Calogero-Moser Spaces and the Invariants of Two Matrices of Degree 3

Normatov, Z.; Turdibaev, Rustam

doi:10.1007/s00031-022-09776-y

Cited by 2 publications

(2 citation statements)

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“…In this case, we do not have any radical ideal. 24 These generators and relations have, in fact, been worked out by mathematicians in [89,90], where, in their notation, Φ1 = X, Φ2 = Y , Φ1 = A, Φ2 = B. Note that the problem of identifying the generators of Sym N (C 2 ) and computing the explicit relations among them is closely related to the study of the N -th Calogero-Moser space [91,92].…”

Section: Z 3 Twisted Compactificationmentioning

confidence: 99%

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Discrete global symmetries: gauging and twisted compactification

Giacomelli,

Harding,

Mekareeya

et al. 2024

J. High Energ. Phys.

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Discrete global symmetries of 4d $$ \mathcal{N} $$ N = 2 SCFTs are studied via two operations: gauging and twisted compactification. We consider gauging of discrete symmetries in several well-known 4d $$ \mathcal{N} $$ N = 2 SCFTs, including SU(n) SQCD with 2n flavors, theories of class $$ \mathcal{S} $$ S of type A2n−1, and Argyres-Douglas theories of type (AN, AN), as well as propose new 4d SCFTs as a result. The wreathing technique, which involves gauging a subgroup of the automorphism group of the quiver diagram of the corresponding 3d mirror theory, is exploited. This allows us to understand several properties of discretely gauged theories, including moduli spaces and how discrete gauging affects the mixed ’t Hooft anomaly between the 1-form symmetry and the 0-form flavor symmetry. Many examples are viewed through the lens of the Argyres-Seiberg duality and its generalization. We also examine discrete gauging of SU(2) SQCD with 4 flavors by various ℤ2 and ℤ2 × ℤ2 subgroups of the permutation group S4 using the superconformal index. Regarding compactification, we propose a magnetic quiver for 4d $$ \mathcal{N} $$ N = 2 SU(n) SQCD with 2n flavors compactified on a circle with a ℤ2 twist. The twisted compactification by non-invertible symmetries of the 4d $$ \mathcal{N} $$ N = 4 SYM theory with gauge group SU(N) is revisited. The non-invertible symmetry naturally gives rise to a ℤk action on the scalar fields parametrizing the moduli space. Upon examining the ℤk invariant chiral ring of the Higgs branch, we find that, in addition to the largest branch of the moduli space that is expected to be captured by the ABJ(M) theory, there exist in general nilpotent operators that lead to a branch of the moduli space which is a radical ideal.

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Section: Z 3 Twisted Compactificationmentioning

confidence: 99%

“…us now consider U(4) SYM, whose Higgs branch is Sym 4 (C 2 ). The coordinate ring is discussed in[90, Theorem 4.1]. There are 14 generators that can be written in an su(2) covariant way as…”

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confidence: 99%