Brain Webs for Brane Webs

Abstract

We propose a new technique for classifying 5d Superconformal Field Theories arising from brane webs in Type IIB String Theory, using technology from Machine Learning to identify different webs giving rise to the same theory. We concentrate on webs with three external legs, for which the problem is analogous to that of classifying sets of 7-branes. Training a Siamese Neural Network to determine equivalence between any two brane webs shows an improved performance when webs are considered equivalent under a weaker set of conditions. Thus, Machine Learning teaches us that the conjectured classification of 7-brane sets is not complete, which we confirm with explicit examples.

Machine Learning Algebraic Geometry for Physics

“…and the asymptotic charge invariant , defined as = gcd det p i p j q i q j , ∀ i, j . (6.3) However, as counter examples in [32] explicitly show, these classifiers are not enough to fully specify a set of 7-branes, and are thus to be thought of as necessary but not sufficient conditions for equivalence. With this in mind, we define the following two notions of equivalent webs:…”

“…The goal of [32], as reviewed here, was to teach a Siamese neural network (SNN) to identify equivalent webs, given by their web matrices (6.1), according to these two notions. Specifically an SNN was trained that took as input 2 × 3 matrices W i and produced a 10-dimensional embedding x i ∈ R 10 for each web matrix such that the Euclidean distance between embeddings of equivalent webs was minimised and the distanced between inequivalent webs maximised.…”

“…In this work we review a selection of contemporary studies into the use of ML in algebraic geometry for physics. Specifically each section finds focus on application to: §2 hypersurfaces [28], §3 polytopes [29], §4 Hilbert series [30], §5 amoebae [31], §6 brane webs [32], §7 quiver mutation [33], §8 dessins d'enfants [34], and §9 Hessian manifolds.…”

Machine Learning for Hilbert Series

“…PCA puts focus on a data representation's largest principal components, which are found through diagonalisation of the data's covariance matrix. ML has also been successfully applied to a variety of physically motivated scenarios, including: Calabi-Yau manifolds [32][33][34][35][36][37][38][39][40], polytopes [41,42], graph theory [43], knot theory [44,45], amoebae [46], brane webs [47], integrability [48], Seiberg duality among quivers [49], and the related dessin d'enfant Galois orbits [50].…”

Cluster Algebras: Network Science and Machine Learning

“…The techniques for ML range from nonlinear function fitting and landscape searching, to clustering and pattern recognition; and in [24][25][26][27][28] they were first introduced to the string landscape. Further to their success in the algebraic geometry sector of string theory [29][30][31][32][33][34][35][36][37][38][39][40] and the related highenergy physics [41][42][43][44][45][46], strong results from ML application have also been seen in various fields of mathematics [38,[47][48][49][50][51][52][53][54][55]. Particularly relevant to the present context are [56] where the study of ML on algebraic structures was initiated, [57] where ML was applied to quiver mutation, as well as [58] where ML was utilized in classification problems in commutative algebra and [59] where learning strategies were imposed in the key step of Buchberger algorithm in algebraic geometry.…”