Supergravity Description of Field Theories on Curved Manifolds and a No Go Theorem

Abstract

In the first part of this paper we find supergravity solutions corresponding to branes on worldvolumes of the form R d × Σ where Σ is a Riemann surface. These theories arise when we wrap branes on holomorphic Riemann surfaces inside K3 or CY manifolds. In some cases the theory at low energies is a conformal field theory with two less dimensions. We find some non-singular supersymmetric compactifications of M-theory down to AdS 5 . We also propose a criterion for permissible singularities in supergravity solutions.In the second part of this paper, which can be read independently of the first, we show that there are no non-singular Randall-Sundrum or de-Sitter compactifications for large class of gravity theories.

Oxidised cosmic acceleration

“…To summarise: c ρ is negative for all accelerating w if γ > 1 or γ < γ ρ−1/3 (G. 11) and in the range γ ρ−1/3 < γ < 1 then c ρ is negative if w < w ρ⋆ (G.12) This is illustrated in Figure 8.…”

“…The results proven here are releated to some well-known "no-go" theorems, which show that static compactifications cannot yield pure de Sitter solutions, or accelerating Friedmann-Robertson-Walker (FRW) universes, unless the SEC is violated [10,11]. Here we describe two ways in which these no-gos can be improved, as briefly summarised in [12].…”

“…Some previous no-go theorems [10,11] showed that de Sitter expansion or accelerating cosmologies obtained from static compactifications must violate the SEC, which asserts that…”

Warped Ricci-flat reductions

“…While singular in the anti-de Sitter cases, these geometries are completely smooth for de Sitter and are similar in structure to the "bubble of nothing" [47]. Unlike direct products of AdS and a sphere or warped products of de Sitter and a hyperbolic space, both of which are supported by flux, our solutions are supported entirely by the warp factor, are hence not bound by the no-go theorem [11], and do not appear to arise from a limit of the former solutions.…”

“…The five-dimensional theory (9) also has solutions that smoothly interpolate between dS 2 × S 3 in the infinite past and a dS 5 -type spacetime in the infinite future [46]. These solutions can be obtained from the AdS black hole solutions in D = 5 U(1) 3 gauged supergravity simply by changing the sign of the scalar potential, and can all be embedded in eleven dimensions using the KK reduction Ansatz (11). Like the previouslymentioned dS 3 , these solutions have a fake superpotential in the equal-charge case.…”