On the spectrum of superspheres
On the spectrum of superspheres
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关于超球体的光谱
DOI：
10.1007/jhep03(2015)013
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发表时间：
2014
影响因子：
5.4
通讯作者：
V. Tlapák
中科院分区：
文献类型：
--
作者：
A. Cagnazzo;V. Schomerus;V. Tlapák
在奇维超球等协集超空间上的抽象sigma模型在物理学，特别是AdS/CFT对应中起着重要的作用。本文应用近年来关于协集空间模型谱和超群WZNW模型的一般结果，研究了具有目标空间S3 bbb2的共形sigma模型。我们构造了它的顶点算子，并给出了它们的异常维的显式公式，至少在sigma模型耦合中是领先的。这些结果被用来重新审视由Candu和Saleur推测的超球和OSP(4 bb0 2) Gross-Neveu模型之间的非摄动对偶性。利用Gross-Neveu模型中12BPS $$ \frac{1}{2}\mathrm{B}\mathrm{P}\mathrm{S} $$算子的强大全环结果，我们能够在Gross-Neveu耦合的某一有限值下恢复sigma模型的整个零模谱。此外，我们认为在双Gross-Neveu描述中正确地实现了sigma模型约束和运动方程。另一方面，并没有考虑到sigma模型的高（er）梯度算子。这种差异可能与高梯度算子的不稳定性有关，这种不稳定性先前在安德森定位的背景下已被观察到。
A bstractSigma models on coset superspaces, such as odd dimensional superspheres, play an important role in physics and in particular the AdS/CFT correspondence. In this work we apply recent general results on the spectrum of coset space models and on supergroup WZNW models to study the conformal sigma model with target space S3|2. We construct its vertex operators and provide explicit formulas for their anomalous dimensions, at least to leading order in the sigma model coupling. The results are used to revisit a non-perturbative duality between the supersphere and the OSP(4|2) Gross-Neveu model that was conjectured by Candu and Saleur. With the help of powerful all-loop results for 12BPS$$ \frac{1}{2}\mathrm{B}\mathrm{P}\mathrm{S} $$ operators in the Gross-Neveu model we are able to recover the entire zero mode spectrum of the sigma model at a certain finite value of the Gross-Neveu coupling. In addition, we argue that the sigma model constraints and equations of motion are implemented correctly in the dual Gross-Neveu description. On the other hand, high(er) gradient operators of the sigma model are not all accounted for. It is possible that this discrepancy is related to an instability from high gradient operators that has previously been observed in the context of Anderson localization.