Gauge/string duality for Wilson loop expectations

Establish the conjectured gauge/string duality for Wilson loop expectations in two-dimensional Yang–Mills theory, including an explicit rigorous description in terms of the corresponding string-theoretic surface models.

Background

The paper develops rigorous random-surface and Gromov–Witten interpretations for the Yang–Mills partition function on a torus, but does not establish an analogous result for Wilson loop observables.

Wilson loop expectations involve traces of holonomies along loops and are more difficult because the relevant string-side objects are described by combinatorial surfaces or maps rather than directly by the ramified coverings and stable maps used for the partition function. The paper records the broader conjecture from the physics literature as an unresolved direction.

References

To conclude, let us note that physicists also conjectured that this duality goes beyond the partition function, and holds for Wilson loop expectations, which are integrals of traces of holonomies along loops in the base surface with respect to the Yang--Mills measure .

— The central heat trace on large compact classical groups  (2511.08288 - Lemoine et al., 11 Nov 2025) in Section “Applications to gauge/string duality,” subsection “Yang–Mills/Gromov–Witten duality”