String GUT Scenarios with Stabilised Moduli

TL;DR

The paper addresses how to realize string-scale unification with stabilised moduli in type IIB compactifications by combining poly-instanton corrections with race-track dynamics in KKLT/LVS. By achieving exponential control over the effective superpotential parameters $W_0^{\rm eff}$ and $A^{\rm eff}$, the authors obtain large-volume minima with $M_s\approx M_X$ and explore three MSSM realizations on different four-cycles, yielding distinct SUSY-breaking patterns: (i) gravity mediation at the TeV scale, (ii) mixed anomaly–gravity mediation with split SUSY, and (iii) LVS-like gravity mediation with TeV-scale soft terms. They discuss cosmological-constant tuning, the potential for quintessence, and the need for explicit globally consistent embeddings, while highlighting challenges in achieving realistic soft terms and addressing the CMP in some scenarios. Overall, the work demonstrates a string-theoretic mechanism to connect GUT-scale physics to low-energy SUSY phenomenology via stabilised moduli, while outlining remaining theoretical and phenomenological hurdles.

Abstract

Taking into account the recently proposed poly-instanton corrections to the superpotential and combining the race-track with a KKLT respectively LARGE Volume Scenario in an intricate manner, we show that we gain exponential control over the parameters in an effective superpotential. This allows us to dynamically stabilise moduli such that a conventional MSSM scenario with the string scale lowered to the GUT scale is realised. Depending on the cycles wrapped by the MSSM branes, two different scenarios for the hierarchy of soft masses arise. The first one is a supergravity mediated model with M_3/2=1TeV while the second one features mixed anomaly-supergravity mediation with M_3/2=10^10GeV and split supersymmetry. We also comment on dynamically lowering the scales such that the tree-level cosmological constant is of the order Λ=(10^-3eV)^4.

Figures (5)

• Figure 1: Distribution of $M_{3/2}$ with $\tau_1=25\pm 0.25$ and $\mathcal{V}/\sqrt{g_s}\simeq1.26\cdot10^5$ for a scan over natural values of $a,b,\mathcal{A},\mathcal{B}$. The statistical mean of this distribution is $\left\langle \log_{10}\left( M_{3/2}/{\rm TeV} \right)\right\rangle =1.79$ and the standard deviation is $\sigma = 0.98$.
• Figure 2: F-term potential of the GUT model 1 in the vicinity of the minimum.
• Figure 3: F-term potential of the GUT model 2 in the vicinity of the minimum.
• Figure 4: F-term potential of the GUT model 3 in the vicinity of the minimum.
• Figure 5: F-term potential of the $\Lambda$ model in the vicinity of the minimum.