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.
Bibliographical noteFunding Information:
The authors thank the Institute for Mathematics and its Applications for their hospitality and for their hosting of the workshop “SageMath and Macaulay2: An Open Source Initiative” that inspired the genesis of this paper. The open source software sage , including its cluster algebra and quiver package , was especially fundamental to this project. J. B. thanks Zijing Wu for useful discussions. The research of S. F. was supported by the U.S. National Science Foundation Grants No. PHY-1820721 and No. DMS-1854179. Y. H. H. thanks STFC for Grant No. ST/J00037X/1. E. H. thanks STFC for the Ph.D. studentship. G. M. thanks the NSF for Grants No. DMS-1745638 and No. 1854162.
© 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.
Copyright 2020 Elsevier B.V., All rights reserved.