自旋3/2费米子焊接理论：2+1维度的新拓扑研究

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"这篇论文详细介绍了在2+1维度中焊接自旋3/2费米子的理论研究。焊接程序首次被应用到自旋3/2的费米子理论，这是在拓扑大规模超重力理论背景下进行的。研究者证明了如何将这种三阶导数的理论焊接起来，形成一个类似于新质量重力的线性化四阶双峰模型。此外，通过焊接两个二阶自对偶模型，他们构建了一个与爱因斯坦-希尔伯特-菲尔兹-保罗理论线性化版本相似的理论。该研究在物理学领域具有重要意义，特别是在高能物理和引力理论的交叉研究中。" 本文的核心内容围绕自旋3/2费米子的焊接理论展开。自旋3/2粒子是一种具有比普通费米子更高自旋的粒子，通常出现在量子场论和广义相对论的研究中。在这项工作中，研究人员成功地将这一概念应用于2+1维空间时间中，这是一个对于理解和研究量子引力理论的重要框架。 "焊接"在这里是指在理论物理学中的一种技术，它允许不同的场或理论成分在特定条件下被组合或连接。在这个特定的情况下，焊接程序被用来连接或融合自旋3/2费米子的理论部分，以创建新的理论结构。这种方法使得理论的性质发生变化，如从三阶导数理论转化为四阶理论，这与新质量重力的线性化版本相匹配。 "新拓扑大规模超重力"（NewTopologicallyMassiveSupergravity）是一种包含拓扑效应的重力理论，其中的费米子部分可以通过焊接程序被处理。这个过程不仅揭示了自旋3/2粒子在非平凡拓扑结构中的行为，也提供了一种理解重力与高自旋粒子相互作用的新视角。同时，论文还讨论了焊接两个二阶自对偶模型的结果。自对偶模型在理论物理学中扮演着重要角色，它们在保持某些对称性的前提下简化了理论。通过焊接，研究人员构造了一个与爱因斯坦-希尔伯特-菲尔兹-保罗理论线性化版本相似的理论。爱因斯坦-希尔伯特-菲尔兹-保罗理论是广义相对论的一个扩展，考虑了自旋1/2粒子（费米子）的贡献，是经典引力理论的组成部分。这项工作以开放访问的形式发表，意味着所有感兴趣的人都可以自由阅读和使用其研究成果，这对于促进科学知识的传播和进一步研究具有积极意义。论文的接收、修订和接受日期表明了研究过程的快速进展，而编辑J. Hisano的名字也表明了该研究得到了领域专家的认可。

Physics Letters B 783 (2018) 387–391

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Soldering spin-3/2 fermions in D = 2 + 1

E.L. Mendonça

∗

, D.S. Lima, A.L.R. dos Santos

UNESP – Campus de Guaratinguetá – DFQ, Av. Dr. Ariberto Pereira da Cunha, 333, CEP 12516-410, Guaratinguetá, SP, Brazil

a r t i c l e i n f o a b s t r a c t

Article history:

Received

11 May 2018

Received

in revised form 13 June 2018

Accepted

3 July 2018

Available

online 9 July 2018

Editor:

J. Hisano

The soldering procedure has been for the ﬁrst time generalized to the case of spin-3/2 fermionic theories.

We have demonstrated that the fermionic part of the so-called “New Topologically Massive Supergravity”

theory, which is of third order in derivatives, can be soldered in order to obtain a fourth order doublet

model

analogue to the linearized version of the New Massive Gravity theory, while the soldering of two

second order self-dual models give us a theory similar to the linearized version of the Einstein–Hilbert–

Fierz–Pauli

theory.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

In D = 2 + 1dimensions self-dual models describes massive

particles with spin +s or −s. Depending on the spin, we have a

different number of self-dual descriptions. In the spin-1 case for

example we have two self-dual descriptions, while in the spin-2

case we have four. The models differ each other by an order in

derivatives and by gauge invariance under a given symmetry or a

set of them.

have studied in [1]the connection among three massive

spin-3/2self-dual versions of ﬁrst, second and third order in

derivatives through symmetry arguments. We have also considered

an analogue version of the Proca (or Fierz–Pauli) theory which is

second order in derivatives and which by means of the Fierz–Pauli

conditions describes correctly two massive propagating modes of

helicities +3/2 and −3/2. This doublet model

is by its turn con-

nected

to a fourth order doublet model which we believe is free

of ghosts. We have argued that, due the similarities, the fourth

order model could be interpreted as the spin-3/2version of the

linearized New Massive Gravity (NMG) [2]. However, it is unclear

so far if it is possible to obtain the doublet models from the self-

dual

ones as well as the ﬁrst order self-dual model from the de-

composition

of the second order doublet model. That is what we

Corresponding author.

E-mail

addresses: eliasleite@feg.unesp.br (E.L. Mendonça),

diegos.lima88@hotmail.com (D.S. Lima), alessandroribeiros@yahoo.com.br

(A.L.R. dos Santos).

All along the work we use the terminology of singlet models meaning that the

models carries only a unique helicity +3/2or −3/2, while the doublet models car-

ries

both of them together.

are going to address in the following lines using the soldering ap-

proach,

which we brieﬂy describe in the next paragraphs.

The

soldering approach is only one of the several tools we

have to investigate dualities. The technique was ﬁrst introduced by

Stone many years ago [3], and since then it has been used on the

study of dual aspects of physical systems with many applications

in different contexts as well as in different dimensions. Electro-

magnetic

dualities can be explored through the soldering proce-

dure

providing new point of views of the same physics [4]. The

quantization of strings and also other theoretical models encour-

aged

the study of chiral bosons in the nineties. In this context the

authors in [5](seealso references therein) have used the solder-

ing

formalism to combine the opposite chiralities of the Schwinger

model. As a consequence they have noticed that the formalism

could be generalized leading us either to the vector or to the axial

models depending on a constant parameter α =±1. A brief and

interesting note [6] has showed us that even in the presence of

non-commutative ﬁeld theories the soldering formalism can be ap-

plied.

Although the several generalizations and applications of the

technique we do not know an example of the soldering procedure

applied to the case of fermionic ﬁelds.

[7]the authors have noticed that in the spin-1 case the ﬁrst

order self-dual model can be understood as the “square root” of

the Proca theory (which carries a doublet of spins ±1), in such a

way that it is equivalent to the direct sum of ﬁrst order self-dual

models with opposite helicities. We can notice that once the ﬁrst-

order

self-dual model is equivalent to the Maxwell–Chern–Simons

(MC S) model (the second order description) one can expect that

the direct sum of two MCS models will also produce the Proca

theory, but that is not true. To obtain the Proca theory from the

https://doi.org/10.1016/j.physletb.2018.07.005

0370-2693/

SCOAP

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