Moduli Stabilisation on the Worldsheet

Abstract

We consider compactifications of type II string theory using exact internal CFT's with central charge $c=9+\epsilon$, $|\epsilon |\ll 1$, leading to an effective potential for the dilaton. For $\epsilon >0$ the potential is positive and the dilaton is ultimately driven to weak coupling. For $\epsilon <0$ the dilaton is driven to strong coupling, but we can stabilise the background by including D-branes. The resulting minimum admits an $Ad{S}_4$ solution where the cosmological constant is of the order ${\epsilon }^3$ and the string coupling constant is of order $\epsilon$. Furthermore these CFT's typically do not possess any massless or tachyonic modes. Thus these vacua provide exact CFT descriptions of moduli stabilisation in weakly coupled string theory.

21 pages, 3 figures

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