Wilson Loop and Ds/cft Correspondence

We calculate Wilson loop (quark anti-quark potential) in dS/CFT correspondence. The brane-world model is considered where bulk is two 5d Euclidean de Sitter spaces and boundary (brane) is 4d de Sitter one. Starting from the Nambu-Goto action, the calculation of the effective tension (average energy) is presented. Unlike to the case of supergravity calculation of Wilson loop in AdS/CFT set-up, there is no need to regularize the Nambu-Goto action (the volume of de Sitter space is finite). It turns out that at sufficiently small curvature of 5d background the energy (potential) is positive and linear on the distance between quark and anti-quark what indicates to the possibility of confinement. PACS numbers: 04.50.+h, 04.70.Dy, 11.25.Db [email protected] 2 [email protected], [email protected] 1 AdS/CFT correspondence [1] is the duality between (d+ 1)-dimensional supergravity in the AdS background and d-dimensional CFT living on its boundary. In particulary, AdS5/CFT4 is described by the near horizon limit of D3-branes in Type IIB string theory. Hull has shown [2] that if we consider Type IIB∗ string theory, which is given by the time-like T-duality from Type II string theory, D-brane is transformed into E-brane and its near lightcone limit gives the de Sitter space instead of the AdS space, which is the near horizon limit of D-brane. This indicates to the existence of dS/CFT correspondence. Moreover, the universality of holographic principle suggests that AdS/CFT correspondence should not be something specific. Indeed, despite some technical problems the formulation of dS/CFT correspondence has been recently proposed [3] (for earlier attempts in this direction, see [4]). The large number of recent works [6, 7] has been devoted to exploring of dS/CFT correspondence from various points of view. There are number of problems in dS/CFT correspondence like: (still unknown) CFT dual to de Sitter space is expected to be Euclidean and not unitary, the boundaries where dual CFT should live are topologically disconnected, etc. Nevertheless, it became clear that most of properties and phenomena of AdS/CFT correspondence have their analogs in dS/CFT correspondence. In the very interesting paper [5] there was suggested the way to calculate Wilson loop (quark anti-quark potential) using dual supergravity description in AdS/CFT set-up. In the present letter we try to develop the analagous formulation to find the potential between quark and anti-quark in the framework of dS/CFT correspondence. Despite the fact that dual CFT is still unknown the calculation of Nambu-Goto static potential leads to acceptable description of Wilson loop. Let us consider 5 dimensional de Sitter (dS) space as a bulk space dsdS = gμνdx dx = −dt + e 2t l 4 ∑