From equivariant volumes to equivariant periods
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866916282840907776 |
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| author | Cassia, Luca Piazzalunga, Nicolo Zabzine, Maxim |
| author_facet | Cassia, Luca Piazzalunga, Nicolo Zabzine, Maxim |
| contents | We consider generalizations of equivariant volumes of abelian GIT quotients obtained as partition functions of 1d, 2d, and 3d supersymmetric GLSM on $S^1$, $D^2$ and $D^2 \times S^1$, respectively. We define these objects and study their dependence on equivariant parameters for non-compact toric Kähler quotients. We generalize the finite-difference equations (shift equations) obeyed by equivariant volumes to these partition functions. The partition functions are annihilated by differential/difference operators that represent equivariant quantum cohomology/K-theory relations of the target and the appearance of compact divisors in these relations plays a crucial role in the analysis of the non-equivariant limit. We show that the expansion in equivariant parameters contains information about genus-zero Gromov-Witten invariants of the target. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_13269 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | From equivariant volumes to equivariant periods Cassia, Luca Piazzalunga, Nicolo Zabzine, Maxim High Energy Physics - Theory Mathematical Physics Algebraic Geometry Symplectic Geometry We consider generalizations of equivariant volumes of abelian GIT quotients obtained as partition functions of 1d, 2d, and 3d supersymmetric GLSM on $S^1$, $D^2$ and $D^2 \times S^1$, respectively. We define these objects and study their dependence on equivariant parameters for non-compact toric Kähler quotients. We generalize the finite-difference equations (shift equations) obeyed by equivariant volumes to these partition functions. The partition functions are annihilated by differential/difference operators that represent equivariant quantum cohomology/K-theory relations of the target and the appearance of compact divisors in these relations plays a crucial role in the analysis of the non-equivariant limit. We show that the expansion in equivariant parameters contains information about genus-zero Gromov-Witten invariants of the target. |
| title | From equivariant volumes to equivariant periods |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2211.13269 |