超群规范线性西格玛模型及其物理数学
Supergroup Gauged Linear Sigma Models and their Physical Mathematics
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中文总结 AI 辅助
本文构造了带超规范群的二维超对称规范线性西格玛模型，将其应用于数学，推广了卡拉比-丘相关对应关系、拓扑转变等数学成果，为超格拉斯曼流形/超群的相关研究提供了物理视角。
中文摘要 AI 辅助
我们构造了具有$\boldsymbol{\text{U}(1|1)^N}$超规范群（可能带有超势）的二维$\boldsymbol{\text{N}=(2,2)}$规范线性西格玛模型。尽管这些模型是非幺正的，我们仍可研究其超对称态空间，并探索它们在数学中的应用。特别地，我们发现超格拉斯曼流形中超曲面完全交上的非线性西格玛模型与超规范朗道-金兹堡轨形之间存在关联，该关联可约化为完全交的常规卡拉比-丘/朗道-金兹堡对应，这构成了Clader[1]与Zhao[2]所证明对应关系的超格拉斯曼流形/超群推广。类似地，我们发现超格拉斯曼流形乘积中超曲面上的非线性西格玛模型与混合型非线性西格玛模型/超规范朗道-金兹堡轨形之间存在关联，该关联可约化为乘积空间中超曲面的常规混合型卡拉比-丘/朗道-金兹堡对应，这构成了Fan-Jarvis-Ruan[3]所证明对应关系的超格拉斯曼流形/超群推广。我们还发现，超格拉斯曼流形上的卡拉比-丘超向量丛可发生物理相关的温和拓扑变化，该变化可约化为常规Atiyah型 flopping 转变，这构成了数学中卡拉比-丘向量丛双有理等价的超格拉斯曼流形推广。类似地，我们发现超格拉斯曼流形中的二次型卡拉比-丘完全交也可发生物理相关的拓扑变化，该变化可约化为常规锥状转变，这构成了Kuznetsov-Perry[4]所证明的卡拉比-丘二次型同调射影对偶的超格拉斯曼流形推广。
英文摘要
We construct 2d $\mathcal{N}=(2,2)$ gauged linear sigma models with $\mathrm{U}(1|1)^N$ supergauge group possibly with superpotential. Despite being nonunitary, one can still study their space of supersymmetric states and explore their applications to mathematics. In particular, we find a relation between a nonlinear sigma model on a Calabi-Yau complete intersection of hypersurfaces in a super-Grassmannian and a supergauged Landau-Ginzburg orbifold, which can reduce to a regular Calabi-Yau/Landau-Ginzburg correspondence for complete intersections. This defines a super-Grassmannian/supergroup generalization of the correspondence proved by Clader [1] and Zhao [2]. Similarly, we find a relation between a nonlinear sigma model on a Calabi-Yau hypersurface in a product of super-Grassmannians and a hybrid NLSM/supergauged Landau-Ginzburg orbifold, which can reduce to a regular hybrid Calabi-Yau/Landau-Ginzburg correspondence for hypersurfaces in product space. This defines a super-Grassmannian/supergroup generalization of the correspondence proved by Fan-Jarvis-Ruan [3]. We also find that Calabi-Yau supervector bundles over a super-Grassmannian can undergo a physically related mild topology change which is reducible to a regular Atiyah-type flop transition. This defines a super-Grassmannian generalization of a birational equivalence of Calabi-Yau vector bundles in mathematics. Similarly, we find that a Calabi-Yau complete intersection of quadrics in a super-Grassmannian can also undergo a physically related topology change which is reducible to a regular conifold transition. This defines a super-Grassmannian generalization of a homological projective duality for Calabi-Yau quadrics by Kuznetsov-Perry [4] in mathematics.
发表机构
- National University of Singapore（新加坡国立大学）
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