Moduli Stabilisation on the Worldsheet

TL;DR

This paper explores exact conformal field theory compactifications of type II string theory with slight deviations in central charge, leading to stable moduli configurations and potential for weak or strong coupling regimes.

Contribution

It introduces a novel approach using approximate internal CFTs with central charge near 9 to achieve moduli stabilization in string theory.

Findings

Positive epsilon yields weak coupling and positive potential.

Negative epsilon leads to strong coupling but can be stabilized with D-branes.

The vacua are free of massless or tachyonic modes and describe exact CFT solutions.

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 $AdS_4$ 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.