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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.


Branson, Thomas (2007), "Q-curvature, spectral invariants, and representation theory" (PDF), Symmetry, Integrability and Geometry (SIGMA) 3

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