3d dualities from 4d dualities

By O. Aharony, Shlomo S. Razamat, N. Seiberg, Brian Willett. 2013

329 citations recorded by the source corpus.

A bstractMany examples of low-energy dualities have been found in supersymmetric gauge theories with four supercharges, both in four and in three space-time dimensions. In these dualities, two theories that are different at high energies have the same low-energy limit. In this paper we clarify the relation between the dualities in four and in three dimensions. We show that every four dimensional duality gives rise to a three dimensional duality between theories that are similar, but not identical, to the dimensional reductions of the four dimensional dual gauge theories to three dimensions. From these specific three dimensional dualities one can flow to many other low-energy dualities, including known three dimensional dualities and many new ones. We discuss in detail the case of three dimensional SU(Nc) supersymmetric QCD theories, showing how to derive new duals for these theories from the four dimensional duality.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6efae1f62148638b69d8e13b86ed3ac459ce9315

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Citations in the corpus

The Casimir energy in curved space and its supersymmetric counterpart (2015, methodology): “This is similar to the regularization presented in appendix B of [55].”
A Duality Web in 2+1 Dimensions and Condensed Matter Physics (2016, unknown): “Also, it was shown in [12] that these 2 + 1d dualities follow upon compactification on a circle from the previously found dualities [13] in 3+1 dimensions.”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “In section 6, we will discuss pairs of 4d dual theories and show that their Mg,p × S1 partition functions agree; then the argument above shows that, by taking the β → 0 limit on both sides, the Mg,p partition functions of their reductions agree, providing strong evidence for their duality in 3d, as ”
Localization techniques in quantum field theories (2016, methodology): “In [42] it was conjectured (see also footnote 20) that that the correct contribution of the CS term contains an additional phase:”
N=1 theories of class S_k (2015, background): “Moreover, the reduction on a circle will produce additional superpotentials involving monopole operators [45].”
Comments on global symmetries, anomalies, and duality in (2 + 1)d (2017, background): “Recently, a convergence of ideas from condensed matter physics [1-6], supersymmetric quantum field theory [7-19], and string theory [20-34] has led to a large set of new boson/fermion dualities [35-45] and new fermion/fermion dualities [46,38,39,47,45].”
Localization on Hopf surfaces (2014, methodology): “Comparing with the supersymmetric index I(p, q) with fugacities p, q given for instance in [40], we obtain the relation advertised in the introduction”
Particle-Vortex Duality from 3D Bosonization (2016, background): “Combining studies of supersymmetric theories [28, 29, 30, 31], RG flows [32, 33], operator maps [34] and level-rank dualities [35] results in a consistent picture.”
Cardy formulae for SUSY theories in d = 4 and d = 6 (2014, background): “t with (4.5). The supersymmetric index corresponding to the space S3 b×S 1 has been computed in various theories, and in some cases its β→ 0 asymptotics has been explicitly discussed. See for example [36,37,38]. Our claim (4.5) agrees with these computations. In the preceding discussions we have not”
Theta, time reversal and temperature (2017, background): “25 An analogous situation was encountered in [59].”
Baryons, monopoles and dualities in Chern-Simons-matter theories (2015, background): “However, in some cases this turns out to be equivalent to an SU(N) theory (see, for instance, the discussion in [13]; this is called “ungauging”), and presumably this also happens here in the fermionic theory when we go from (2.”
Chern-Simons-matter dualities with SO and USp gauge groups (2016, background): “Another approach to finding such dualities with finite N and k is based on starting with a pair of dual N = 2 supersymmetric theories [11-23] and turning on a relevant operator that breaks supersymmetry.”
Reading between the lines of four-dimensional gauge theories (2013, background): “These issues play an important role in the relation between IR dualities of four dimensional gauge theories and those of three dimensional gauge theories [1, 2].”