Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories

Abstract

It has been conjectured that Chern-Simons (CS) gauged 'regular' bosons in the fundamental representation are 'level-rank' dual to CS gauged critical fermions also in the fundamental representation. Generic relevant deformations of these conformal field theories lead to one of two distinct massive phases. In previous work, the large N thermal free energy for the bosonic theory in the unHiggsed phase has been demonstrated to match the corresponding fermionic results under duality. In this note we evaluate the large N thermal free energy of the bosonic theory in the Higgsed phase and demonstrate that our results, again, perfectly match the predictions of duality. Our computation is performed in a unitary gauge by integrating out the physical excitations of the theory -i.e. W bosonsat all orders in the 't Hooft coupling. Our results allow us to construct an exact quantum effective potential forφφ, the lightest gauge invariant scalar operator in the theory. In the zero temperature limit this exact Landau-Ginzburg potential is non-analytic atφφ = 0. The extrema of this effective potential at positiveφφ solve the gap equations in the Higgsed phase while the extrema at negativeφφ solve the gap equations in the unHiggsed phase. Our effective potential is bounded from below only for a certain range of x 6 (the parameter that governs sextic interactions of φ). This observation suggests that the regular boson theory has a stable vacuum only when x 6 lies in this range. 1 anshuman@theory.tifr.res.in 2 indranil.halder@tifr.res.in 3 sachin.jain@iiserpune.ac.in 4 lavneet@theory.tifr.res.in 5 minwalla@theory.tifr.res.in 6 naveensp@theory.tifr.res.in A Previously known results for the large N free energy 32 A.1 Results for the critical fermion theory 33 A.2 Results for regular bosons in the unHiggsed Phase 35 A.3 Duality in the unHiggsed phase and a prediction for the Higgsed phase 36 A.3.1 unHiggsed phase: sgn(X F ) = −sgn(λ B ) 37 A.3.2 Higgsed phase: sgn(X F ) = sgn(λ B ) 37 B The tadpole from W boson loops 38 C The critical boson scaling limit 41 -1 -

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.…”

Scattering amplitudes in $$ \mathcal{N} $$ = 3 supersymmetric SU(N) Chern-Simons-matter theory at large N

“…Some of these flows lead to supersymmetric fixed points where the bosonization duality [31][32][33][34] is related to the already well known Giveon-Kutasov duality [35][36][37]. 4 Recent computations have also investigated the duality in the Higgsed phase [38,39], finite temperature, background fields and additional flavors (see [40][41][42][43]). In particular, the puzzle of matching the dimensions of monopole operators [44] has led to the conjecture of the duality for finite N, κ [45].…”