Supersymmetric Solutions with Fluxes from Algebraic Killing Spinors
Supersymmetric Solutions with Fluxes from Algebraic Killing Spinors
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DOI：
10.4310/atmp.2003.v7.n5.a2
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发表时间：
2003-06
影响因子：
1.5
通讯作者：
C. N. Gowdigere;D. Nemeschansky;N. Warner
中科院分区：
文献类型：
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作者：
C. N. Gowdigere;D. Nemeschansky;N. Warner
给出了构造张量规范场非平凡通量下的超对称解的一般框架。这种技术包括为度规做一个一般的Ansatz，然后根据非常简单的旋量域上的投影来定义终止旋量。这些投影，以及通过它们的旋量，是由度量Ansatz在代数上确定的。然后，杀戮旋量方程在代数上固定张量规范场，并与Bianchi恒等式一起，为所有度量函数提供了一个方程组。我们通过构建一个在m理论中保持八个超对称性的无限大流量族来说明这一点。这个家族构成了m2膜上软破碎大N标量费米子理论的所有径向对称库仑分支流。我们把这个问题简化为求解一个单变量的非线性偏微分方程。这个方程控制着费米子质量的流动，然后解出它的函数就产生了整个m理论的代数解根据这个函数和它的一阶导数。虽然控制方程是非线性的，但它有一个非常简单的微扰理论，从中可以看到库仑分支是如何编码的。
We give a general framework for constructing supersymmetric solutions in the presence of non-trivial fluxes of tensor gauge fields. This technique involves making a general Ansatz for the metric and then defining the Killing spinors in terms of very simple projectors on the spinor fields. These projectors and, through them, the spinors, are determined algebraically in terms of the metric Ansatz. The Killing spinor equations then fix the tensor gauge fields algebraically, and, with the Bianchi identities, provide a system of equations for all the metric functions. We illustrate this by constructing an infinite family of massive flows that preserve eight supersymmetries in M-theory. This family constitutes all the radially symmetric Coulomb branch flows of the softly broken, large N scalar-fermion theory on M2-branes. We reduce the problem to the solution of a single, non-linear partial differential equation in two variables. This equation governs the flow of the fermion mass, and the function that solves it then generates the entire M-theory solution algebraically in terms of the function and its first derivatives. While the governing equation is non-linear, it has a very simple perturbation theory from which one can see how the Coulomb branch is encoded.