Background metric in supergravity theories

Physics

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Scientific paper

In supergravity theories, we investigate the conformal anomaly of the path-integral determinant and the problem-of fermion zero modes in the presence of a nontrivial background metric. Except in SO(3)-invariant supergravity, there are nonvanishing conformal anomalies. As a consequence, amplitudes around the nontrivial background metric contain unpredictable arbitrariness. The fermion zero modes which are explicitly constructed for the Euclidean Schwarzschild metric are interpreted as an indication of the supersymmetric multiplet structure of a black hole. The degree of degeneracy of a black hole is 24n in SO(n) supergravity.

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