多味焊接
Multiflavor Soldering
摘要：
在二维空间中，两个手征相反的手征玻色子的简单相加不会导致完全无质量的标量场。类似地，在三维空间中，两个螺旋度相反的麦克斯韦-陈-西蒙斯场$\pm 1$相加也不会产生宇称不变的麦克斯韦-普罗卡理论。为了获得预期的结果，需要在相反的手性（螺旋度）状态之间的干扰项。所谓的焊接过程提供了2D和3D情况下的缺失干涉拉格朗日。在二维空间中，这种干涉项允许将两个手征费米子行列式融合成一个非手征费米子行列式。在最近的一项工作中，我们已经推广了这一过程，允许出现一个额外的参数，需要两个可能的值，并导致两个不同的焊接拉格朗日。在这里，我们应用这种广义焊接的玻色子理论，出现在一个部分玻色子化的3D规范Thirring与$N$口味。口味的多样性允许新类型的焊接，并帮助我们理解3D中玻色子化的不同微扰方法之间的联系。特别是，我们得到了一个干扰项，它把我们从一个多味麦克斯韦-陈-西蒙斯理论的一对自对偶和反自对偶理论时，我们结合在一起的两个费米子决定因素的+1/2和-1/2螺旋费米子。一组纯粹的非相互作用的陈-西蒙斯场扮演着重要的角色，它们相当于费米子行列式中的归一化因子，在原始理论中扮演着观众的角色，但在焊接过程中扮演着积极的角色。我们的研究结果表明，广义焊接可以用来提供双重理论在二维和三维的情况下。
英文摘要：
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.
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