巨引力子算符乘积展开系数的通用标度函数
A universal scaling function for giant graviton OPE coefficients
AI总结：
研究平面\(\mathcal{N}=4\)超杨-米尔斯理论中两个最大巨引力子与有限扭转自旋算符的OPE系数大自旋极限情况，开发系统方法计算标度函数\(d(g)\)，给出弱、强耦合及有限耦合结果，揭示其不受有限尺寸修正影响。
AI中文摘要：
我们考虑平面\(\mathcal{N}=4\)超杨-米尔斯理论中两个最大巨引力子与一个具有有限扭转的自旋算符的算符乘积展开（OPE）系数在大自旋极限\(S\to\infty\)的情况。该OPE系数在整体归一化因子下呈现\(S^{d(g)}\)形式的幂律标度。我们提供有力证据表明指数\(d(g)\)不受有限尺寸修正影响。进而，OPE系数的全圈渐近表达式可精确确定\(d(g)\)。我们开发了一种系统方法来计算任意\(‘t\)胡夫特耦合\(g\)值下的标度函数\(d(g)\)。在弱耦合时，结果与直至三圈阶的现有场论结果完美吻合。在强耦合时，给出前三阶的具体预测。还给出有限耦合结果，表明其在弱耦合和强耦合区域之间平滑插值。
英文摘要：
We consider the large spin limit $S\to\infty$ of the OPE coefficient for two maximal giant gravitons and a spinning operator with finite twist in planar $\mathcal{N}=4$ super-Yang-Mills theory. Up to an overall normalization factor, this OPE coefficient exhibits a power-law scaling of the form $S^{d(g)}$. We provide strong evidence that the exponent $d(g)$ is free from finite size corrections. Consequently, the all-loop asymptotic expression for the OPE coefficient can be used to determine $d(g)$ exactly. We develop a systematic method to compute the scaling function $d(g)$ for arbitrary values of the 't Hooft coupling $g$. At weak coupling, our result agrees perfectly with the available field-theoretic results up to three-loop order. At strong coupling, we present the first three orders as concrete predictions. We further provide the finite-coupling result and show that it interpolates smoothly between the weak- and strong-coupling regimes.
