论文标题
边界形成式田间理论中的费米亚：交叉对称性和$ε$ - expansion
Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $ε$-Expansion
论文作者
论文摘要
我们将运动方程与交叉对称性结合使用来限制相互作用的费米子边界综合场理论的特性。这种组合是确定运算符产品扩展系数和异常尺寸的一种有效方法，并在$ε$扩展的前几个订单中确定。该过程的两种必要成分是对边界和散装纺纱块块的了解。散装纺纱条形块首次得出。然后，我们考虑一些示例。对于$ ϕ $一个标量字段和$ψ$，我们研究了$ ϕ \ bar单ψ$耦合$ 4-ε$ dimensions的效果，$ ϕ^2 \ barψ$耦合在$ 3-ε$ dimensions中，以及$ 3 -am $ dimensions，a $（\ barψ2 $ couple $ 2 $ 2 $ 2 $ 2+2 $ 2+2+我们能够为这些理论中的操作员计算一些新的异常维度。最后，我们将表面算子的异常维度与表面附近电荷密度的行为联系起来。
We use the equations of motion in combination with crossing symmetry to constrain the properties of interacting fermionic boundary conformal field theories. This combination is an efficient way of determining operator product expansion coefficients and anomalous dimensions at the first few orders of the $ε$ expansion. Two necessary ingredients for this procedure are knowledge of the boundary and bulk spinor conformal blocks. The bulk spinor conformal blocks are derived here for the first time. We then consider a number of examples. For $ϕ$ a scalar field and $ψ$ a fermionic field, we study the effects of a $ϕ\bar ψψ$ coupling in $4- ε$ dimensions, a $ϕ^2 \bar ψψ$ coupling in $3 -ε$ dimensions, and a $(\bar ψψ)^2$ coupling in $2+ε$ dimensions. We are able to compute some new anomalous dimensions for operators in these theories. Finally, we relate the anomalous dimension of a surface operator to the behavior of the charge density near the surface.
