Exact half-BPS flux solutions inMtheory withD(2,1;c′;0)2

Abstract

We construct the most general local solutions to 11-dimensional supergravity (or M theory), which are invariant under the superalgebra Dð2; 1; c 0 ; 0Þ È Dð2; 1; c 0 ; 0Þ for all values of the parameter c 0 . The BPS constraints are reduced to a single linear partial differential equation on a complex function G. The physical fields of the solutions are determined by c 0 , a freely chosen harmonic function h, and the complex function G. h and G are both functions on a two-dimensional compact Riemannian manifold. We obtain the expressions for the metric and the field strength in terms of G, h, and c 0 and show that these are indeed valid solutions of the Einstein, Maxwell, and Bianchi equations. Finally we give a construction of one parameter deformations of AdS 7 Â S 4 and AdS 4 Â S 7 as a function of c 0 .

On holographic defect entropy

“…First, we introduce the deformation of refs. [44,59], involving one new parameter, 8 γ ∈ [0, ∞), which generically deforms OSp(4|2, R) × OSp(4|2, R) to D(2, 1; γ, 0) × D(2, 1; γ, 0). Only when γ = 1, where D(2, 1; γ, 0) = OSp(4|2, R), is the super-isometry a subgroup of OSp(8|4, R).…”

“…The metric for this two-parameter deformation of M-theory Janus is [41,44,59] 74) where g S 3 and gS3 are metrics on two unit-radius S 3 's, w = x/2+iy is a complex coordinate defined on a strip, x ∈ (−∞, ∞) and y ∈ [0, π/2], and the warp factors f 2 1 , ρ 2 , f 2 2 , and f 2 3 depend only on w andw. For the solution with super-isometry D(2, 1; γ, 0)×D(2, 1; γ, 0), the warp factors are specified by a harmonic function h(w,w) and a complex function H(w,w): where 2∂ w H = (H +H)∂ w ln h. The real constants {C 1 , C 2 , C 3 } obey C 1 + C 2 + C 3 = 0, with γ = C 2 /C 3 .…”

Type II solutions on AdS3 × S3 × S3 with large superconformal symmetry

“…Beyond the cases with maximal supersymmetry (for AdS 3 ), solutions with N = (4, 0) were constructed from AdS 3 ×S 3 ×S 3 ×S 1 using T-duality (and its non-abelian counter part) in [15,16] and a class of AdS 3 ×S 2 ×S 2 ×CY 2 solutions in M-theory was found in [18]. Another interesting example is a flow from AdS 5 × T 1,1 to a twice T-dualised version of AdS 3 × S 3 × S 3 × S 1 preserving N = (4, 2) [14] (other flows across dimensions were found in [10][11][12], but these exhibit large N = (4,4)). Finally, somewhat related to this story, there is also a family of N = (2, 0) solution in IIB that are AdS 3 × S 3 × S 3 × S 1 only topologically [9].…”

AdS3 solutions with from S3 × S3 fibrations

“…Superconformal field theories in two dimensions have a rich structure of possible superconformal algebras associated to them, this is contrary to higher dimensional examples where the number of preserved supercharges uniquely fixes the associated algebra. The classification and construction of holographic duals realising this vast array of algebras is certainly an interesting problem which is still largely unknown (however [8][9][10][11][12][13][14][15][16][17] for early classification results). Recently, more attention has been given to populating the space of supergravity solutions with various superconformal algebras.…”