Abstract
M5-branes on an ADE singularity are described by certain six-dimensional “conformal matter” superconformal field theories. Their Higgs moduli spaces contain information about various dynamical processes for the M5s; however, they are not directly accessible due to the lack of a Lagrangian formulation. Using anomaly matching, we compute their dimensions. The result implies that M5 fractions can recombine in several different ways, where the M5s are leaving behind frozen versions of the singularity. The anomaly polynomial gives hints about the nature of the freezing. We also check the Higgs dimension formula by comparing it with various existing conjectures for the CFTs one obtains by torus compactifications down to four and three dimensions. Aided by our results, we also extend those conjectures to compactifications of theories not previously considered. These involve class mathcal{S} theories with twisted punctures in four dimensions, and affine-Dynkin-shaped quivers in three dimensions.
Highlights
The dynamics of M5-branes is one of the most mysterious corners of string theory
The resulting superconformal field theory (SCFT), which is denoted by TG(N − 1), has N = (1, 0) supersymmetry and a G × G flavor symmetry
For G = Ek, one can obtain an effective description by using a dual F-theory description involving seven-branes wrapping a chain of curves. It consists of a more exotic sequence of gauge groups, coupled to copies of the so-called E-string theory, a theory with one tensor multiplet and E8 flavor symmetry. Both in the Dk and in Ek examples, the number of tensor multiplets is a multiple of the number of M5-branes; this is naturally interpreted as the fact that each M5 can break in several fractional M5s [3]. (In the Dk case, this was observed earlier in the IIA frame using NS5s on O6-planes [4].)
Summary
The dynamics of M5-branes is one of the most mysterious corners of string theory. It is described by a six-dimensional N = (2, 0) superconformal field theory (SCFT) without a known Lagrangian description. For G = Ek, one can obtain an effective description by using a dual F-theory description involving seven-branes wrapping a chain of curves It consists of a more exotic sequence of gauge groups (called “conformal matter” in [3]), coupled to copies of the so-called E-string theory, a theory with one tensor multiplet and E8 flavor symmetry. While TG(N ) satisfy the HN constraints by construction, there are other interesting examples These consist of theories where the M5 fractions get reassembled in several different ways, leaving behind a “frozen” [15,16,17,18] (or partially so) version of the ΓG singularities, where the flavor gauge group becomes a group Gfr which can be non--laced (or empty).
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