Abstract
We present a construction of the most general BPS black holes of STU supergravity ( mathcal{N} = 2 supersymmetric D = 4 supergravity coupled to three vector super-multiplets) with arbitrary asymptotic values of the scalar fields. These solutions are obtained by acting with a subset of the global symmetry generators on STU BPS black holes with zero values of the asymptotic scalars, both in the U-duality and the heterotic frame. The solutions are parameterized by fourteen parameters: four electric and four magnetic charges, and the asymptotic values of the six scalar fields. We also present BPS black hole solutions of a consistently truncated STU supergravity, which are parameterized by two electric and two magnetic charges and two scalar fields. These latter solutions are significantly simplified, and are very suitable for further explicit studies. We also explore a conformal inversion symmetry of the Couch-Torrence type, which maps any member of the fourteen-parameter family of BPS black holes to another member of the family. Furthermore, these solutions are expected to be valuable in the studies of various swampland conjectures in the moduli space of string compactifications.
Highlights
Theories to the so-called STU supergravity, which comprises N = 2 supergravity coupled to three vector supermultiplets
We present a construction of the most general BPS black holes of STU supergravity (N = 2 supersymmetric D = 4 supergravity coupled to three vector supermultiplets) with arbitrary asymptotic values of the scalar fields
Studies of BPS black holes in four-dimensional ungauged supergravity theories, such as the extremal STU black holes of the N = 2 supergravity theory coupled to three vector supermultiplets, have been a subject of intense research ever since their discovery [3, 5]
Summary
We shall provide explicit expressions for the bosonic sector of four-dimensional ungauged STU supergravity in the three different formulations we shall be using in this paper, and the explicit relations between them. We shall consider the formulation of STU supergravity that one would obtain by reducing eleven-dimensional supergravity on S7, performing an appropriate truncation from N = 8 to N = 2 supersymmetry, and turning off the gauge coupling constant in the four-dimensional theory. This formulation of STU supergravity is sometimes referred to as the U -duality invariant formulation. We shall consider STU supergravity in an intermediate formulation which we refer to as the 3+1 formulation In this case, instead of dualising two field strengths in the heterotic formulation only one is dualised
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