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Polyakov formula

From Wikipedia, the free encyclopedia

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. Proposed by Alexander Markovich Polyakov this formula arose in the study of the quantum theory of strings. 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.

References

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  • Polyakov, Alexander (1981), "Quantum geometry of bosonic strings", Physics Letters B, 103 (3): 207–210, Bibcode:1981PhLB..103..207P, doi:10.1016/0370-2693(81)90743-7