Gromov-Witten theory of product stacks

Andreini, Elena; Jiang, Yunfeng; Tseng, Hsian-Hua

doi:10.48550/arxiv.0905.2258

Cited by 15 publications

(24 citation statements)

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“…One of the applications of the result above is to Gromov-Witten theory, where it has been checked and applied to simplify computations of Gromov-Witten invariants of gerbes, see [33,34,35,36,37,38]. Another application is to gauged linear sigma models [15], where it answers old questions about the meaning of the Landau-Ginzburg point in a GLSM for a complete intersection of quadrics, as well as corrects old lore on GLSM's.…”

Section: Review Of Two-dimensional Theories With Altered Topological ...mentioning

confidence: 99%

“…For the two-dimensional decomposition conjecture pertinent to sigma models on gerbes, there is now abundant evidence, including all-genera partition function computations in orbifold examples [14], checks in mirror symmetry and quantum cohomology [14], applications to gauged linear sigma models [15], and now checks of predictions for Gromov-Witten invariants [33,34,35,36,37,38]. By contrast, in the four-dimensional case above, we have no independent evidence, no examples, only the arguments above.…”

Section: A Four-dimensional Decomposition Conjecturementioning

confidence: 99%

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Sums over topological sectors and quantization of Fayet–Iliopoulos parameters

Hellerman¹,

Sharpe²

2011

Advances in Theoretical and Mathematical Physics

109

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In this paper we discuss quantization of the Fayet-Iliopoulos parameter in supergravity theories with altered nonperturbative sectors, which were recently used to argue a fractional quantization condition. Nonlinear sigma models with altered nonperturbative sectors are the same as nonlinear sigma models on special stacks known as gerbes. After reviewing the existing results on such theories in two dimensions, we discuss examples of gerby moduli 'spaces' appearing in four-dimensional field theory and string compactifications, and the effect of various dualities. We discuss global topological defects arising when a field or string theory moduli space has a gerbe structure. We also outline how to generalize results of Bagger-Witten and more recent authors on quantization issues in supergravities from smooth moduli spaces to smooth moduli stacks, focusing particular attention on stacks that have gerbe structures.

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Section: Review Of Two-dimensional Theories With Altered Topological ...mentioning

confidence: 99%

Section: A Four-dimensional Decomposition Conjecturementioning

confidence: 99%

Sums over topological sectors and quantization of Fayet–Iliopoulos parameters

Hellerman¹,

Sharpe²

2011

Advances in Theoretical and Mathematical Physics

109

View full text Add to dashboard Cite

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“…As for ordinary prestable curves in order to describe the Picard group of a twisted curve along with its torsion subgroups we will make use of dual graphs encoding the topological type of the curve and the isotropy groups of its special points. In [7] we introduced gerby modular graphs generalizing Definition 3.4. They will allows us to suitably label strata and irreducible components of stacks parametrizing twisted curves and twisted stable maps and will make much easier our notation in Section 6.2.…”

Section: 2mentioning

confidence: 99%

“…where k = |E loop τ |, r l = γ(e l ) for any e l ∈ E loop τ and φ(−) is the Euler totient function 7 . Moreover, by tensoring any N s with different possible choices of r-torsion line bundles in Pic C we get r 2g−b 1 (τ ) non isomorphic twisted stable maps.…”

mentioning

confidence: 99%

Gromov-Witten theory of banded gerbes over schemes

Andreini,

Jiang,

Tseng

2011

Preprint

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Let X be a smooth complex projective algebraic variety. Let G be a Gbanded gerbe with G a finite abelian group. We prove an exact formula expressing genus g orbifold Gromov-Witten invariants of G in terms of those of X. Contents 1. Introduction Conventions Acknowledgments 2. Orbifold Gromov-Witten theory 2.1. Twisted stable maps 2.2. Virtual Fundamental Class 2.3. Gromov-Witten invariants and Descendant Potential 3. Twisted curves 3.1. The Picard group of prestable curves 3.2. The Picard group of twisted curves 3.3. The Brauer group 4. Rephrasing the moduli problem 5. The structure morphism p 6. Push-forward formula 6.1. Comparison of Obstruction Theories 6.2. Proof of the pushforward formula 7. Orbifold Gromov-Witten theory of banded gerbes 7.1. Orbifold Gromov-Witten invariants 7.2. Decomposition of Gromov Witten theory Appendix A. A few useful facts about degree of morphisms References

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“…(If the subgroup is abelian, this means that the theory has a finite global one-form symmetry, in modern language, but decomposition is defined more generally.) See [14][15][16] for detailed discussions of such examples, and see also [17][18][19][20][21][22] for applications to Gromov-Witten theory, [23][24][25][26][27][28][29] for applications to phases of gauged linear sigma models (GLSMs), [30] for applications in heterotic string compactifications, [12] for applications to elliptic genera of two-dimensional pure supersymmetric gauge theories, and [10] for four-dimensional analogues, for example.…”

Section: Introductionmentioning

confidence: 99%

A generalization of decomposition in orbifolds

Robbins,

Sharpe,

Vandermeulen

2021

Preprint

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This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions of theories. However, decomposition can be, at least naively, broken in orbifolds if the orbifold has discrete torsion in the trivially-acting subgroup. (Formally, this breaks finite global one-form symmetries.) Nevertheless, even in such cases, one still sees rudiments of decomposition. In this paper, we generalize decomposition in orbifolds to include such examples of discrete torsion, which we check in numerous examples. Our analysis includes as special cases (and in one sense generalizes) quantum symmetries of abelian orbifolds.

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Gromov-Witten theory of product stacks

Cited by 15 publications

References 0 publications

Sums over topological sectors and quantization of Fayet–Iliopoulos parameters

Sums over topological sectors and quantization of Fayet–Iliopoulos parameters

Gromov-Witten theory of banded gerbes over schemes

A generalization of decomposition in orbifolds

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