Abstract
We consider the 6d (1,0) SCFT on a stack of N M5-branes probing a ℂ2/ℤ2 singularity. In particular, we study its compactifications to four dimensions on a smooth genus-g Riemann surface with non-trivial flavor flux, yielding a family of 4d CFTs. By tracking the M-theory origin of the global symmetries of the 4d CFTs, we detect the emergence of an accidental symmetry and the spontaneous symmetry breaking of a U(1) generator. These effects are visible from geometric considerations and not apparent from the point of view of the compactification of the 6d field theory. These phenomena leave an imprint on the ’t Hooft anomaly polynomial of the 4d CFTs, which is obtained from recently developed anomaly inflow methods in M-theory [1]. In the large-N limit, we identify the gravity dual of the 4d setups to be a class of smooth AdS5 solutions first discussed by Gauntlett-Martelli-Sparks-Waldram. Using our anomaly polynomial, we compute the conformal central charge and a non-Abelian flavor central charge at large N , finding agreement with the holographic predictions.
Highlights
’t Hooft anomalies are among the most important observables to compute in a geometrically engineered QFT, especially if a Lagrangian description of the theory is not available
By tracking the M-theory origin of the global symmetries of the 4d CFTs, we detect the emergence of an accidental symmetry and the spontaneous symmetry breaking of a U(1) generator
These effects are visible from geometric considerations and not apparent from the point of view of the compactification of the 6d field theory. These phenomena leave an imprint on the ’t Hooft anomaly polynomial of the 4d CFTs, which is obtained from recently developed anomaly inflow methods in M-theory [1]
Summary
The main setup of interest is a stack of N M5-branes probing a C2/Z2 orbifold singularity in M-theory. The region near an orbifold fixed point of the sphere corresponds to a single center Taub-NUT space, the metric near each pole is ds2 ∼= 1 Dφ2 +V V dR2 +R2 ds2(Sψ2 ) , k V= , 2R. When all nI = 1, the space is smooth with k − 1 two-cycles This corresponds to a resolution of the orbifold singularity. M-theory, in the supergravity limit, can be studied on the space (2.2) where we replace the two orbifold singularities with their smooth resolutions. This local deformation is always possible since the asymptotic space of Gibbons-Hawking is fixed by the total charge. The 8-form I8vec,N is the anomaly polynomial of a 6d (1,0) vector multiplet of SU(2)N,
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