论文标题
CFT距离猜想
A CFT Distance Conjecture
论文作者
论文摘要
我们制定了一系列的猜想，将共形流形的几何形状与在$ d> 2 $时空维度中的保形场理论中的本地运算符相关的几何形状有关。我们专注于相对于Zamolodchikov公制的无限距离的限制点的共形歧管。我们的中心猜想是，无限距离处的所有理论都具有出现的高自旋对称性，该对称是由无限的电流塔产生的，其异常尺寸在远处呈指数式消失。陈述几何，非紧密的共形歧管的直径必须在较高自旋间隙中对数分化。在全息环境中，我们的猜想与Swampland计划中的距离猜想有关。在重力上解释，他们暗示在固定ADS半径处的模量空间中接近无限距离，高自旋磁场的塔以指数速率从下方界定的，以普朗克单位的限制。我们讨论了三个和四个维度中超宪法场理论的保形歧管的进一步含义。
We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in $d>2$ spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.
