The Generalized Dilaton Supersymmetry Breaking Scenario

TL;DR

The paper argues that the conventional dilaton-dominated SUSY breaking scenario, built on a tree-level Kähler potential $K=-\log(S+\bar S)$ and a superpotential $W(S)$ with exponential form, cannot realize a global (or even a simple local) minimum with zero cosmological constant at a realistic dilaton value $\mathrm{Re}S\sim2$. It thus advocates a generalized framework allowing an arbitrary $K$ while retaining the exponential structure of $W$, deriving generalized soft-term expressions that depend on $K$-derivatives and identifying a key constraint $(-a+K_S)^2-3K_{S\bar S}=0$ under one-exponential dominance. The authors further explore non-perturbative Kähler potentials motivated by stringy effects, showing that, with suitable $K_{np}$ forms, one can stabilize the dilaton near $\mathrm{Re}S\sim2$ using a single condensate without fine-tuning, though achieving exact $V=0$ is delicate and may require more complex modeling, including possible singularities in $K''$. Overall, the work provides a more flexible, predictive framework for dilaton-driven SUSY breaking and highlights the importance of non-perturbative Kähler corrections in string phenomenology and dilaton stabilization.

Abstract

We show that the usual dilaton dominance scenario, derived from the tree level Kähler potential, can never correspond to a global minimum of the potential at $V=0$. Similarly, it cannot correspond to a local minimum either, unless a really big conspiracy of different contributions to the superpotential $W(S)$ takes place. These results, plus the fact that the Kähler potential is likely to receive sizeable string non-perturbative contributions, strongly suggest to consider a more general scenario, leaving the Kähler potential arbitrary. In this way we obtain generalized expressions for the soft breaking terms but a predictive scenario still arises. Finally, we explore the phenomenological capability of some theoretically motivated forms for non-perturbative Kähler potentials, showing that it is easy to stabilize the dilaton at the realistic value $S\sim 2$ with just one condensate and no fine-tuning.