2020/04/08 by Mikhail Evtikhiev
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Coulomb #Group (periodic table) #Hilbert–Poincaré series #Langlands dual group #Langlands program #Moduli space #Orbifold #Quiver #Rank (graph theory) #hep-th
paper · pdf · doi:10.1007/jhep06(2020)125
12 pages
arxiv created 2020/04/08 · openalex created_date 2020/04/17 · openalex publication_date 2020/06/19 · arxiv updated 2020/07/15 · openalex updated_date 2026/08/05
A bstract In this paper we discuss various N = 3 SCFTs in 4 dimensions and in particular those which can be obtained as a discrete gauging of an N = 4 SYM theories with non- simply laced groups. The main goal of the project was to compute the Coulomb branch superconformal index and moduli space Hilbert series for the N = 3 SCFTs that are obtained from gauging a discrete subgroup of the global symmetry group of N = 4 Super Yang-Mills theory. The discrete subgroup contains elements of both SU(4) R-symmetry group and the S-duality group of N = 4 SYM. This computation was done for the simply laced groups (where the S-duality groups is SL(2 , ℤ) and Langlands dual of the algebra L\mathfrakg <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mi>L</mml:mi> </mml:msup> <mml:mi>g</mml:mi> </mml:math> is simply \mathfrakg <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>g</mml:mi> </mml:math> ) by Bourton et al. [1], and we extended it to the non-simply laced groups. We also considered the orbifolding groups of the Coulomb branch for the cases when Coulomb branch is relatively simple; in particular, we compared them with the results of Argyres et al. [2], who classified all N ≥ 3 moduli space orbifold geometries at rank 2 and with the results of Bonetti et al. [3], who listed all possible orbifolding groups for the freely generated Coulomb branches of N ≥ 3 SCFTs. Finally, we have considered sporadic complex crystallographic reflection groups with rank greater than 2 and analyzed, which of them can correspond to an N = 3 SCFT with a principal Dirac pairing.