arXiv 1107.57462011-07-28hep-thgr-qc

爱因斯坦-麦克斯韦-介子-轴子理论中的所有极值瞬子

All extremal instantons in Einstein-Maxwell-dilaton-axion theory

Mustapha Azreg-Aïnou, Gérard Clément, Dmitri V. Gal'tsov

备注：: 59 pages, revtex4
发表信息：: Phys. Rev. D 84 (2011) 104042
DOI：: 10.1103/PhysRevD.84.104042

摘要：

我们构造了截断为一个矢量场的$\mathcal{N}=4,\, D=4$超引力（EMDA理论）的所有极值瞬子解。这些对应于零测地线的目标空间的西格玛模型$G/H=Sp(4,\mathbb{R})/GL(2,\mathbb{R})$的四维欧几里德EMDA的圆上的紧化获得。它们满足一个无力条件的渐近收费和他们的一部分（对应于幂零轨道的$Sp(4,\mathbb{R})$ U-对偶）大概是超对称的。空间的有限作用的解决方案被发现是出乎意料的大，包括，除了已知的洛伦兹解的欧几里德版本，一些新的渐近局部平坦（ALF）瞬子赋予电，磁，介子和轴子费用。我们还描述了新的类的充电渐近局部欧几里德（ALE）瞬子以及一些例外的解决方案。我们的分类方案是基于矩阵生成器的代数分类，根据他们的秩，根据性质的电荷矢量和根据独立的谐波函数与不平等的费用。除了$G$的幂零轨道，我们发现的解决方案，满足渐近无力条件，但不是超对称的。用匹配背景扣除法计算了瞬子的重整化在壳作用量。

英文摘要：

We construct explicitly all extremal instanton solutions to $\mathcal{N}=4,\, D=4$ supergravity truncated to one vector field (Einstein-Maxwell-dilaton-axion (EMDA) theory). These correspond to null geodesics of the target space of the sigma-model $G/H=Sp(4,\mathbb{R})/GL(2,\mathbb{R})$ obtained by compactification of four-dimensional Euclidean EMDA on a circle. They satisfy a no-force condition in terms of the asymptotic charges and part of them (corresponding to nilpotent orbits of the $Sp(4,\mathbb{R})$ U-duality) are presumably supersymmetric. The space of finite action solutions is found to be unexpectedly large and includes, besides the Euclidean versions of known Lorentzian solutions, a number of new asymptotically locally flat (ALF) instantons endowed with electric, magnetic, dilaton and axion charges. We also describe new classes of charged asymptotically locally Euclidean (ALE) instantons as well as some exceptional solutions. Our classification scheme is based on the algebraic classification of matrix generators according to their rank, according to the nature of the charge vectors and according to the number of independent harmonic functions with unequal charges. Besides the nilpotent orbits of $G$, we find solutions which satisfy the asymptotic no-force condition, but are not supersymmetric. The renormalized on-shell action for instantons is calculated using the method of matched background subtraction.

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