Euclidean Supergravity

Abstract

Supergravity with eight supercharges in a four-dimensional Euclidean space is constructed at the full non-linear level by performing an off-shell time-like reduction of five-dimensional supergravity. The resulting four-dimensional theory is realized off-shell with the Weyl, vector and tensor supermultiplets and a corresponding multiplet calculus. Hypermultiplets are included as well, but they are themselves only realized with on-shell supersymmetry. The off-shell reduction leads to a full understanding of the Euclidean theory. A complete multiplet calculus is presented along the lines of the Minkowskian theory. Unlike in Minkowski space, chiral and anti-chiral multiplets are real and supersymmetric actions are generally unbounded from below. Precisely as in the Minkowski case, where one has different formulations of Poincaré supergravity by introducing different compensating supermultiplets, one can also obtain different versions of Euclidean supergravity.

42 pages

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Cited by in corpus (23)

• The Unreasonable Effectiveness of Higher-Derivative Supergravity in AdS${}_4$ Holography
• Topologically twisted indices in five dimensions and holography
• Euclidean Black Saddles and AdS${}_4$ Black Holes
• Supersymmetric solitons and a degeneracy of solutions in AdS/CFT
• On the quantum entropy function in 4d gauged supergravity
• BRST quantization and equivariant cohomology: localization with asymptotic boundaries
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• Twisting and localization in supergravity: equivariant cohomology of BPS black holes
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• One-loop determinants for black holes in 4d gauged supergravity
• Topological AdS/CFT
• Non-topological logarithmic corrections in minimal gauged supergravity
• The joy of factorization at large $N$: five-dimensional indices and AdS black holes
• Special Geometry, Hessian Structures and Applications
• Five-dimensional vector multiplets in arbitrary signature
• Killing Spinors for Finite Temperature Euclidean Solutions at the BPS Bound
• Localization on $Ad{S}_3\times S^2$ I: the 4d/5d connection in off-shell Euclidean supergravity
• Maximally symmetric nuts in 4d $\mathcal{N}=2$ higher derivative supergravity
• Higher-Derivative Supergravity, AdS${}_4$ Holography, and Black Holes
• On the localization manifold of 5d supersymmetric spinning black holes
• Ten-dimensional lifts of global supersymmetry on curved spaces
• Heisenberg-invariant self-dual Einstein manifolds
• On the exact entropy of $\mathcal{N}=2$ black holes