Mirror Symmetry of K3 and Torus

TL;DR

This paper explores mirror symmetry for K3 surfaces and tori, calculating key geometric functions and confirming the absence of instanton corrections, aligning with algebraic geometry expectations.

Contribution

It provides explicit calculations of periods, mirror maps, and correlation functions for K3 surfaces and tori, demonstrating no instanton corrections occur.

Findings

No instanton corrections on K3 and torus

Calculated mirror maps and prepotentials

Confirmed algebraic geometry predictions

Abstract

We discuss a K3 and torus from view point of "mirror symmetry". We calculate the periods of the K3 surface and obtain the mirror map, the two-point correlation function, and the prepotential. Then we find there is no instanton correction on K3 (also torus), which is expected from view point of Algebraic geometry.