Resolving spacetime singularities in flux compactifications & KKLT

Abstract

In flux compactifications of type IIB string theory with D3 and seven-branes, the negative induced D3 charge localized on seven-branes leads to an apparently pathological profile of the metric sufficiently close to the source. With the volume modulus stabilized in a KKLT de Sitter vacuum this pathological region takes over a significant part of the entire compactification, threatening to spoil the KKLT effective field theory. In this paper we employ the Seiberg-Witten solution of pure SU(N) super Yang-Mills theory to argue that wrapped seven-branes can be thought of as bound states of more microscopic exotic branes. We argue that the low-energy worldvolume dynamics of a stack of n such exotic branes is given by the (A1, An−1) Argyres-Douglas theory. Moreover, the splitting of the perturbative (in α′) seven-brane into its constituent branes at the non-perturbative level resolves the apparently pathological region close to the seven-brane and replaces it with a region of $$ \mathcal{O} $$ O (1) Einstein frame volume. While this region generically takes up an $$ \mathcal{O} $$ O (1) fraction of the compactification in a KKLT de Sitter vacuum we argue that a small flux superpotential dynamically ensures that the 4d effective field theory of KKLT remains valid nevertheless.

LVS de Sitter Vacua are probably in the Swampland

“…10D supergravity is then not a reliable description of such a compactification anymore. 14 Note that the main issue here is not the singularity itself-indeed, it is plausible that it is resolved by string theory in some way (see [67] for an interesting proposal). The problem is rather that the 4D EFT describing this highly stringy regime is unknown and might look very different from the naive EFT derived from a dimensional reduction of 10D supergravity.…”

“…On the other hand, in KKLT dS vacua, the singularities surrounding the O-planes grow to a much larger size 15. It was argued in[67] that the KKLT dS minimum survives beyond the supergravity regime. However, this is not convincing, as the Kähler potential is then an unknown function due to large curvature and warping corrections.…”

“…However, this is not convincing, as the Kähler potential is then an unknown function due to large curvature and warping corrections. A further problem is that, according to[67], the resolution of the singularity leads to a recombination of positive and negative D3-brane charges in the bulk. This is worrisome, as it may significantly reduce the tadpole compared to the naive one and thus limit the fluxes that can be used for…”

The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories

“…This is due to non-trivial relations between CB operators such that the coordinates u's in CB are not generically the VEVs of primary operators in the SCFT hence their scaling dimensions ∆(u) can be less than 1, see more discussions in [132]. 28 Another interesting result has been proposed in [141]. The authors considered type IIB string theory compactified on a K3 surface wrapped by n D7-branes.…”

Small Cosmological Constants in String Theory

“…In this paper we overcome these obstacles. We exhibit compactifications in which the superpotential takes the form (1.1), containing at least h 1,1 independent nonperturbative terms, all with constant Pfaffians, and with W 0 as small as 10 − 95 . The examples are explicit orientifolds of Calabi-Yau threefold hypersurfaces with 4 ≤ h 2,1 ≤ 7 and 51 ≤ h 1,1 ≤ 214, in which all tadpoles are cancelled.…”