References 70 publications

Undoing decomposition

Undoing decomposition

Categorical Equivalence and the Renormalization Group

Some recent advances in gauged linear sigma models

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