Abstract:We investigate supergravity instantons in Euclidean AdS 5 × S 5 /Z k . These solutions are expected to be dual to instantons of N = 2 quiver gauge theories. On the supergravity side the (extremal) instanton solutions are neatly described by the (lightlike) geodesics on the AdS moduli space for which we find the explicit expression and compute the on-shell actions in terms of the quantised charges. The lightlike geodesics fall into two categories depending on the degree of nilpotency of the Noether charge matrix carried by the geodesic: for degree 2 the instantons preserve 8 supercharges and for degree 3 they are non-SUSY. We expect that these findings should apply to more general situations in the sense that there is a map between geodesics on moduli-spaces of Euclidean AdS vacua and instantons with holographic counterparts.
ABSTRACT. In the study of stationary solutions in extended supergravities with symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play an important role. In this paper we discuss two approaches to determine the nilpotent orbits of a real symmetric pair. We apply our methods to an explicit example, and thereby classify the nilpotent orbits of (SL2(R)) 4 acting on the fourth tensor power of the natural 2-dimensional SL2(R)-module. This makes it possible to classify all stationary solutions of the so-called STUsupergravity model.
We investigate the holographic dual to supergravity instanton solutions in AdS 5 × S 5 /Z k , which are described entirely in terms of geodesics on the AdS moduli space. These instantons are expected to be holographically dual to instantons in an N = 2 necklace quiver gauge theory in four dimensions with k gauge nodes, at large N. For the supersymmetric instantons we find a precise match between the on-shell actions and the vevs of Tr[F 2 ] and Tr[F ∧F ] computed on both sides of the duality. This correspondence requires an exact identification between the massless supergravity scalars and the dual gauge couplings which we give in detail. We also find a candidate for the supergravity dual of a quasi-instanton in the quiver theory, which is a non-supersymmetric extremal solution.manifold (1.1) has exactly k Abelian isometries that act as shifts of k real scalars. This fixes the Wick-rotation uniquely to [2]If one restricts to instanton solutions with spherical symmetry (i.e. respecting the rotational SO(5) symmetry of Euclidean AdS 5 ) for simplicity, then the scalar field equations of motion reduce to geodesic equations on M moduli and the Einstein equations of motion decouple from the scalar fields into a universal form, [2,6,7]. The metric is then only sensitive to the constant velocity of the geodesics (in an affine parametrization), which we denote as cwhere φ I denote the moduli, G IJ is the metric on (1.2) and a dot is a derivative with respect to the affine coordinate. Not surprisingly the description of geodesics on a coset space like (1.2) can be understood entirely using group theory [1]. The properties and meaning of geodesics depend strongly on whether they are time-like (c > 0), space-like (c < 0) or null (c = 0). When c < 0 the instantons are called super-extremal and the geometry describes a smooth two-sided wormhole that asymptotes to AdS on both sides [8]. A very explicit and concrete embedding of such wormholes was found inside AdS 5 × S 5 /Z k when k > 1 [2]. When k = 1 the scalars are singular and the corresponding wormholes are not considered as physical [9]. These Euclidean "axionic" wormholes have a long history in cosmology, QCD, holography and quantum gravity (see for instance [2, 10-17] ) which was reviewed in the comprehensive paper [18].When c > 0 the instantons are called sub-extremal and the geometry corresponds to a singular "spiky" deformation of AdS. The holographic description of these instantons is unclear but for c small enough a suggestion was made in [9] in the case of AdS 5 × S 5 . In this paper we find that the same interpretation holds water as well in AdS 5 × S 5 /Z k .The focus of our paper is on the extremal instantons, for c = 0. When k > 1 it was found that these instantons come into two families, supersymmetric or not, whereas for k = 1 there are only supersymmetric solutions. One can expect that the supersymmetric instantons are the easiest to understand. When k = 1 these instantons are simply the D(-1)/D3 bound states zoomed in near the horizon of the D3. Their hol...
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