Large dimensions and small curvatures from supersymmetric brane back-reaction

Abstract

We compute the back-reaction of pairs of codimension-two branes within an explicit flux-stabilized compactification, to trace how its properties depend on the parameters that define the brane-bulk couplings. Both brane tension and magnetic couplings to the stabilizing flux play an important role in the resulting dynamics, with the magnetic coupling allowing some of the flux to be localized on the branes (thus changing the flux-quantization conditions). We find that back-reaction lifts the classical flat directions of the bulk supergravity, and we calculate both the scalar potential and changes to the extra-dimensional and on-brane geometries that result, as functions of the assumed brane couplings. When linearized about simple rugby-ball geometries the resulting solutions allow a systematic exploration of the system's response. Several of the systems we explore have remarkable properties. Among these are a propensity for the extra dimensions to stabilize at exponentially large sizes, providing a mechanism for generating extremely large volumes. In some circumstances the brane-dilaton coupling allows the bulk dilaton to adjust to suppress the on-brane curvature parametrically below the change in brane tension, potentially providing a mechanism for reducing the vacuum energy. We explore the stability of this suppression to quantum effects in the case where their strength is controlled by the value of the field along the classical flat direction, and find it can (but need not) be stable.

Anisotropic modulus stabilisation: strings at LHC scales with micron-sized extra dimensions

“…We find in §3 a generic prediction of a rich spectrum of states whose masses are light enough to be relevant to terrestrial tests of gravity, yet which are not already explicitly ruled out. We argue that for very anisotropic compactifications the low-energy world transverse to the branes is effectively 2-dimensional, implying that brane back-reaction is an important complication to the LARGE-volume dynamics at very low energies [26,27]. On one hand, this puts detailed calculations of the low-energy properties beyond the present state of the art, motivating more detailed a better understanding of back-reaction in hopes of making more precise comparisons with observations.…”

“…Although it remains an unsolved problem as to how this dynamics works in string theory, the effects of on-brane loops [83][84][85][86] and back-reaction [26,27,[87][88][89][90] have been studied for non-supersymmetric, codimension-2 branes in simpler 6D extra-dimensional models. These simpler systems resemble their 10D cousins in that the back-reaction is also competitive with bulk physics in stabilising the extra dimensions, yet doesn't destroy the presence of large-volume solutions.…”

“…These simpler systems resemble their 10D cousins in that the back-reaction is also competitive with bulk physics in stabilising the extra dimensions, yet doesn't destroy the presence of large-volume solutions. Intriguingly they can also allow on-brane curvatures to be parametrically smaller than naive estimates based on the brane tensions would suggest [26,27].…”

Bulk stabilization, the extra-dimensional Higgs portal and missing energy in Higgs events

“…A similarly robust mechanism for stabilizing large dimensions has been missing for standard ADD models, but an analogue was recently found [22] for their supersymmetric generalizations [23,24,25] by applying to them a 6D cousin [26] of the Goldberger-Wise mechanism. In such theories the extra dimensions are stabilized classically through flux-stabilization, as is often possible for supersymmetric systems (and for which 6D systems provided the first examples [24]).…”

“…As shown in ref. [22], this can be achieved classically through its couplings to branes, whose interactions need not share the scale invariance of the bulk. In particular it is not difficult to arrange for moderately large negative values.…”