M-理论解在$D(2,1;γ) \oplus D(2,1;γ)$下的不变性
M-theory Solutions Invariant under $D(2,1;γ) \oplus D(2,1;γ)$
摘要：
利用等距超代数D（2，1;γ）\oplus D（2，1; γ），将半BPS解的构造方法简化并推广到11维超引力场.它们的时空形式为AdS_3 x S^3 x S^3，在黎曼曲面上弯曲。它描述了M2膜的近视界几何，这些膜沿着一条公共弦终止于或相交于M5膜。BPS方程的通解由约化数据集（γ，h，G）指定，其中γ是等距超代数的实参数，h和G是ε上的函数，其微分方程和正则性条件仅依赖于γ的符号。γ的大小仅通过h，G的映射进入超引力场，从而将所有解提升到由下式参数化的族中：|γ|.通过分析超引力场的正则性条件，我们证明了两个一般性定理：（i）具有二维CFT对偶的唯一解是AdS_3 x S^3 x S^3 x R^2，平坦R^2的模离散标识;（ii）γ< 0的解不能有一个以上的渐近高维AdS区域.我们对H和G在边界附近的奇点进行了分类，并确定了四个局部解：渐近AdS_4/Z_2或AdS_7'区域;高度弯曲的M5-膜;以及称为“帽”的坐标奇点。通过把这些“乐高”碎片放在一起，我们恢复了所有已知的具有上述对称性的整体正则解，包括M5上$γ< 0$的自对偶弦，以及γ> 0的Janus解，但现在推广到由下式参数化的族：|γ|.我们还构造了当γ< 0时渐近于AdS_4/Z_2的新的正则解，并猜想它们是自对偶弦的一个不同的超共形极限.
英文摘要：
We simplify and extend the construction of half-BPS solutions to 11-dimensional supergravity, with isometry superalgebra D(2,1;γ) \oplus D(2,1;γ). Their space-time has the form AdS_3 x S^3 x S^3 warped over a Riemann surface Σ. It describes near-horizon geometries of M2 branes ending on, or intersecting with, M5 branes along a common string. The general solution to the BPS equations is specified by a reduced set of data (γ, h, G), where γis the real parameter of the isometry superalgebra, and h and G are functions on Σwhose differential equations and regularity conditions depend only on the sign of γ. The magnitude of γenters only through the map of h, G onto the supergravity fields, thereby promoting all solutions into families parametrized by |γ|. By analyzing the regularity conditions for the supergravity fields, we prove two general theorems: (i) that the only solution with a 2-dimensional CFT dual is AdS_3 x S^3 x S^3 x R^2, modulo discrete identifications of the flat R^2, and (ii) that solutions with γ< 0 cannot have more than one asymptotic higher-dimensional AdS region. We classify the allowed singularities of h and G near the boundary of Σ, and identify four local solutions: asymptotic AdS_4/Z_2 or AdS_7' regions; highly-curved M5-branes; and a coordinate singularity called the "cap". By putting these "Lego" pieces together we recover all known global regular solutions with the above symmetry, including the self-dual strings on M5 for $γ< 0$, and the Janus solution for γ> 0, but now promoted to families parametrized by |γ|. We also construct exactly new regular solutions which are asymptotic to AdS_4/Z_2 for γ< 0, and conjecture that they are a different superconformal limit of the self-dual string.
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