Comments on $$AdS_2$$ solutions from M2-branes on complex curves and the backreacted Kähler geometry

We address the geometrical structure of the ‘skewed’ correlator of two space-like separated (almost) oppositely directed Wilson lines. Similar objects occur in the analysis of the transverse-momentum broadening probability function, the first moment of which is associated with the jet quenching parameter. We start from the Euclidean space formulation and then transform the result to the Minkowski light-cone geometry, arguing that this procedure is consistent in the leading order of the perturbative expansion. We discuss as well the issues of the UV, rapidity and IR singularities, and the possible use of the proposed approach in lattice simulations.     

Geometries with Killing Spinors and Supersymmetric <Emphasis Type="Italic">AdS</Emphasis> Solutions

The seven and nine dimensional geometries associated with certain classes of supersymmetric AdS ₃ and AdS ₂ solutions of type IIB and D = 11 supergravity, respectively, have many similarities with Sasaki-Einstein geometry. We further elucidate their properties and also generalise them to higher odd dimensions by introducing a new class of complex geometries in 2n + 2 dimensions, specified by a Riemannian metric, a scalar field and a closed three-form, which admit a particular kind of Killing spinor. In particular, for n ≥ 3, we show that when the geometry in 2n + 2 dimensions is a cone we obtain a class of geometries in 2n + 1 dimensions, specified by a Riemannian metric, a scalar field and a closed two-form, which includes the seven and nine-dimensional geometries mentioned above when n = 3, 4, respectively. We also consider various ansätze for the geometries and construct infinite classes of explicit examples for all n.     

Re-visiting supersymmetric Janus solutions: a perturbative construction

We construct holographic Janus solutions, which describe a conformal interface in the theory of M2-branes, in four-dimensional gauged supergravities using a perturbative method. In particular, we study three Einsteinscalar systems and their BPS equations, which are derived by Bobev, Pilch, and Warner(2014). The actions of our interest are all consistent truncations of D=11 supergravity, chosen to be invariant under SO(4)×SO(4),SU(3)×U(1)×U(1), and G_2 symmetry subgroups of SO(8). The utility of our semi-analytic result is illustrated by the calculation of minimal area surface and the associated holographic entanglement entropy.