We propose leading order α′‐corrections to the Poisson‐Lie T‐duality transformation rules of the metric, B‐field, and dilaton. Based on Double Field Theory, whose corrections to this order are known, we argue that they map conformal field theories to conformal field theories. Remarkably, Born geometry plays a central role in the construction.

Starting from a general N = 2 SCFT, we study the network of N = 1 SCFTs obtained from relevant deformations by nilpotent mass parameters. We also study the case of flipper field deformations where the mass parameters are promoted to a chiral superfield, with nilpotent vev. Nilpotent elements of semi-simple algebras admit a partial ordering connected by a corresponding directed graph. We find strong evidence that the resulting fixed points are connected by a similar network of 4D RG flows. To illustrate these general concepts, we also present a full list of nilpotent deformations in the case of explicit N = 2 SCFTs, including the case of a single D3-brane probing a D-or E-type F-theory 7-brane, and 6D (G, G) conformal matter compactified on a T 2 , as described by a single M5-brane probing a D-or E-type singularity. We also observe a number of numerical coincidences of independent interest, including a collection of theories with rational values for their conformal anomalies, as well as a surprisingly nearly constant value for the ratio a IR /c IR for the entire network of flows associated with a given UV N = 2 SCFT. The arXiv submission also includes the full dataset of theories which can be accessed with a companion Mathematica script.

Recent work on 6D superconformal field theories (SCFTs) has established an intricate correspondence between certain Higgs branch deformations and nilpotent orbits of flavor symmetry algebras associated with T-branes. In this paper, we return to the stringy origin of these theories and show that many aspects of these deformations can be understood in terms of simple combinatorial data associated with multi-pronged strings stretched between stacks of intersecting 7-branes in F-theory. This data lets us determine the full structure of the nilpotent cone for each semi-simple flavor symmetry algebra, and it further allows us to characterize symmetry breaking patterns in quiver-like theories with classical gauge groups. An especially helpful feature of this analysis is that it extends to "short quivers" in which the breaking patterns from different flavor symmetry factors are correlated.1 The caveat to this statement is that in all known constructions, there is a non-trivial tensor branch. Additionally, in F-theory there can be "frozen" singularities [8][9][10]. We note that all such models still are described by elliptic threefolds with collapsing curves in the base.2 See also references [38,31] for a related discussion of partial ordering in the case of certain 4D SCFTs.

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