Bosonization of the Thirring model in 2+1 dimensions

Abstract

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.

Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation

“…This is a powerful approach that will allows us to identify the equivalent bosonic theory describing our model in the low-energy regime. By defining k µ =χγ µ χ , j µ =ψγ µ ψ , the corresponding generating functional has the form In order to integrate out the fermion field χ , we follow 19,28 (see also [29][30][31] ) and express the third term in the action as where a µ is an Hubbard-Stratonovich vector field. By replacing this back into the generating functional Z, we obtain…”

“…We now show that our effective topological field theory in Eq. (31) allows us to describe the 1D gapless modes trapped along defect lines (namely, 1D domain walls) that we can add on the 2D gapped boundary. In fact, defect lines behave as an effective spacial boundary for the 2 + 1-D bosonic model in Eq.…”

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

“…However, due to the gauge symmetry in the theory described by L T M , some of them can be eliminated. In order to identify which ones propagate as massive physical modes or which are spurious (gauge dependent) modes, it is instructive to perform a decomposition in time-space on the equations of motions ( 9) and (10). For this purpose, let us split B µν into the independent components B 0i and B ij and to introduce spatial vectors X and Y defined by…”

“…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].…”

Bosonization in 2+1 dimensions via Chern-Simons bosonic particle-vortex duality

“…Due to the fermionic sign structure of the wave function, the situation is, however, much more complex in higher dimensions. In recent years, there has been intense activity surrounding bosonization dualities in 2 þ 1 dimensions [4][5][6][7][8][9][10][11][12][13][14], but indeed it has turned out to be very difficult to obtain exact statements. For instance, while the free massive Dirac fermion in 1 þ 1 dimensions can be exactly mapped into a sine-Gordon model with a particular value of the coupling constant [15][16][17], a similar statement in 2 þ 1 dimensions is argued to hold only at the infrared stable fixed point of the dual bosonic theory.…”