In the paper "A Duality Web in 2+1 Dimensions and Condensed Matter Physics",
https://arxiv.org/abs/1606.01989
it is claimed on page 1 that the two theories
|DBϕ|2−g|ϕ|4⟷−14e2ˆfμνˆfμν+|Dˆbˆϕ|2−ˆg|ˆϕ|4+12πϵαβγˆbα∂βBγ
are dual and flow to Wilson-Fisher fixed point in the IR, where ˆfμν=∂μˆbν−∂νˆbμ.
The classical mass dimensions are [ϕ]=[ˆϕ]=1/2, [B]=[ˆb]=1, [g]=[ˆg]=1, and [e]=1/2. In the IR limit, I expect that e→∞ and g,ˆg→∞, so I can drop the kinetic term of ˆb field dˆb∧∗dˆb, and the theories become strongly coupled.
However, from this bachelor thesis, the exact β-function of real ϕ4 scalar is computed via using the Wetterich's exact RG flow equation, which is widely used in the quantum gravity community.
https://www.ru.nl/publish/pages/760966/bachelorscriptie_arthur_vereijken.pdf
It shows that the theory
S=∫dDx{12ϕ(x)(−∂2+m2)ϕ(x)+λ4!ϕ(x)4}
≡∫dDx{12ϕ(x)(−ZΛ∂2+Λ2˜m2Λ)ϕ(x)+Λ4−D4!λΛϕ(x)4}
has a Wilson-Fisher fixed point at
Z∗=1
˜m∗=D−416−D
˜λ∗=9⋅2D+5πD/2Γ(D/2+1)(4−D)(16−D)3
In D=2+1, the Wilson-Fisher fixed point has a finite coupling, with negative mass-squared −1/13, and so has a spontaneous symmetry breaking.
However, in the paper by Nathan Seiberg, T. Senthil, Chong Wang, Edward Witten, it clearly says that the Wilson-Fisher fixed point in 2+1 dimensions is massless.
Am I misunderstanding anything here?