Relations between elliptic curves and topological quantum field theory

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I heard that there are relations between elliptic curves and topological quantum field theory (TQFT).

I googled and found that something called "elliptic genus" might be the key word to relate these two fields. (It might be wrong, though.)

However, I still lack knowledge to search good references.

Could you give me some references that explain the relations between elliptic curves and TQFT for people who have some basic knowledge of these two fields separately?