Bosonization of the Thirring Model in 2+1 Dimensions

Abstract

In this work we provide a bosonized version of the Thirring model in 2+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+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.

arXiv comment13 pages; 1 table; references added; improved discussions; minor corrections in Sec. III; published version

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• Dualization between supersymmetric self-dual and topologically massive models coupled to matter in four-dimensional superspace
• Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation