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Abstract
Abstract The problem of gauge dependence of the effective action in multidimensional supergravities (SG) is investigated. As an example d =5 SGs are considered. The convenient gauge-dependent effective action (EA) and gauge-invariant Vilkovisky-De Witt EA in d =5, N =2, 4, 6, 8 SGs on the background R 4 ×S 1 with accuracy to linear curvature terms are obtained. The convenient three-gauge-parameter-dependent EA in d =5, N =2 gauged SG on the background R 4 ×S 1 is calculated. The Vilkovisky-De Witt EA in d =5 SGs on the background R 4 ×S 1 at non-zero temperature is also obtained.
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