Gauge dependence of the effective action in multidimensional theories of supergravity

Using the 5-dimensional supergravity as an example, the problem of gauge dependence of the effective action (EA) of multidimensional SUGRA's is discussed. The standard and the Vikovisky-De Witt EA's are computed up to the terms linear in curvature for d=5, N=2, 4, 6, 8 SUGRA's on the R₄,×S₁ background, where R₄, is a 4-dimensional curved space, and S₁ a 1-dimensional sphere. The standard EA obtained in d=5, N= 2 gauge SUGRA on the R ₄ ⁰ ×S₁, where R ₄ ⁰ is a flat 4-dimensional space, depends on three gauge parameters. The gauge-invariant Vilkovsky-De Witt EA is computed for a d=5 SUGRA with broken symmetry on the r ₄ ⁰ ×S₁ background, where R ₄ ⁰ is a 4-dimensional space with nonzero temperature.Translated from Izvestiya Vyssihkh Uchebnykh Zavedenii, Fizika, No. 5, pp. 53–59, May, 1989.I am grateful to I. L. Bukhbinder, I. V. Tyutin, and A. A. Tseitlin for many useful discussions.