Duality Between 3D Massive Thirring and Maxwell-Chern-Simons Models from 2D Bosonization

Hernaski, Carlos A.; Gomes, Pedro R. S.

doi:10.1103/physrevlett.121.041601

Cited by 7 publications

(5 citation statements)

References 37 publications

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“…Furthermore, it has been proved a fruitful approach in the study of the recently discovered dualities in three-dimensional field theories -the web of dualities [25,26], where the quantum wires can be thought as a discretized version of a 2+1 dimensional fermionic theory. This method made possible explicit derivations of dualities in theories involving fermions [27][28][29].…”

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confidence: 99%

“…At the first sight, it seems that we can get rid of both parameters ∆ and m through an appropriate field redefinition. However, this is not the case because, in addition to the effective theory (29), the identifications in (19) imply a certain relation between the total charge of the wires system and the magnetic field (through the magnetic flux). Indeed, the charge of each wire is dxρ j (x), where the density in the bosonic language reads ρ j = 1 π ∂ x θ j (x).…”

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confidence: 99%

“…Incidentally, the energy gap ∆ enters in the Chern-Simons term and in (30) in such way that it can be simultaneously eliminated from both expressions through the field redefinition B → 1 √ 4π∆ B, where we have included numerical factors in the rescaling to bring (30) to the usual normalization, that is, Q = d 2 x B 2π ∈ Z. However, we cannot do the same with the odd integer m. It will always be present either in the CS term of the effective action (29) or in the relation between charge and flux (30). This shows that m is truly the only parameter of the microscopic Hamiltonian that manifests itself in the low-energy effective field theory (topological sector).…”

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confidence: 99%

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From quantum wires to the Chern-Simons description of the fractional quantum Hall effect

2019

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We show the explicit connection between two distinct and complementary approaches to the fractional quantum Hall system (FQHS): the quantum wires formalism and the topological low-energy effective description given in terms of an Abelian Chern-Simons theory. The quantum wires approach provides a description of the FQHS directly in terms of fermions arranged in an array of one-dimensional coupled wires. In this sense it is usually referred to as a microscopic description. On the other hand, the effective theory has no connection with the microscopic modes, involving only the emergent topological degrees of freedom embodied in an Abelian Chern-Simons gauge field, which somehow encodes the collective dynamics of the strongly correlated electrons. The basic strategy pursued in this work is to bosonize the quantum wires system and then consider the continuum limit. By examining the algebra of the bosonic operators in the Hamiltonian, we are able to identify the bosonized microscopic fields with the components of the field strength (electric and magnetic fields) of the emergent gauge field. Thus our study provides a bridge between the microscopic physical degrees of freedom and the emergent topological ones without relying on the bulk-edge correspondence. * Electronic address: weslei@uel.br † Electronic address: pedrogomes@uel.br ‡ Electronic address: hernaski@uel.br

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From quantum wires to the Chern-Simons description of the fractional quantum Hall effect

2019

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“…Since no single fermion state can be excited in the large mass limit, the mapping actually shows that the bound-state sector 2 of the Thirring model can be described by a bosonic gauge field governed by the MCS dynamics. Therefore the large mass limit of the 1 In this context, it is worth to mention an interesting recent approach to deal with fermions in 3D in terms of quantum wires [27][28][29], where one spatial dimension is discretized so that the 3D problem is transformed into a set of 2D ones, and all the machinery of 2D bosonization can be used. In the large N expansion, the bound-state condition can be determined exactly by examining the pole structure of the auxiliary vector field A μ arising when we write the Thirring interaction as −ðg=2Þðψγ μ ψÞ 2 ¼…”

Section: D Thirring Modelmentioning

confidence: 99%

Bosonization of the Thirring model in 2+1 dimensions

2020

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In this work we provide a bosonized version of the Thirring model in 2 þ 1 dimensions in the case of single fermion species, where we do not have the benefit of large N expansion. In this situation there are very few analytical methods to extract nonperturbative information. Meanwhile, nontrivial behavior is expected to take place precisely in this regime. To establish the bosonization of the Thirring model, we consider a deformation of a basic fermion-boson duality relation in 2 þ 1 dimensions. The bosonized model interpolates between the ultraviolet and infrared regimes, passing several consistency checks and recovering the usual bosonization relation of the web of dualities in the infrared limit. In addition the duality predicts the existence of a nontrivial ultraviolet fixed point in the Thirring model.

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“…This duality can be further generalized for non-abelian fields [6] and even for higher dimensions [7,8]. Recently, the bosonization lead to new 2 + 1 relations called web of dualities [9,10].…”

Section: Introductionmentioning

confidence: 99%

Dual equivalence between self-dual and topologically massive $B\wedge F$ models coupled to matter in $3+1$ dimensions

Maluf,

Silveira,

Silva

et al. 2020

Preprint

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In this work, we revisit the duality between a self-dual non-gauge invariant theory and a topological massive theory in 3 + 1 dimensions. The self-dual Lagrangian is composed by a vector field and an antisymmetric field tensor whereas the topological massive Lagrangian is build using a B ∧ F term. Though the Lagrangians are quite different, they yield to equations of motion that are connected by a simple dual mapping among the fields. We discuss this duality by analyzing the degrees of freedom in both theories and comparing their propagating modes at the classical level. Moreover, we employ the master action method to obtain a fundamental Lagrangian that interpolates between these two theories and makes evident the role of the topological B ∧ F term in the duality relation. By coupling these theories with matter fields, we show that the duality holds provided a Thirring-like term is included. In addition, we use the master action in order to probe the duality upon the quantized fields. We carried out a functional integration of the fields and compared the resulting effective Lagrangians.

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Duality Between 3D Massive Thirring and Maxwell-Chern-Simons Models from 2D Bosonization

Cited by 7 publications

References 37 publications

From quantum wires to the Chern-Simons description of the fractional quantum Hall effect

From quantum wires to the Chern-Simons description of the fractional quantum Hall effect

Bosonization of the Thirring model in 2+1 dimensions

Dual equivalence between self-dual and topologically massive $B\wedge F$ models coupled to matter in $3+1$ dimensions

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