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Quiver Mutations, Seiberg Duality and Machine Learning

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arxiv 2006.10783 v1 pith:ISFOKASM submitted 2020-06-18 hep-th math.AGmath.COstat.ML

Jiakang Bao , Sebastián Franco , Yang-Hui He , Edward Hirst , Gregg Musiker , Yan Xiao This is my paper · ORCID
classification hep-thmath.AGmath.COstat.ML
keywords dualitylearningmachineseibergclassesdeterminationgaugequestions
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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 multi-class 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.

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Cited by 5 Pith papers

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    Verifier-gated LM repair improves success on broken quiver-gauge-theory claims, but the best exploitation policy reverses between deepseek-chat and qwen-plus.

  2. Tilting Mutations and Quiver-Invariant Dualities in Brane Tilings

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    Three families of tilting mutations on brane tilings produce quiver-invariant dualities, linking five doublets and one triplet of toric phases of H^{1,1,2,1}.

  3. Learning to Trace Seiberg Dualities

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    Hybrid graph-transformer networks guiding A* and beam search find Seiberg-duality paths between ~10-node quivers more efficiently than BFS or pure physics heuristics, with a measured complexity breaking point.

  4. BPS spectroscopy with reinforcement learning

    hep-th 2025-01 conditional novelty 6.0 of 10

    A PPO reinforcement learning agent finds quiver mutation sequences that enumerate finite BPS spectra and minimal chambers of complete N=2 theories, with new chamber counts for SU(2) Nf=4.

  5. Metaheuristic Generation of Brane Tilings

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    Simulated annealing over permutation tuples can generate consistent brane tilings, yielding a 26-field example not present in catalogues that stop at 24 fields.

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