The Higgs branch of 4D N=2 superconformal field theories can be analyzed via the Hilbert series of the Higgs branch or, in special cases, by computing the Hall-Littlewood index. For any class S theory corresponding to a genus-zero Riemann surface, they are conjectured to be identical. We present several families of counterexamples. We find that for any class S theory with four or more Z2-twisted punctures, they do not match. We construct 3D mirrors for such theories and analyze their Coulomb branch Hilbert series to compute the Higgs branch Hilbert series of the 4D theory. We further construct a=c theories in class S using the twisted punctures, and these theories, which includes the D4(SU(2n+1)) theories, have Hall-Littlewood index different from the Hilbert series of the Higgs branch. We conjecture that this is the case for all a=c theories with nonempty Higgs branch, including N≥3 superconformal field theories.
Jinwoo Kang, M., Lawrie, C., Lee, K., Sacchi, M., Song, J. (2022). Higgs branch, Coulomb branch, and Hall-Littlewood index. PHYSICAL REVIEW D, 106(10) [10.1103/physrevd.106.106021].
Higgs branch, Coulomb branch, and Hall-Littlewood index
Matteo Sacchi;
2022
Abstract
The Higgs branch of 4D N=2 superconformal field theories can be analyzed via the Hilbert series of the Higgs branch or, in special cases, by computing the Hall-Littlewood index. For any class S theory corresponding to a genus-zero Riemann surface, they are conjectured to be identical. We present several families of counterexamples. We find that for any class S theory with four or more Z2-twisted punctures, they do not match. We construct 3D mirrors for such theories and analyze their Coulomb branch Hilbert series to compute the Higgs branch Hilbert series of the 4D theory. We further construct a=c theories in class S using the twisted punctures, and these theories, which includes the D4(SU(2n+1)) theories, have Hall-Littlewood index different from the Hilbert series of the Higgs branch. We conjecture that this is the case for all a=c theories with nonempty Higgs branch, including N≥3 superconformal field theories.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.