Conformal geometry | Spectral theory

Polyakov formula

In differential geometry and mathematical physics (especially string theory), the Polyakov formula expresses the conformal variation of the zeta functional determinant of a Riemannian manifold. The corresponding density is local, and therefore is a Riemannian curvature invariant. In particular, whereas the functional determinant itself is prohibitively difficult to work with in general, its conformal variation can be written down explicitly. (Wikipedia).

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Related pages

Functional determinant | Differential geometry | Conformal geometry | String theory | Minakshisundaram–Pleijel zeta function | Riemannian manifold | Curvature invariant