N = 2 Sigma Model with Twisted Mass and Superpotential: Central Charges and Solitons
N = 2 Sigma Model with Twisted Mass and Superpotential: Central Charges and Solitons
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具有扭曲质量和超势的 N = 2 Sigma 模型：中心电荷和孤子
DOI：
10.1103/physrevd.68.045006
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发表时间：
2003
影响因子：
5
通讯作者：
M. Shifman
中科院分区：
文献类型：
--
作者：
A. Losev;M. Shifman
我们考虑Kahler目标空间上具有扭曲质量的超对称σ模型。Kahler空间被假定具有全纯Killing向量。引入一个特殊类型的超势已知与N = 2超代数（Alvarez-Gaume和Freedman）是一致的。我们证明了该代数在反子{QL，QL}和{QR，QR}中获得中心荷.这些中心电荷没有平行线，它们只能存在于二维空间。我们发现的N = 2超代数的中心扩展为一种新现象铺平了道路-部分超对称性的自发破缺。在一般情况下，1/2的超对称性自发破缺（真空能量密度为正），而剩余的1/2则是线性实现的。在这个模型中，没有定义标准费米子数，因此维滕指数和切科蒂-芬德利-因特里加托-瓦法指数都是无用的。我们将展示如何构建一个指数，用于计数短多重态的内部代数术语是定义良好的，尽管没有标准的费米子数。最后，我们概述了反交换子{<$QL，QR}中量子反常的推导。
We consider supersymmetric sigma models on the Kahler target spaces, with twisted mass. The Kahler spaces are assumed to have holomorphic Killing vectors. Introduction of a superpotential of a special type is known to be consistent with N = 2 superalgebra (Alvarez-Gaume and Freedman). We show that the algebra acquires central charges in the anticommutators {QL,QL} and {QR,QR}. These central charges have no parallels, and they can exist only in two dimensions. The central extension of the N = 2 superalgebra we found paves the way to a novel phenomenon — spontaneous breaking of a part of supersymmetry. In the general case 1/2 of supersymmetry is spontaneously broken (the vacuum energy density is positive), while the remaining 1/2 is realized linearly. In the model at hand the standard fermion number is not defined, so that the Witten index as well as the Cecotti-Fendley-Intriligator-Vafa index are useless. We show how to construct an index for counting short multiplets in internal algebraic terms which is well-defined in spite of the absence of the standard fermion number. Finally, we outline derivation of the quantum anomaly in the anticommutator { ¯ QL,QR}.