Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
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DOI：
10.1007/jhep06(2016)174
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发表时间：
2016-05
影响因子：
5.4
通讯作者：
A. Tseytlin;L. Wulff
中科院分区：
文献类型：
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作者：
A. Tseytlin;L. Wulff
我们确定的约束施加在10维目标超空间几何的要求经典卡帕对称的Green-Schwarz超弦。在第一类情况下，我们发现背景必须满足第一类超引力方程的推广。这些方程依赖于一个任意的向量X a，并暗示了GS sigma模型的单圈尺度不变性。在特殊的情况下，当X a是一个标量的梯度（标量）恢复标准的I型方程相当于超弦sigma模型的2D Weyl不变性条件。在第二类情况下，我们找到了10维超引力方程的广义版本，其中玻色子部分在arXiv：1511.05795中引入。这些方程取决于两个向量Xa和Ka，它们服从一阶微分关系（NS-NS扇区中的方程仅取决于组合Xa = Xa + Ka）。在Ka = 0的特殊情况下，我们发现Xa = a，从而得到标准的II型超引力方程。新的广义解被发现，如果K a被选为一个Killing向量（因此，它们只存在于度量允许等距）。广义方程的非平凡解描述了K-等距背景，可以通过T-对偶映射到II型超引力解，其中包含一个线性等距破坏项。这种背景的例子最近出现在AdSn × Sn sigma模型的可积η-变形的上下文中。因此，一般来说，经典的κ对称性并不意味着GS sigma模型的2d Weyl不变性条件（相当于II型超引力方程），而只是较弱的标度不变性条件。
We determine the constraints imposed on the 10d target superspace geometry by the requirement of classical kappa-symmetry of the Green-Schwarz superstring. In the type I case we find that the background must satisfy a generalization of type I supergravity equations. These equations depend on an arbitrary vector X a and imply the one-loop scale invariance of the GS sigma model. In the special case when X a is the gradient of a scalar ϕ (dilaton) one recovers the standard type I equations equivalent to the 2d Weyl invariance conditions of the superstring sigma model. In the type II case we find a generalized version of the 10d supergravity equations the bosonic part of which was introduced in arXiv: 1511.05795. These equations depend on two vectors X a and K a subject to 1st order differential relations (with the equations in the NS-NS sector depending only on the combination X a= X a+ K a). In the special case of K a= 0 one finds that X a=∂ a ϕ and thus obtains the standard type II supergravity equations. New generalized solutions are found if K a is chosen to be a Killing vector (and thus they exist only if the metric admits an isometry). Non-trivial solutions of the generalized equations describe K-isometric backgrounds that can be mapped by T-duality to type II supergravity solutions with dilaton containing a linear isometry-breaking term. Examples of such backgrounds appeared recently in the context of integrable η-deformations of AdS n× S n sigma models. The classical kappa-symmetry thus does not, in general, imply the 2d Weyl invariance conditions for the GS sigma model (equivalent to type II supergravity equations) but only weaker scale invariance type conditions.