The subject of the paper is the study of five dimensional superconformal field theories. The main proposal consists in using techniques from Machine Learning as tools to classify such theories. From the point of view of String Theory, five dimensional superconformal theories can be associated to Brane webs. They can be constructed physically using certain configurations of intersecting D-branes. Then a certain projection of such configurations defines a web on a plane. Such a description is however redundant. Different webs related by a certain action of \(SL(2,C)\) or a set of moves, known as Hanany-Witten moves, describe physically equivalent theories. The classification problem then consists in classifying equivalence classes of webs up to this equivalence relations. The authors attempt to tackle this problem using Machine Learning.
More precisely, the authors study configurations of \((p,q)\) 5-branes, where \(p\) and \(q\) are units of charge under the RR and NSNS 2-forms of type IIB String Theory respectively. Such branes can end on \([p,q]\) 7-branes, which then play the role of external legs in the brane web. The redundancy of such webs is characterized by the action of \(SL(2,C)\) on each \((p,q)\) vector, and by the Hanany-Witten moves, encoded in a certain monodromy matrix \(M_{p,q}\). The full configuration can be parametrized by a web matrix.
Interestingly, the problem of the classification of such webs contains the sub-problem of classifying 7-brane configurations, without any 5-brane. Such a problem was addressed in [O. DeWolfe et al., Adv. Theor. Math. Phys. 3, No. 6, 1785–1833 (1999; Zbl 0967.81051)], where it was conjectured that inequivalent sets of 7-branes are characterized by the total monodromy matrix and by a certain charge invariant. However by inspecting explicit examples of brane configurations, the authors of the present paper find out that such a characterization is only necessary but not sufficients for two 7-brane configurations to be inequivalent. This leads to two notions of equivalence: strong (up to \(SL(2,C)\) action and Hanany-Witten moves) and weak (with the same invariants).
The authors use Machine Learning techniques to understand the classification problem, by training a Siamese Neural Network (which consists of two or more identical sub-networks) to determine if two given webs are equivalent or not. They construct an appropriate dataset and train the network accordingly. They find that the network performs much better with the notion of weak equivalence. They conclude that the true set of classifiers is much subtler that previously thought. The results are also strengthened by an independent study using topological data analysis.
The paper proposes to use Machine Learning techniques to understand a certain physical problem. Such problem can be reduced to an interesting algebraic problem. Regardless of its physical origin, this is an interesting problem on its own, with several (quite difficult) ramifications. The paper is very clear and not much background in string theory is needed to understand its main points. Researchers with interests in Machine Learning and its applications will find a lot of open problems to address.