The large $N$ limit of superconformal field theories and supergravity

Noncommutative brane-world, (Anti) de Sitter vacua and extra dimensions

“…Nevertheless, the construction of dS vacua has been achieved by taking into account a small number of D 3 -branes along with the AdS vacua in a type IIB string theory [3]. On the other hand, anti de Sitter (AdS) spaces are well understood in a string theory due its established correspondence with the gauge theory at its boundary [4,5].…”

“…In particular, we revisit a curved brane-world [13] underlying a noncommutative U (1) gauge theory on a D 3 -brane [22]. We obtain generalized dS 4 and AdS 4 geometries leading to an axially symmetric and a spherically symmetric black holes.…”

Braneworld cosmology in (anti)-de Sitter Einstein-Gauss-Bonnet-Maxwell gravity

“…In this Section, we will extend this analogy to the FRW equations under consideration. Let us first investigate this analogy in Einstein gravity for the usual (n + 1)-dimensional FRW Universe with a metric 1) where the n-dimensional spatial hypersurfaces with negative, zero or positive curvature are parametrized by k = −1, 0, 1, respectively 6 . We limit our discussion mainly to that of the closed universe (k = 1), with a spatial volume defined by V = a n d n x √ g. The standard FRW equations may then be written as 2) where …”

“…The action is given by 1 1) where c is an arbitrary coupling constant, κ 2 parametrizes the (d + 1)-dimensional Planck mass, the Riemann tensor, R µνξσ , and its contractions are constructed from the metric, g µν , and its derivatives, g ≡ detg µν and Λ represents the bulk cosmological constant. By extremising the variations of the action (2.1) with respect to the metric tensor and gauge field, respectively, we obtain the field equations…”

“…The holographic principle in string/M-theory is formulated in terms of the AdS/CFT or dS/CFT correspondences [1,2,3]. These correspondences have bridged the gap between previously distinct branches of high energy physics.…”