Hierarchy of RG flows in 6d (1, 0) orbi-instantons

Abstract

N M5-branes probing the intersection between the orbifold ℂ2/ΓADE and an E8 wall give rise to 6d (1, 0) SCFTs known as ADE-type orbi-instantons. At fixed N and order of the orbifold, each element of Hom(ΓADE, E8) defines a different SCFT. The SCFTs are connected by Higgs branch RG flows, which generically reduce the flavor symmetry of the UV fixed point. We determine the full hierarchy of these RG flows for type A, i.e. ℂ2/ℤk, for any value of N and k. The hierarchy takes the form of an intricate Hasse diagram: each node represents an IR orbi-instanton (homomorphism), and each edge an allowed flow, compatibly with the 6d a-theorem. The partial order is defined via quiver subtraction of the 3d magnetic quivers associated with the 6d SCFTs, which is equivalent to performing a so-called Kraft-Procesi transition between homomorphisms.

Back to heterotic strings on ALE spaces. Part I. Instantons, 2-groups and T-duality

“…where the v i are a function of the w i , which in turn are encoded by λ as explained in details in [22]. The corresponding LS charge is we expect that it induces an RG flow among the corresponding LSTs RG flows among orbi-instanton theories have been widely studied, and therefore one can relatively simply chart such RG flows [41,51,52].…”

Hierarchies of RG flows in 6d (1, 0) massive E-strings

“…Notable examples of such constructions can be found in [3,[6][7][8][9]. In particular in [8,9] the authors of the present paper focused on Higgs branch RG flows for an infinite class of 6d SCFTs known as A-type orbi-instantons.…”

“…Notable examples of such constructions can be found in [3,[6][7][8][9]. In particular in [8,9] the authors of the present paper focused on Higgs branch RG flows for an infinite class of 6d SCFTs known as A-type orbi-instantons. These can be engineered in M-theory, and are the datum of the number N of M5-branes, the order k of the orbifold C 2 /Z k they are probing, and a boundary condition at infinity given by a representation ρ : Z k → E 8 , where E 8 is the gauge symmetry on an M9-wall that the M5's are probing (on top of the orbifold point) [2].…”

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We extend the analysis of [9] to the 6d (1, 0) SCFTs known as massive E-string theories, which can be engineered in massive Type IIA with 8 − n 0 < 8 D8-branes close to an O8 − (or O8 * if n 0 = 8, 9). For each choice of n 0 = 1, .

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Fibrations and Hasse diagrams for 6d SCFTs

“…In certain situations, it turns out to be necessary to extend the standard notion of quiver: non simply laced quivers [88][89][90][91][92], wreathed quivers [68,93], decorated quivers [1]. A Hasse diagram, or phase diagram, not only is a highly discriminant invariant one can associate to a QFT with 8 supercharges, but it also shows how the theory is related to others under various kinds of deformations or flows (see [74,[94][95][96][97][98][99][100][101] for a selection of recent works along these lines).…”