We introduce a unified mathematical framework that elegantly describes minimally supersymmetry gauge theories in even dimensions, ranging from six dimensions to zero dimensions, and their dualities. This approach combines and extends recent developments on graded quivers with potentials, higher Ginzburg algebras, and higher cluster categories (also known as m-cluster categories). Quiver mutations studied in the context of mathematics precisely correspond to the order-(m+1) dualities of the gauge theories. Our work indicates that these equivalences of quiver gauge theories sit inside an infinite family of such generalized dualities.
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We would like to thank A. Garver, S. Gurvets, A. Hasan, R.-K. Seong, and especially S. Lee and C. Vafa for enjoyable discussions. We are also indebted to S. Oppermann for useful correspondence. S. F. gratefully acknowledges support from the Simons Center for Geometry and Physics, Stony Brook University, where some of the research for this paper was performed during the Simons Summer Workshop. The work of S. F. is supported by the U.S. National Science Foundation Grant No. PHY-1518967 and by a Professional Staff Congress of the City University of New York (PSC-CUNY) award. The work of G. M. is supported by NSF Grant No. DMS-1362980.
© 2018 authors. Published by the American Physical Society.