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 stroke me as something deep and subtle connecting physics to mathematics.

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.