Quiver mutations, Seiberg duality, and machine learning

Abstract

We initiate the study of applications of machine learning to Seiberg duality, focusing on the case of quiver gauge theories, a problem also of interest in mathematics in the context of cluster algebras. Within the general theme of Seiberg duality, we define and explore a variety of interesting questions, broadly divided into the binary determination of whether a pair of theories picked from a series of duality classes are dual to each other, as well as the multiclass determination of the duality class to which a given theory belongs. We study how the performance of machine learning depends on several variables, including number of classes and mutation type (finite or infinite). In addition, we evaluate the relative advantages of Naive Bayes classifiers versus convolutional neural networks. Finally, we also investigate how the results are affected by the inclusion of additional data, such as ranks of gauge/flavor groups and certain variables motivated by the existence of underlying Diophantine equations. In all questions considered, high accuracy and confidence can be achieved.

Cluster Algebras: Network Science and Machine Learning

“…We analyse how these graphs take shape as they are generated and introduce the application of ML techniques to study their respective cluster algebras. In spirit this extends the work in [57] where ML was applied to quiver exchange graphs to learn the underlying Seiberg duality. In order to perform the cluster mutation, and keep track of the seeds computationally, the sage 'Cluster Algebra and Quiver' package was used [69,70]; the exchange graphs were then represented and analysed with use of the python package networkx [71]; and finally completion of the ML investigations made use of the scikit-learn library [72].…”

“…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.…”

Some Open Questions in Quiver Gauge Theory

“…Its use initiated in this field with the examination of string landscapes [122][123][124][125], and has since quickly developed these techniques to a wide range of subfields related to gauge theories. In particular, ML has seen great success in topics discussed in this paper, examining: plethystics [126,127], amoebae [128], Seiberg duality [129], and dessins d'enfants [130].…”

Brain Webs for Brane Webs

“…Neural Networks (NNs) are a primary tool within supervised ML, whose application on labelled data acts as a nonlinear function fitting to map inputs to outputs, both represented as tensors over Q using decimals. In recent years the advancement of computational power has played perfectly into the hands of these many-parameter techniques, leading to a programme of application of these tools to datasets arising in theoretical physics [18][19][20][21][22][23][24][25][26][27][28] and the relevant mathematics [29][30][31][32][33][34][35][36]. Motivated by this, we initiate the program of applying ML techniques to the classification of 5-brane webs and 5d SCFTs, concentrating on the simplest case of webs with exactly three external legs.…”