The scalars of N=2, D=5 and attractor equations

We compute four-derivative corrections to the AdS supergravity actions arising from the near-horizon geometry of N M5-branes wrapped on either one or two Riemann surfaces. This setup features the novel presence of both gauged isometries as well as nontrivial hypermultiplets. We argue that the 5d Chern-Simons terms receive not only higher-derivative corrections but also contributions from Killing vector parameters, which we find must also be corrected. We check the central charges found by our supergravity methods against the dual field theory results and find perfect agreement at leading and subleading order in N . Along the way, we find higher derivative corrections to general AdS 5 and AdS 3 × Σ g geometries.

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“…We will use the notation and conventions of [76] throughout. For applications to supergravity, see [77], [72] and especially [51].…”

Section: Hypercomplex and Quaternionic Geometriesmentioning

confidence: 99%

Higher derivative corrections and central charges from wrapped M5-branes

Baggio

Halmagyi

Mayerson

et al. 2014

J. High Energ. Phys.

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“…, 2r and i, j = 1, 2) and Σ ABCD is completely symmetric. We do not use vielbeins in this paper, but the interested reader may find a discussion of quaternionic-Kähler manifold in terms of vielbeins in the article on quaternionic-Kähler manifolds in [14] and a definition of quaternionic-Kähler manifolds that starts from vielbeins has been given in [15], see also [16,17,7].…”

Section: )mentioning

confidence: 99%

Flows on Quaternionic-K�hler and Very Special Real Manifolds

Alekseevsky

Cortés

Devchand

et al. 2003

Communications in Mathematical Physics

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BPS solutions of 5-dimensional supergravity correspond to certain gradient flows on the product M × N of a quaternionic-Kähler manifold M of negative scalar curvature and a very special real manifold N of dimension n ≥ 0. Such gradient flows are generated by the "energy function" f = P 2 , where P is a (bundle-valued) moment map associated to n + 1 Killing vector fields on M . We calculate the Hessian of f at critical points and derive some properties of its spectrum for general quaternionic-Kähler manifolds. For the homogeneous quaternionic-Kähler manifolds we prove more specific results depending on the structure of the isotropy group. For example, we show that there always exists a Killing vector field vanishing at a point p ∈ M such that the Hessian of f at p has split signature. This generalizes results obtained recently for the complex hyperbolic plane (universal hypermultiplet) in the context of 5-dimensional supergravity. For symmetric quaternionic-Kähler manifolds we show the existence of non-degenerate local extrema of f , for appropriate Killing vector fields. On the other hand, for the non-symmetric homogeneous quaternionic-Kähler manifolds we find degenerate local minima. This work was supported by the priority programme "String Theory"of the Deutsche Forschungsgemeinschaft.

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“…In addition to the warp factor in the bulk, brane world scenarios often contain bulk scalar fields. Examples include the dilaton in Horava-Witten theory [1] (associated with the volume of the compactified 6d Calabi-Yau space) where the 5d effective theory can be obtained [2]; the Randall-Sundrum model [3] with phenomenological stabilization [5] where the choice of the bulk/brane potentials must be consistent with the 5d warp geometry [6,7], the scalar sector of the supergravity realization of the Randall-Sundrum model [8], bulk supergravity with domain walls [10] and others.…”

Section: Introductionmentioning

confidence: 99%

Warped geometry of brane worlds

Felder

Frolov

Kofman

2002

Class. Quantum Grav.

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We study the dynamical equations for extra-dimensional dependence of a warp factor and a bulk scalar in 5d brane world scenarios with induced brane metric of constant curvature. These equations are similar to those for the time dependence of the scale factor and a scalar field in 4d cosmology, but with the sign of the scalar field potential reversed. Based on this analogy, we introduce novel methods for studying the warped geometry. We construct the full phase portraits of the warp factor/scalar system for several examples of the bulk potential. This allows us to view the global properties of the warped geometry. For flat branes, the phase portrait is two dimensional. Moving along typical phase trajectories, the warp factor is initially increasing and finally decreasing. All trajectories have timelike gradient-dominated singularities at one or both of their ends, which are reachable in a finite distance and must be screened by the branes. For curved branes, the phase portrait is three dimensional. However, as the warp factor increases the phase trajectories tend towards the two dimensional surface corresponding to flat branes. We discuss this property as a mechanism that may stretch the curved brane to be almost flat, with a small cosmological constant. Finally, we describe the embedding of branes in the 5d bulk using the phase space geometric methods developed here. In this language the boundary conditions at the branes can be described as a 1d curve in the phase space. We discuss the naturalness of tuning the brane potential to stabilize the brane world system.

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The scalars of N=2, D=5 and attractor equations

Cited by 3 publications

References 40 publications

Higher derivative corrections and central charges from wrapped M5-branes

Higher derivative corrections and central charges from wrapped M5-branes

Flows on Quaternionic-K�hler and Very Special Real Manifolds

Warped geometry of brane worlds

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