Bosonization of Thirring Model in Arbitary Dimension

Abstract

We propose to use a novel master Lagrangian for performing the bosonization of the D-dimensional massive Thirring model in D = d + 1 ≥ 2 dimensions. It is shown that our master Lagrangian is able to relate the previous interpolating Lagrangians each other which have been recently used to show the equivalence of the massive Thirring model in (2+1) dimensions with the Maxwell-Chern-Simons theory. Starting from the phase-space path integral representation of the master Lagrangian, we give an alternative proof for this equivalence up to the next-toleading order in the expansion of the inverse fermion mass. Moreover, in (3+1)dimensional case, the bosonized theory is shown to be equivalent to the massive antisymmetric tensor gauge theory. As a byproduct, we reproduce the well-known result on bosonization of the (1+1)-dimensional Thirring model following the same strategy. Finally a possibility of extending our strategy to the non-Abelian case is also discussed. *

The Gauged Thirring Model in 3+1 Dimensions

“…Actually, the 2+1 dimensional massive Thirring model can be bosonized into the Maxwell-Chern-Simons theory in which the gauge boson mass is generated through the Chern-Simons term without breaking the gauge invariance [44,26]. This scenario can be extended into the higher dimensional case [26,27]. In 3+1 dimensional case, it is shown [27] that the Thirring model can be mapped into the antisymmetric tensor gauge theory.…”

“…Even in the case of β = 0, it has been shown that the kinetic term for the field A µ is generated due to radiative corrections [28], only when the fermion mass is dynamically generated in the chiral limit m 0 = 0. In the case of massive fermion, particularly very massive fermion, the generation of the kinetic term can be seen also through the procedure of bosonization [44,26,27]. To see the effect coming from the dynamical gauge field A µ , we have here introduced the kinetic term from the beginning.…”

“…In light of the above argument, it is interesting to pursue the gauge-invariant generalization of the Thirring model, which we call the gauged Thirring model. Quite recently, the Thirring model was itself reformulated as a gauge theory [24,25,26,27]. There it has been realized that the gauge structure is actually involved in the original Thirring model and the kinetic term for the gauge field which is absent in the original Lagrangian is generated through radiative corrections only when the fermion is massive.…”

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

“…But since this is a local symmetry, the mismatch should not worry us. In fact it is long known that even the Thirring model can be turned into a gauge theory by introducing auxiliary fields [12][13][14][15][16][17]. Of more relevance is the pairing of global symmetries, since these are connected with the existence of conserved charges.…”

“…In an independent line of development this matter is clarified starting with a reformulation of the TM as a gauge theory [12][13][14][15]. Furthermore, the idea is generalized to arbitrary dimensions and the connection between several intermediate models is revealed using master Lagrangians [16,17]. In addition to the interest in the context of high-energy physics, the TM model appears frequently in condensed matter systems.…”