Solver Agent: an Agentic AI Framework for Theoretical Physics Computations Applied to F-theory Uplifts of O3-planes and S-folds
TL;DR
This work introduces Solver Agent, an AI framework based on large language models for calculations and proofs in mathematics and theoretical physics, and provides methods for toric computations and four-form flux analysis in four-dimensional $\mathcal{N}=1$ compactifications with non-abelian gauge sectors.
Abstract
We introduce Solver Agent, an AI framework based on large language models for calculations and proofs in mathematics and theoretical physics. The solution process is tracked through a persistent ledger that records assumptions, derivations, and computations. A central agent delegates tasks to specialized sub-agents, while independent agents verify both intermediate steps and the final result. This setup improves the traceability, reproducibility, and verification of computer-assisted calculations. Applying Solver Agent, we study global F-theory uplifts of Type IIB orientifolds and their S-fold generalizations. We establish sufficient conditions for Weierstrass models over projective threefolds with terminal $\mathbb{Z}_k$ quotient singularities ($k\in\{2,3,4,6\}$) to give $\mathbb{Q}$-factorial projective elliptically fibered Calabi-Yau fourfolds with isolated Gorenstein terminal quotient singularities. These geometries realize O3-planes and S-folds, where local D3-brane probes of the latter yield four-dimensional $\mathcal{N}=3$ superconformal field theories. Using stringy invariants, we derive fixed-point contributions to Hodge data and Euler characteristics, and show that these Euler corrections determine the localized D3-brane charges required for tadpole cancellation. We illustrate these results using toric hypersurface constructions, where a single three-dimensional polytope determines both the Type IIB Calabi-Yau threefold and the F-theory base; here, the orientifold double cover naturally forms a bisection of an alternative genus-one-fibered uplift with discrete $\mathbb{Z}_2$ gauge symmetry. Finally, we provide methods for toric computations and four-form flux analysis in four-dimensional $\mathcal{N}=1$ compactifications with non-abelian gauge sectors.
