Multiflavor Soldering

TL;DR

This paper extends the soldering procedure to 3D bosonic theories with multiple flavors, enabling the construction of dual theories by combining fermionic determinants of opposite helicities and revealing new connections between perturbative bosonization approaches.

Contribution

It introduces a generalized soldering method for multiflavor 3D theories, linking different bosonization techniques and constructing dual theories from fermionic determinants.

Findings

Generalized soldering produces interference terms connecting multiflavor Maxwell-Chern-Simons and dual theories.

Fermionic determinants of opposite helicities can be combined to yield self-dual and anti-self-dual theories.

Pure Chern-Simons fields act as spectators but are crucial in the soldering process.

Abstract

In two dimensions the simple addition of two chiral bosons of opposite chiralities does not lead to a full massless scalar field. Similarly, in three dimensions the addition of two Maxwell-Chern-Simons fields of opposite helicities $\pm 1$ will not produce a parity invariant Maxwell-Proca theory. An interference term between the opposite chiralities (helicities) states is required in order to obtain the expected result. The so called soldering procedure provides the missing interference Lagrangian in both 2D and 3D cases. In two dimensions such interference term allows to fuse two chiral fermionic determinants into a nonchiral one. In a recent work we have generalized this procedure by allowing the appearance of an extra parameter which takes two possible values and leads to two different soldered Lagrangians. Here we apply this generalized soldering in a bosonic theory which has appeared in a partial bosonization of the 3D gauged Thirring with $N$ flavors. The multiplicity of flavors allow new types of solderings and help us to understand the connection between different perturbative approaches to bosonization in 3D. In particular, we obtain an interference term which takes us from a multiflavor Maxwell-Chern-Simons theory to a pair of self-dual and anti-self-dual theories when we combine together both fermionic determinants of +1/2 and -1/2 helicity fermions. An important role is played by a set of pure non-interacting Chern-Simons fields which amount to a normalization factor in the fermionic determinants and act like spectators in the original theory but play an active role in the soldering procedure. Our results suggest that the generalized soldering could be used to provide dual theories in both 2D and 3D cases.