Criteria for higher-order stabilization and universally flat directions

Determine conditions under which higher-order terms in the Gukov–Vafa–Witten superpotential stabilize moduli that are massless at quadratic order in the type IIB 1^9 and 2^6 Landau–Ginzburg orientifold models, and characterize any universally flat directions enforced by structural algebraic relations among superpotential couplings.

Background

In these LG models, some fields remain massless at quadratic order but can be stabilized by higher-order terms in the superpotential, while other directions may remain exactly flat. The paper emphasizes that stabilization is governed not only by the presence of couplings but also by their algebraic relations.

Clarifying when higher-order stabilization occurs versus when exact flat directions persist is essential for understanding isolation of Minkowski vacua and for interpreting bounds such as the tadpole conjecture beyond quadratic mass counting.

References

Despite the recent progress, several questions remain open. The second is conceptual: when do higher-order terms stabilize massless fields, and when do they instead leave exact flat directions? In my talk I briefly raised the possibility of ``universally flat directions,'' namely directions that survive for structural reasons even though all fields appear somewhere in the superpotential.

— AI usage in string theory, a case study: String Vacua in the Interior of Moduli Space  (2604.01384 - Wrase, 1 Apr 2026) in Section 8 (Open questions and outlook)