6D RG Flows and Nilpotent Hierarchies

Abstract

With the eventual aim of classifying renormalization group flows between 6D superconformal field theories (SCFTs), we study flows generated by the vevs of "conformal matter," a generalization of conventional hypermultiplets which naturally appear in the F-theory classification of 6D SCFTs. We consider flows in which the parent UV theory is (on its partial tensor branch) a linear chain of gauge groups connected by conformal matter, with one flavor group G at each end of the chain, and in which the symmetry breaking of the conformal matter at each end is parameterized by the orbit of a nilpotent element, i.e. T-brane data, of one of these flavor symmetries. Such nilpotent orbits admit a partial ordering, which is reflected in a hierarchy of IR fixed points. For each such nilpotent orbit, we determine the corresponding tensor branch for the resulting SCFT. An important feature of this algebraic approach is that it also allows us to systematically compute the unbroken flavor symmetries inherited from the parent UV theory.

v2: 53 pages, 12 figures, clarifications added, typos corrected

References in corpus (9)

• 6d Conformal Matter
• T-Branes and Monodromy
• Anomaly polynomial of general 6d SCFTs
• Holography for (1,0) theories in six dimensions
• F-theory and the Classification of Little Strings
• 6d holographic anomaly match as a continuum limit
• Anomaly polynomial of E-string theories
• N = 1 SCFTs from Brane Monodromy
• Conformal anomaly c-coefficients of superconformal 6d theories

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