Bose-Fermi Chern-Simons dualities in the Higgsed phase

Abstract

It has been conjectured that fermions minimally coupled to a Chern-Simons gauge field define a conformal field theory (CFT) that is level-rank dual to Chern-Simons gauged Wilson-Fisher Bosons. The CFTs in question admit relevant deformations parametrized by a real mass. When the mass deformation is positive, the duality of the two deformed theories has previously been checked in detail in the large N limit by comparing explicit all orders results on both sides of the duality. In this paper we perform a similar check for the case of negative mass deformations. In this case the bosonic field condenses triggering the Higgs mechanism. The effective excitations in this phase are massive W bosons. By summing all leading large N graphs involving these W bosons we find an all orders (in the 't Hooft coupling) result for the thermal free energy of the bosonic theory in the condensed phase. Our final answer perfectly matches the previously obtained fermionic free energy under the conjectured duality map. 1 sayantan@aei.mpg.de, sayantan.choudhury@aei.mpg.de 2 anshuman@theory.tifr.res.in 3 indranil.halder@tifr.res.in 4 sachin.jain@iiserpune.ac.in 5 lavneet@theory.tifr.res.in 6 minwalla@theory.tifr.res.in 7 naveensp@theory.tifr.res.in 1 See [10, 11] for further results on correlation functions. 2 See [12-15] for more precise versions of the duality map. 3 See [5,9,10,16,17,20,[23][24][25][33][34][35][36][37][38][39][40][41][42][43][44][45][46] for other large-N computations that provide additional evidence for this duality.

Mass-deformed N=3 supersymmetric Chern-Simons-matter theory

“…In this context, the bosonization duality generalizes the already well known dualities such as Giveon-Kutasov duality in supersymmetric Chern-Simons-Matter theories [32][33][34]. For other recent works in the field, we refer the reader to [35][36][37][38][39] and in particular to the applications of the finite N generalizations of the duality [40][41][42][43][44][45][46][47].…”

Large N renormalization group flows in 3d $$ \mathcal{N} $$ = 1 Chern-Simons-Matter theories

“…For weak gauge coupling (large CS level) there are non-trivial weakly coupled fixed points for ω near the origin [6,7], but nothing is known about the behavior when the gauge coupling or the superpotential couplings are strong. In this paper we analyze the dynamics in the 't Hooft large N limit, of large N and large Chern-Simons level with a fixed 't Hooft coupling λ , where many computations can be explicitly performed (using methods developed in [8][9][10][11][12][13][14][15][16][17]). We will see that there are several different fixed points for the marginal couplings at finite large values of N.…”

Chern-Simons dualities with multiple flavors at large N

“…At both finite and zero temperature we focus almost exclusively on the large N fixed points. It would be interesting to further probe these theories by relevant mass and quartic deformations, including to study their Higgs phases as in [22]. We have also left U (N ) k Chern-Simons theory coupled to N s regular scalars and N f critical fermions for future study.…”

“…22) and, in the scalar equation, λ 4 there → N f λ 4 + λ 4 , while in the fermionic equation λ 4 there → N s λ 4 + λ 4 . These replacements effectively account for the multiple flavors.…”