SciPost Phys. 5, 015 (2018) ·
published 14 August 2018
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· pdf
We derive the algebraic description of the Coulomb branch of 3d
$\mathcal{N}=4$ $USp(2N)$ SQCD theories with $N_f$ fundamental hypermultiplets
and determine their low energy physics in any vacuum from the local geometry of
the moduli space, identifying the interacting SCFTs which arise at
singularities and possible extra free sectors. The SCFT with the largest moduli
space arises at the most singular locus on the Coulomb branch. For $N_f>2N$
(good theories) it sits at the origin of the conical variety as expected. For
$N_f =2N$ we find two separate most singular points, from which the two
isomorphic components of the Higgs branch of the UV theory emanate. The SCFTs
sitting at any of these two vacua have only odd dimensional Coulomb branch
generators, which transform under an accidental $SU(2)$ global symmetry. We
provide a direct derivation of their moduli spaces of vacua, and propose a
Lagrangian mirror theory for these fixed points. For $2 \le N_f < 2N$ the most
singular locus has one or two extended components, for $N_f$ odd or even, and
the low energy theory involves an interacting SCFT of one of the above types,
plus free twisted hypermultiplets. For $N_f=0,1$ the Coulomb branch is smooth.
We complete our analysis by studying the low energy theory at the symmetric
vacuum of theories with $N < N_f \le 2N$, which exhibits a local Seiberg-like
duality.
SciPost Phys. 3, 024 (2017) ·
published 28 September 2017
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· pdf
We study the complete moduli space of vacua of 3d $\mathcal{N}=4$ $U(N)$ SQCD
theories with $N_f$ fundamentals, building on the algebraic description of the
Coulomb branch, and deduce the low energy physics in any vacuum from the local
geometry of the moduli space. We confirm previous claims for good and ugly SQCD
theories, and show that bad theories flow to the same interacting fixed points
as good theories with additional free twisted hypermultiplets. A Seiberg-like
duality proposed for bad theories with $N \le N_f \le 2N-2$ is ruled out: the
spaces of vacua of the putative dual theories are different. However such bad
theories have a distinguished vacuum, which preserves all the global
symmetries, whose infrared physics is that of the proposed dual. We finally
explain previous results on sphere partition functions and elucidate the
relation between the UV and IR $R$-symmetry in this symmetric vacuum.
