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arXiv 1004.2799hep-th
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基于SO(2N+1)李代数的无Anomaly超对称SO(2N+2)/U(N+1)西格玛模型

Anomaly-Free Supersymmetric SO(2N+2)/U(N+1) sigma-Model Based on the SO(2N+1) Lie Algebra of the Fermion Operators

Seiya Nishiyama, Joao da Providencia, Constanca Providencia, Flavio Cordeiro

摘要:

在由费米子湮灭-产生算符和对算符张成的SO(2N+1)李代数的基础上,提出了扩展超对称(SUSY)西格玛模型.引入了标准变换,即SO(2N)Bogoliubov变换到SO(2N+1)群的推广.将SO(2N+1)群嵌入到SO(2N+2)群中,利用SO(2N+2)/U(N+1)陪集变量,研究了Kaehler流形上的SUSY西格玛模型,陪集空间SO(2N+2)/U(N+1).我们构造了Killing势,它是SO(2N)/U(N)陪集空间中势到SO(2N+2)/U(N+1)陪集空间中势的推广.它等价于广义密度矩阵,其对角块部分与具有Fayet-Ilipoulos项的约化标量势有关。对f变形约化标量势进行了优化,得到了关于西格玛模型场真空期望值的SO(2N+1)群参数的一个解.然而,解决方案,只是一小部分的所有解决方案,从无异常的超对称陪集模型。为了一致地构建陪集模型,我们必须在SO(2N+2)群的无反常旋量表示(rep)中嵌入陪集坐标,并基于每个正手征旋量rep给出相应的无反常SO(2N +2)/U(N +1)模型的Kaehler势和Killing势。在Kaehler陪集空间SO(2 N)/U(N)上建立了SUSY西格玛模型,研究了SUSY模型中从未有过的新的方面.我们得到一个f变形的约化标量势。相对于无反常超对称西格玛模型场的真空期望值,它是最小的。因此,对于无反常的SO(2.5+2)/(SU(5+1)*U(1))SUSY西格玛模型,我们发现了一个有趣的f变形解.

英文摘要:

The extended supersymmetric (SUSY) sigma-model has been proposed on the bases of SO(2N+1) Lie algebra spanned by fermion annihilation-creation operators and pair operators. The canonical transformation, extension of an SO(2N) Bogoliubov transformation to an SO(2N+1) group, is introduced. Embedding the SO(2N+1) group into an SO(2N+2) group and using SO(2N+2)/U(N+1) coset variables, we have investigated the SUSY sigma-model on the Kaehler manifold, the coset space SO(2N+2)/U(N+1). We have constructed the Killing potential, extension of the potential in the SO(2N)/U(N) coset space to that in the SO(2N+2)/U(N+1) coset space. It is equivalent to the generalized density matrix whose diagonal-block part is related to a reduced scalar potential with a Fayet-Ilipoulos term. The f-deformed reduced scalar potential is optimized with respect to vacuum expectation value of the sigma-model fields and a solution for one of the SO(2N+1) group parameters has been obtained. The solution, however, is only a small part of all solutions obtained from anomaly-free SUSY coset models. To construct the coset models consistently, we must embed a coset coordinate in an anomaly-free spinor representation (rep) of SO(2N+2) group and give corresponding Kaehler and Killing potentials for an anomaly-free SO(2N+2)/U(N+1) model based on each positive chiral spinor rep. Using such mathematical manipulation we construct successfully the anomaly-free SO(2N+2)/U(N+1) SUSY sigma-model and investigate new aspects which have never been seen in the SUSY sigma-model on the Kaehler coset space SO(2N)/U(N). We reach a f-deformed reduced scalar potential. It is minimized with respect to the vacuum expectation value of anomaly-free SUSY sigma-model fields. Thus we find an interesting f-deformed solution very different from the previous solution for an anomaly-free SO(2.5+2)/(SU(5+1)*U(1)) SUSY sigma-model.

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