论文标题
S $^2 \ times $ s $^2 $，自发对称性断裂和埃菲莫夫马鞍点的全息Qfts
Holographic QFTs on S$^2\times $S$^2$, spontaneous symmetry breaking and Efimov saddle points
论文作者
论文摘要
研究球体的全息CFT和全息RG流量为$ d $二维的球体。在重力方面，这对应于渐近的$ ads_ {d+1} $几何形状上的爱因斯坦 - 迪拉顿重力，由球体的产物散落。我们专注于$ s^2 \ times s^2 $的全息理论，我们表明，唯一常规的五维散装几何形状具有红外端点，其中一个球体缩小到零尺寸，而另一个球体则保持有限。在$ z_2 $ - 平衡的极限（两个球体具有相同的UV半径）中，我们显示了一套无限离散的常规解决方案的存在，满足了Efimov类似Efimov的离散标度。 $ z_2 $ - 符合的解决方案，其中两个球在端点处的收缩至零是单数的，而最低的自由能的解决方案是规则的，并且会自发断裂$ z_2 $对称性。我们通过在可能的$ Z_2 $ - 符合溶液周围识别大量的不稳定模式来分析这种现象。理论的空间具有两个分支，这些分支是由散装中的对照型转变连接的，该分支是规则的，对应于量子一阶跃迁。我们的结果还表明，$ ads_5 $不承认$ s^2 \ times s^2 $的常规切片。
Holographic CFTs and holographic RG flows on space-time manifolds which are $d$-dimensional products of spheres are investigated. On the gravity side, this corresponds to Einstein-dilaton gravity on an asymptotically $AdS_{d+1}$ geometry, foliated by a product of spheres. We focus on holographic theories on $S^2\times S^2$, we show that the only regular five-dimensional bulk geometries have an IR endpoint where one of the sphere shrinks to zero size, while the other remains finite. In the $Z_2$-symmetric limit, where the two spheres have the same UV radii, we show the existence of a infinite discrete set of regular solutions, satisfying an Efimov-like discrete scaling. The $Z_2$-symmetric solution in which both spheres shrink to zero at the endpoint is singular, whereas the solution with lowest free energy is regular and breaks $Z_2$ symmetry spontaneously. We explain this phenomenon analytically by identifying an unstable mode in the bulk around the would-be $Z_2$-symmetric solution. The space of theories have two branches that are connected by a conifold transition in the bulk, which is regular and correspond to a quantum first order transition. Our results also imply that $AdS_5$ does not admit a regular slicing by $S^2\times S^2$.
