TITLE: Mathematical uses of string theory
QUESTION [33 upvotes]: It is widely believed that correctness of string theory as a physical theory will not be decided in the near future. Regardless whether this will turn out to be correct or not, mathematical concepts derived from string theory may have proved theorems whose correctness (and relevance for mathematics) is undisputed.
What are (important in mathematics) mathematical theorems which wouldn‘t have been proved without the development of string theory?

REPLY [5 votes]: I recall that Richard Wentworth's first paper on precise constants in bosonization formula (which is part of his PhD thesis?) extensively used computational methods from bosonic string theory. I am not sure if the methods have been justified, since his second paper used completely different methods to derive the same result. Later I was informed that Jorgenson proved the same result using much more classical methods like asymptotic expansion of heat kernel, construction and estimate of the paramatrix, etc.  
To me I feel the fact that path integral and $\zeta$-function regularization methods "coincide" in actual computation for topics related to Polyakov measure is not a mere coincidence. I do not really know string theory, but this observation striked me as something deep and subtle connecting physics to mathematics.