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AI usage in string theory, a case study: String Vacua in the Interior of Moduli Space

Timm Wrase

Abstract

These proceedings start with a discussion of my recent experiences with large language models and potential implications for their usage in our field. This is followed by an AI generated summary of my talk at the workshop ``Recent Progress in Computational String Geometry,'' held at the Chennai Mathematical Institute in January 2026. The focus is on four-dimensional $\mathcal{N}=1$ Minkowski vacua in type IIB compactifications that live deep in the interior of moduli space and admit an exact worldsheet description in terms of Landau--Ginzburg models. The main examples are the $1^9$ and $2^6$ models, mirror to rigid Calabi--Yau threefolds and therefore free of Kähler moduli. This makes them ideal laboratories for testing whether fluxes can stabilize all fields and for probing conjectures about the string landscape and the swampland. Based mostly on arXiv:2406.03435, arXiv:2407.16756, we review how higher-order terms in the flux superpotential can stabilize fields that remain massless at quadratic order, how isolated Minkowski vacua arise in the $2^6$ model, and why these constructions provide sharp data for the tadpole and massless Minkowski conjectures. We also emphasize the role of arXiv:2407.16758 by other authors, where the first Minkowski vacua of this type with all fields massive were identified.

AI usage in string theory, a case study: String Vacua in the Interior of Moduli Space

Abstract

These proceedings start with a discussion of my recent experiences with large language models and potential implications for their usage in our field. This is followed by an AI generated summary of my talk at the workshop ``Recent Progress in Computational String Geometry,'' held at the Chennai Mathematical Institute in January 2026. The focus is on four-dimensional Minkowski vacua in type IIB compactifications that live deep in the interior of moduli space and admit an exact worldsheet description in terms of Landau--Ginzburg models. The main examples are the and models, mirror to rigid Calabi--Yau threefolds and therefore free of Kähler moduli. This makes them ideal laboratories for testing whether fluxes can stabilize all fields and for probing conjectures about the string landscape and the swampland. Based mostly on arXiv:2406.03435, arXiv:2407.16756, we review how higher-order terms in the flux superpotential can stabilize fields that remain massless at quadratic order, how isolated Minkowski vacua arise in the model, and why these constructions provide sharp data for the tadpole and massless Minkowski conjectures. We also emphasize the role of arXiv:2407.16758 by other authors, where the first Minkowski vacua of this type with all fields massive were identified.

Paper Structure

This paper contains 22 sections, 15 equations, 2 figures, 1 table.

Table of Contents

  1. AI usage in string theory, a case study: String Vacua in the Interior of Moduli Space
  2. Disclaimer and discussion of AI in teaching and research
  3. Introduction
  4. Why study the interior of moduli space?
  5. Why Minkowski vacua are unusually tractable here
  6. Landau--Ginzburg models with $h^{1,1}=0$
  7. Flux vacua, masses, and higher-order stabilization
  8. The $1^9$ model: stabilizing massless fields
  9. Flux taxonomy and quadratic masses
  10. Higher-order terms and stabilized massless fields
  11. A simple effective-field-theory picture
  12. Implications of the $1^9$ analysis
  13. The $2^6$ model: isolated Minkowski vacua
  14. From many massive fields to isolated vacua
  15. The first all-massive Minkowski vacua
  16. ...and 7 more sections

Figures (2)

  • Figure 1: Each blue dot corresponds to a different ISD flux choice with a corresponding Minkowski vacuum. Only choices with $N_{\rm flux} \leq 12$ satisfy the tadpole cancellation condition. Many examples violate the refined tadpole conjecture with 'slope' $\frac{N_{\rm flux}}{2 {\rm rank}(w_{ab}^{(2)})} <\frac{1}{3}$. Within the tadpole bound we are far from stabilizing all 64 moduli. Examples with $N_{\rm flux}=12$ and ${\rm rank}(w_{ab}^{(2)})=16,18,20$ have massless fields that are stabilized through higher order terms in $W$. Figure adapted from Ref. Becker:2024nqu, originally published in JHEP under CC BY 4.0.
  • Figure 2: Each blue dot corresponds to a different ISD flux choice with a corresponding Minkowski vacuum. Only choices with $N_{\rm flux} \leq40$ satisfy the tadpole cancellation condition. Many examples violate the refined tadpole conjecture with 'slope' $\frac{N_{\rm flux}}{2 {\rm rank}(w_{ab}^{(2)})} <\frac{1}{3}$. Within the tadpole bound one can stabilize all 91 moduli. Examples with $N_{\rm flux}=40$ and $n_{\rm massive}= {\rm rank}(w_{ab}^{(2)})=91$ were found by other authors in Ref. Becker:2025mhy and are marked by the red circle. Examples with 86 massive fields and 5 massless but stabilized fields were also found in Ref. Rajaguru:2025kzh. Figure adapted from Ref. Becker:2025mhy, originally published in JHEP under CC BY 4.0.