An Interacting, Higher Derivative, Boundary Conformal Field Theory

Christopher P. Herzog, Yanjun Zhou
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Abstract

We consider a higher derivative scalar field theory in the presence of a boundary and a classically marginal interaction. We first investigate the free limit where the scalar obeys the square of the Klein-Gordon equation. In precisely $d=6$ dimensions, modules generated by $d-2$ and $d-4$ dimensional primaries merge to form a staggered module. We compute the conformal block associated with this module and show that it is a generalized eigenvector of the Casimir operator. Next we include the effect of a classically marginal interaction that involves four scalar fields and two derivatives. The theory has an infrared fixed point in $d=6-{\epsilon}$ dimensions. We compute boundary operator anomalous dimensions and boundary OPE coefficients at leading order in the ${\epsilon}$ expansion for the allowed conformal boundary conditions.
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相互作用、高次方、边界共形场论
我们考虑了存在边界和经典边际相互作用的高导数标量场理论。我们首先研究标量服从克莱因-戈登方程平方的自由极限。在精确的$d=6$维,由$d-2$和$d-4$维基元生成的模块合并成一个交错模块。我们计算了与该模块相关的共形块,并证明它是卡西米尔算子的广义特征向量。接下来,我们加入了涉及四个标量场和两个导数的经典边际相互作用的效果。理论在 $d=6-{\epsilon}$ 维上有一个红外定点。我们在允许的共形边界条件下,在${\epsilon}$展开中计算边界算子反常维数和边界OPE系数。
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