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## The Infrared Physics of Bad Theories

1, 2

SciPost Physics

Stichting SciPost

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### Abstract

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.

### Most cited references36

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### Critical Behavior in (2+1)-Dimensional QED

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### Mirror Symmetry in Three Dimensional Gauge Theories

(1996)
We discuss non-trivial fixed points of the renormalization group with dual descriptions in $$N=4$$ gauge theories in three dimensions. This new duality acts as mirror symmetry, exchanging the Higgs and Coulomb branches of the theories. Quantum effects on the Coulomb branch arise classically on the Higgs branch of the dual theory. We present examples of dual theories whose Higgs/Coulomb branch are the ALE spaces and whose Coulomb/Higgs branches are the moduli space of instantons of the corresponding $$ADE$$ gauge group. In particular, we show that in three dimensions small $$E_8$$ instantons in string theory are described by a local quantum field theory.
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### Chiral-symmetry breaking in three-dimensional electrodynamics

(1984)
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### Author and article information

###### Affiliations
[1]European Organization for Nuclear Research
[2]Durham University
###### Journal
SciPost Physics
SciPost Phys.
Stichting SciPost
2542-4653
2017
September 28 2017
: 3
: 3
10.21468/SciPostPhys.3.3.024