From equivariant volumes to equivariant periods

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Theoretical and Mathematical Physics Pub Date : 2024-06-06 DOI:10.4310/atmp.2023.v27.n4.a1
Luca Cassia, Nicolò Piazzalunga, Maxim Zabzine
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引用次数: 0

Abstract

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.
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从等变体积到等变周期
我们考虑了分别作为 1d、2d 和 3d 超对称 GLSM 在 $S^1$、$D^2$ 和 $D^2 \times S^1$ 上的分割函数而得到的非等边 GIT 商的等变体积的广义。我们定义了这些对象,并研究了它们对非紧凑环凯勒商的等变参数的依赖性。我们把等变体积服从的有限差分方程(移位方程)推广到这些分区函数。分区函数由微分/差分算子湮灭,这些算子代表了目标的等变量子同调/K 理论关系,而这些关系中紧凑除数的出现在非等变极限的分析中起着至关重要的作用。我们证明了等变参数的扩展包含了目标的零属格罗莫夫-维滕不变式的信息。
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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