Symplectically invariant flow equations for N=2, D=4 gauged supergravity with hypermultiplets

Abstract

We consider N=2 supergravity in four dimensions, coupled to an arbitrary number of vector- and hypermultiplets, where abelian isometries of the quaternionic hyperscalar target manifold are gauged. Using a static and spherically or hyperbolically symmetric ansatz for the fields, a one-dimensional effective action is derived whose variation yields all the equations of motion. By imposing a sort of Dirac charge quantization condition, one can express the complete scalar potential in terms of a superpotential and write the action as a sum of squares. This leads to first-order flow equations, that imply the second-order equations of motion. The first-order flow turns out to be driven by Hamilton's characteristic function in the Hamilton-Jacobi formalism, and contains among other contributions the superpotential of the scalars. We then include also magnetic gaugings and generalize the flow equations to a symplectically covariant form. Moreover, by rotating the charges in an appropriate way, an alternative set of non-BPS first-order equations is obtained that corresponds to a different squaring of the action. Finally, we use our results to derive the attractor equations for near-horizon geometries of extremal black holes.

27 pages, uses jheppub.sty. v2: Typos corrected, final version to be published in JHEP. v3: Prefactor in equ. (3.74) corrected

References in corpus (10)

• Building an AdS/CFT superconductor
• Effective Holographic Theories for low-temperature condensed matter systems
• Lectures on Gauged Supergravity and Flux Compactifications
• Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity
• Charge Orbits of Symmetric Special Geometries and Attractors
• Entropy function and attractors for AdS black holes
• BPS black holes in N=2 D=4 gauged supergravities
• On the non-BPS first order flow in N=2 U(1)-gauged Supergravity
• On five-dimensional non-extremal charged black holes and FRW cosmology
• Abelian Hypermultiplet Gaugings and BPS Vacua in N = 2 Supergravity

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