Large Volume Scenarios

How does one hope to get most of the standard model out of string theory? Yesterday, Marcus Berg from the Albert Einstein Institute in Potsdam, gave a talk reviewing two scenarios, known by their abbreviations KKLT (for Kachrou, Kallosh, Linde, Trivedi) and LVS (for Large Volume Scenario) . His preference was for the LVS and his arguments were motivated mostly by the practicality of stabalising cycles inside the compact space.

In summary, The KKLT scenario is a particular set-up of IIB superstring theory, and was proposed as a way to obtain de Sitter vacua from string theory. This was progressive since it was already known that simply the lowest order terms of Sugra were not enough to construct a de Sitter background. KKLT showed that higher order string theory terms could give rise to such a background. In their model the compactified 6 (real) dimensional Calabi-Yau possesses "Klebanov-Strassler" throats and fluxes F_3, H_3 which are non-parallel. The fluxes stabilise the compact space and the addition of anti-D3 branes and associated instantons permits supersymmetry breaking and the emergence of a Minkowski or de-Sitter background. Due to the belief in a small positive cosmological constant the de-Sitter background existing in string theory is highly desirable.

The fluxes in KKLT are used to stabilise the dilaton and hence the string coupling constant, and to stabilise the moduli of the Calabi-Yau space. Marcus Berg gave us a review of how one goes about stabilising such moduli. One begins with ten-dimensional fluxes and a ten-dimensional metric, then upon reduction the part of the kinetic term that exists in the internal space gives rise to potential term in the Lagrangian associated with the moduli appearing through the reduction of the metric. To stabilise the moduli one can minimise the potential term and then find the moduli. The trouble with this, according to Marcus Berg, is that the potential is generically composed of exponentially suppressed terms and linear terms, so that the minimum of the potential occurs only over a very small range of parameters. What's the problem with that? Well simply maybe it is wrongheaded, the correct interpretation may be that a tree-level term is being cancelled against a non-perturbative term in the potential.