6d, N = 1 , 0 $$ \mathcal{N}=\left(1,\;0\right) $$ Coulomb branch anomaly matching

Abstract

6d QFTs are constrained by the analog of 't Hooft anomaly matching: all anomalies for global symmetries and metric backgrounds are constants of RG flows, and for all vacua in moduli spaces. We discuss an anomaly matching mechanism for 6d N = (1, 0) theories on their Coulomb branch. It is a global symmetry analog of Green-Schwarz-WestSagnotti anomaly cancellation, and requires the apparent anomaly mismatch to be a perfect square, ∆I 8 = 1 2 X 2 4 . Then ∆I 8 is cancelled by making X 4 an electric/magnetic source for the tensor multiplet, so background gauge field instantons yield charged strings. This requires the coefficients in X 4 to be integrally quantized. We illustrate this for N = (2, 0) theories. We also consider the N = (1, 0) SCFTs from N small E 8 instantons, verifying that the recent result for its anomaly polynomial fits with the anomaly matching mechanism.

Anomaly of the Electromagnetic Duality of Maxwell Theory

“…In this process, the low energy theory is changed from that of the tensor branch, containing the self-dual tensor field, into that of the Higgs branch, containing 28 = 56/2 chiral fermions in 5+1 dimensions transforming under the fundamental 56dimensional representation of E 7 . Because this is a continuous process, the anomaly at the start and the anomaly at the end should be the same; previously the same argument was used to compute the anomaly polynomial of the E-string theory in [52] (which reproduced earlier results in [53][54][55]), but the same statement is true even for the subtler anomalies we are discussing now. There are also some additional fields on the tensor and Higgs branches, but their anomalies are manifestly the same on both sides, so we can match the anomaly of the self-dual tensor field and the 28 chiral fermions.…”

6d N = 1 , 0 $$ \mathcal{N}=\left(1,\;0\right) $$ theories on S 1 /T 2 and class S theories: part II

“…The Green-Schwarz contribution of (−2)-curves is given by I GS = 1 2 η ij I i I j , and this contribution plays the important role in gauge anomaly cancellation [25] and flavor anomaly matching [20,45]. (See [20] for the conventions used in this paper.)…”

Anomaly of strings of 6d N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ theories

“…For n = 4 and g = so(8), the worldsheet gauge theory is known and is precisely the ADHM construction of charge-Q so (8) instanton. This suggests that, even for other n in table 1, the worldsheet theory is the N = (0, 4) sigma model on the charge-Q instanton moduli space of gauge algebra g. Now, moving along the Higgs branch does not break SU(2) I symmetry and the diffeomorphism symmetry of the worldsheet.…”

“…For example, we now have a better understanding of the landscape of such theories [2][3][4][5][6] and have a general formula for their anomaly polynomials [7,8].…”