Local Calabi-Yau manifolds of type \tilde{A} via SYZ mirror symmetry

Atsushi Kanazawa; Siu-Cheong Lau

Local Calabi-Yau manifolds of type \tilde{A} via SYZ mirror symmetry

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arxiv 1605.00342 v3 pith:NA7JZ5TR submitted 2016-05-02 math.AG hep-thmath.SG

Atsushi Kanazawa , Siu-Cheong Lau This is my paper · ORCID

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abstract

We carry out the SYZ program for the local Calabi--Yau manifolds of type $\widetilde{A}$ by developing an equivariant SYZ theory for the toric Calabi--Yau manifolds of infinite-type. Mirror geometry is shown to be expressed in terms of the Riemann theta functions and generating functions of open Gromov--Witten invariants, whose modular properties are found and studied in this article. Our work also provides a mathematical justification for a mirror symmetry assertion of the physicists Hollowood--Iqbal--Vafa.

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Surface Defects in $A$-type Little String Theories
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The authors give a combinatorial partition function for A-type little string theories with a full-type surface defect and argue that two NS-limit regularizations are both regular due to a recursive pole-cancellation identity.

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