arXiv 2411.044372024-11hep-th

D=3, N=4超引力的类时超对称解

Timelike Supersymmetric Solutions of D=3, N=4 Supergravity

Nihat Sadik Deger, Ceren Ayse Deral

备注：: 20 pages, v2: minor typos fixed
发表信息：: Phys.Rev.D 111 (2025) 4, 046007

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AI总结：

该研究通过Killing旋量双线性方法证明D=3、N=4规范超引力的类时超对称解仅为AdS₃，还发现非规范版本可截断为耦合ℍ²σ模型的超引力，解由全纯函数表示且存在径向依赖及pp波零解。

摘要：

我们使用Killing旋量双线性方法研究D=3、N=4规范超引力的类时超对称解，并证明AdS₃是该类中的唯一解。随后我们考虑该模型的非规范版本，发现对于这类解，非规范理论有效截断为耦合了σ模型的超引力，σ模型的目标空间是2维双曲空间ℍ²；所有解可由两个任意全纯函数表示，时空度规是时间方向与2维空间的翘曲乘积，翘曲因子由ℍ²的凯勒势给出。当决定σ模型标量场的全纯函数非恒定时，σ模型目标流形的度规成为时空度规的一部分；我们还研究了全纯函数的特殊选择，此时时空度规和Killing旋量仅依赖径向坐标，并推导了非规范模型的超对称零解，即闵可夫斯基时空上的pp波。

英文摘要：

We study timelike supersymmetric solutions of a $D=3, N=4$ gauged supergravity using Killing spinor bilinears method and prove that AdS$_3$ is the only solution within this class. We then consider the ungauged version of this model. It is found that for this type of solutions, the ungauged theory effectively truncates to a supergravity coupled to a sigma model with a 2-dimensional hyperbolic target space $\mathbb{H}^2$, and all solutions can be expressed in terms of two arbitrary holomorphic functions. The spacetime metric is a warped product of the time direction with a 2-dimensional space, and the warp factor is given in terms of the Kähler potential of $\mathbb{H}^2$. We show that when the holomorphic function that determines the sigma model scalar fields is not constant, the metric on the sigma model target manifold becomes part of the spacetime metric. We then look at some special choices for these holomorphic functions for which the spacetime metric and the Killing spinors are only radial dependent. We also derive supersymmetric null solutions of the ungauged model which are pp-waves on the Minkowski spacetime.

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