Sphere Partition Function of Calabi-Yau GLSMs.

Area of Science:

• String Theory
• Mathematical Physics
• Algebraic Geometry

Background:

• Calabi-Yau manifolds are central to string theory and algebraic geometry.
• Gauged linear sigma models (GLSMs) provide a powerful computational tool for studying Calabi-Yau geometry.
• The sphere partition function of GLSMs has been established as a method to compute the exact Kähler potential.

Purpose of the Study:

• To propose a universal expression for the sphere partition function of Calabi-Yau GLSMs in hybrid phases.
• To generalize existing results for specific Calabi-Yau constructions.
• To connect these computations with established theories like mirror symmetry and FJRW theory.

Main Methods:

• Developing a universal formula for the sphere partition function in hybrid phases of Calabi-Yau GLSMs.
• Utilizing Givental's I/J-functions and the Gamma class as key components.
• Testing the proposed expression for one- and two-parameter abelian GLSMs.

Main Results:

• A universal expression for the sphere partition function of Calabi-Yau GLSMs in hybrid phases has been formulated.
• The formula encompasses special cases such as Calabi-Yau complete intersections and Landau-Ginzburg orbifolds.
• The results demonstrate consistency with known results from mirror symmetry and FJRW theory for tested examples.

Conclusions:

• The proposed universal expression offers a unified approach to computing sphere partition functions in Calabi-Yau GLSMs.
• This work bridges computational methods in GLSMs with foundational concepts in string theory and algebraic geometry.
• The findings provide a basis for further exploration of Calabi-Yau moduli spaces and related mathematical structures.