de Sitter vacua in type IIB string theory: classical solutions and quantum corrections

Abstract

Abstract:We revisit the classical theory of ten-dimensional two-derivative gravity coupled to fluxes, scalar fields, D-branes, anti D-branes and Orientifold-planes. We show that such set-ups do not give rise to a four-dimensional positive curvature spacetime with the isometries of de Sitter spacetime. We further argue that a de Sitter solution in type IIB theory may still be achieved if the higher-order curvature corrections are carefully controlled. Our analysis relies on the derivation of the de Sitter condition from an explicit background solution by going beyond the supergravity limit of type IIB theory. As such this also tells us how the background supersymmetry should be broken and under what conditions D-term uplifting can be realized with non self-dual fluxes.

D 3 ¯ $$ \overline{\mathrm{D}3} $$ and dS

“…For all these cases, as discussed in [55], the conclusions are similar. It is impossible to satisfy (C.1) without invoking perturbative and/or non-perturbative quantum corrections.…”

“…We expect a positive cosmological solution in the four space-time direction and therefore we should discuss how the no-go condition of Gibbons-Maldacena-Núñez [24][25][26], recently updated in [55], is averted. Our starting point will be a metric ansatz, originally due to [56], specified by a warp factor e 2A , see (1.4), with a compact six-dimensional internal manifold, and a general 4d metric g µν rather than η µν .…”

“…is calculated with the internal unwarped metric, i.e. denotes the trace of the stressenergy tensor of a D3 or D3 brane in the internal space; and both I 6 and V 6 are positive definite quantities expressed in terms of type IIB fluxes in [55] as:…”

“…7 In M-theory the internal space is eight-dimensional which can be thought of as a T 2 fibration over our six-dimensional space with an unwarped metric g kl discussed earlier. 8 The constraint in M-theory now, after adding all the necessary ingredients, is a variant of (C.1) and is given by [55] where the Roman letters now span the internal eight-dimensional space and the Greek letters span the 2 + 1 dimensional spacetime. The other notations are as follows:g 8 above is the uplift of the six-dimensional internal metric to eleven-dimensions, and G (4) is the uplift of the type IIB three and five-form fluxes to eleven-dimensions such that G (4) · G (4) = G mnpa G mnpa , where (m, n, p) span the coordinates of the six-dimensional base and (a, b) span the coordinates of the T 2 fiber.…”

A critical review of classical bouncing cosmologies

“…If bouncing cosmology is to provide an alternative to 32 For a recent assessment on moduli stabilization in Type IIB string theory, see [464], where necessary conditions at the full 10D level were derived. 33 It has been proposed to use the string gas to stabilize internal dimensions as well as the dilaton [466][467][468][469][470], see also [471][472][473][474][475].…”