A test of bosonization at the level of four-point functions in Chern-Simons vector models

105

It has been conjectured that 3d fermions minimally coupled to Chern-Simons gauge fields are dual to 3d critical scalars, also minimally coupled to Chern-Simons gauge fields. The large N arguments for this duality can formally be used to show that Chern-Simons-gauged critical (Gross-Neveu) fermions are also dual to gauged 'regular' scalars at every order in a 1/N expansion, provided both theories are well-defined (when one fine-tunes the two relevant parameters of each of these theories to zero). In the strict large N limit these 'quasi-bosonic' theories appear as fixed lines parameterized by x 6 , the coefficient of a sextic term in the potential. While x 6 is an exactly marginal deformation at leading order in large N , it develops a non-trivial β function at first subleading order in 1/N . We demonstrate that the beta function is a cubic polynomial in x 6 at this order in 1/N , and compute the coefficients of the cubic and quadratic terms as a function of the 't Hooft coupling. We conjecture that flows governed by this leading large N beta function have three fixed points for x 6 at every non-zero value of the 't Hooft coupling, implying the existence of three distinct regular bosonic and three distinct dual critical fermionic conformal fixed points, at every value of the 't Hooft coupling. We analyze the phase structure of these fixed point theories at zero temperature. We also construct dual pairs of large N fine-tuned renormalization group flows from supersymmetric N = 2 Chern-Simons-matter theories, such that one of the flows ends up in the IR at a regular boson theory while its dual partner flows to a critical fermion theory. This construction suggests that the duality between these theories persists at finite N , at least when N is large. arXiv:1808.03317v1 [hep-th] 9 Aug 2018 C Correlators for free fermions 102 D Conventions for Chern-Simons levels 105 D.1 N = 2 Chern-Simons levels 105 D.2 (Non-supersymmetric) Chern-Simons levels 105 D.3 Integrating out massive fundamental fermions 106 E The mapping of ranks and levels under duality 106 F Detailed free energy computations for the zero temperature phase structure 1091 One can also consider U Sp(2N ) theories, but in the large N limit in which we work, they are identical to SO(2N ) theories.2 Several of these properties appear to have their origin in the fact that the coupling of fundamental excitations to Chern-Simons gauge fields makes them effectively non-Abelian anyons. Conversely, the lessons from the study of the theories described above may well apply more generally to all systems with effectively anyonic excitations. 5 The superconformal theory described in this section may be rigorously defined by adding a supersymmetric Yang-Mills term to the action. The resulting theory is free at high energies, but reduces to (1.1) at low energies (at which point the Yang-Mills coupling effectively diverges so the Yang-Mills term in the action is negligible). In other words, theory S is the end point of a N = 2 SUSY renormalization group (RG) flow that starts i...

Section: Quasi-fermionic Theoriesmentioning

confidence: 99%

Flows, fixed points and duality in Chern-Simons-matter theories

Aharony

Jain

Minwalla

2018

105

“…We refer to §3.1 for some basic properties of fermionic wave functions and §3.2 for properties of the mode expansions in N = 1 superspace. Substituting the on-shell mode expansion (5.47) into the effective action (5.22) and taking into account the total momentum conservation, 18 we obtain a quartic polynomial in the creation/annihilation operators given by…”

Section: On-shell Limit and The S-matrixmentioning

confidence: 99%

“…The conjectured bosonization duality has successfully passed a battery of tests in the large N limit, such as thermal partition functions [13][14][15][16], correlation functions of spin s currents [17][18][19][20][21][22][23][24], and S-matrices [25][26][27][28]. As we alluded to earlier, there is significant evidence that the bosonization duality is preserved along RG flows [29,30].…”

mentioning

confidence: 99%

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

Inbasekar

Janagal

Shukla

2020

We study N = 3 supersymmetric Chern-Simons-matter theory coupled to matter in the fundamental representation of SU (N ). In the 't Hooft large N limit, we compute the exact 2 → 2 scattering amplitudes of the fundamental scalar superfields to all orders in the 't Hooft coupling λ. Our computations are presented in N = 1 superspace and make significant use of the residual SO(2) R symmetry in order to solve for the exact four-point correlator of the scalar superfields. By taking the on-shell limit, we are able to extract the exact 2 → 2 scattering amplitudes of bosons/fermions in the symmetric, antisymmetric and adjoint channels of scattering. We find that the scattering amplitude of the N = 3 theory in the planar limit is tree-level exact to all orders in the 't Hooft coupling λ. The result is consistent with the conjectured bosonization duality and is expected to have enhanced symmetry structures such as dual superconformal symmetry and Yangian symmetry.

“…As we will see below, the exceptional range of parameters correspond to states with |E| = |m F |. The quantity J just labels the angular momentum of states; J runs over 40 Note that condition on range of parameters corresponds to n ± ≥ −1 (defined in (C.30) ) excluding the particular case of n + = n − = −1. With further restriction that n + = −1 or n − = −1 is allowed only if ηbm F > 0.…”

Section: C2 Fermionmentioning

confidence: 99%

“…There have been many subsequent studies of finite N versions and generalizations of these dualities; see [14][15][16][17][18][19] for a very partial list of references. 2 See also [40][41][42] for checks of this duality at the level of four point functions of gauge invariant operators. 3 In the case of the fermionic theory the U (1) global symmetry is the obvious global symmetry that 'completes' SU (N F ) to U (N F ).…”

mentioning

confidence: 99%

Matter Chern Simons theories in a background magnetic field

Halder

Minwalla

2019

We study large N 2+1 dimensional fermions in the fundamental representation of an SU (N ) k Chern Simons gauge group in the presence of a uniform background magnetic field for the U (1) global symmetry of this theory. The magnetic field modifies the Schwinger Dyson equation for the propagator in an interesting way; the product between the self energy and the Greens function is replaced by a Moyal star product. Employing a basis of functions previously used in the study of non-commutative solitons, we are able to exactly solve the Schwinger Dyson equation and so determine the fermion propagator. The propagator has a series of poles (and no other singularities) whose locations yield a spectrum of single particle energies at arbitrary t' Hooft coupling and chemical potential. The usual free fermion Landau levels spectrum is shifted and broadened out; we compute the shifts and widths of these levels at arbitrary t'Hooft coupling. As a check on our results we independently solve for the propagators of the conjecturally dual theory of Chern Simons gauged large N fundamental Wilson Fisher bosons also in a background magnetic field but this time only at zero chemical potential. The spectrum of single particle states of the bosonic theory precisely agrees with those of the fermionic theory under Bose-Fermi duality.