Poisson-Lie duals of the η deformed symmetric space sigma model
Poisson-Lie duals of the η deformed symmetric space sigma model
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DOI：
10.1007/jhep11(2017)014
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发表时间：
2017-09
影响因子：
5.4
通讯作者：
B. Hoare;F. K. Seibold
中科院分区：
文献类型：
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作者：
B. Hoare;F. K. Seibold
利用Poisson-Lie对偶方法，将G/H对称空间σ模型的η变形关于单李群G进行对偶化，得到了相应的λ变形模型的解析延拓.本文研究了η变形模型关于G的子群G 0何时可以对偶.从一阶行动的复杂化组和整合出的自由度与不同的子代数，我们发现它是可能的对偶时，G 0是关联到一个子Dynkin图。也可以包括从剩余的Cartan生成器构建的附加U1因子。由此得到的构造将关于G的Poisson-Lie对偶和η变形的完全阿贝尔对偶统一在一个框架中，在两种情况下都是幺模的积分代数。我们推测，将这些结果推广到路径积分形式，可以解释为什么η变形AdS 5× S5超弦不是单圈Weyl不变量，即耦合解不了IIB型超引力方程，而它的完全交换对偶和λ变形模型解了.
Poisson-Lie dualising the η deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated λ deformed model. In this paper we investigate when the η deformed model can be dualised with respect to a subgroup G 0 of G. Starting from the first-order action on the complexified group and integrating out the degrees of freedom associated to different subalgebras, we find it is possible to dualise when G 0 is associated to a sub-Dynkin diagram. Additional U 1 factors built from the remaining Cartan generators can also be included. The resulting construction unifies both the Poisson-Lie dual with respect to G and the complete abelian dual of the η deformation in a single framework, with the integrated algebras unimodular in both cases. We speculate that extending these results to the path integral formalism may provide an explanation for why the η deformed AdS 5× S 5 superstring is not one-loop Weyl invariant, that is the couplings do not solve the equations of type IIB supergravity, yet its complete abelian dual and the λ deformed model are.