Field theory limit of branes and gauged supergravities

We discuss the field theory limit of Dp-branes. In this limit, the black Dpbrane solution approaches a solution which is conformal to adSp+2×S8−p. We argue that the frame in which the conformal factor is equal to one, the dual frame, is a ‘holographic’ frame. The radial coordinate of adSp+2 provides a UV/IR connection as in the case of the D3 brane. The gravitational description involves gauged supergravities, typically with non-compact gauged groups. The near-horizon Dp-brane solution becomes a domain-wall solution of the latter. Holography[1] states that a gravitational system in d + 1-dimensions should have a description in terms of a d-dimensional (boundary) field theory. In addition, the boundary theory should not contain more than one degree of freedom per Planck area. The adS/CFT duality[2, 3, 4] provides an example of such holographic connection[4, 5]. For instance, anti-de Sitter supergravity in five dimensions has a description in terms of (strongly coupled) N = 4 SU(N) SYM theory in four dimensions. This duality was inferred by looking at two descriptions of the D3 brane: one as a black D3 brane and another as a hypersurface where strings can end. Taking the field theory limit, i.e. the limit in which the bulk gravity decouples, one finds that the worldvolume theory is equivalent to strings propagating in the near-horizon limit of the black D3 brane which is adS5 × S. When curvatures are small the YM coupling constant is strong and we obtain that anti-de Sitter supergravity is equivalent to strongly coupled SYM theory. It is natural to consider the same limit for the other branes as well. The difference between the D3 brane and the other branes is that the worldvolume theory of the latter is not conformal. Therefore, the dual supergravity cannot be anti-de Sitter supergravity. By holography we expect that when the YM coupling constant becomes large a gravitational description in one dimension higher takes over. Indeed we will see that this is the case[6]: The gravity description is in terms of certain gauged supergravities in p + 2 dimensions, typically with non-compact gauge groups, which possess supersymmetric domain-wall vacua. These domain-wall vacua are spacetimes conformal to adSp+2 (for p = 5 we get E instead). Let us consider the field theory limit [2, 7] of D-branes. We want to consider a limit in which the bulk gravity decouples and we left with a decoupled worldvolume theory. To decouple closed string loop effects we send gs → 0. To suppress higher dimension operators we go to low energies, α′ → 0. This implies that the gravitational coupling