论文标题
有限耦合的八角形
Octagon at finite coupling
论文作者
论文摘要
我们研究了平面n = 4 sym中无限沉重的半bp算子的一类特殊类别的四点相关函数，该功能将分解成两个八角形构象的产物。我们证明，这些函数满足了非线性间差方程的系统，该方程足够强大，可以完全确定它们对“ thooft耦合和两个交叉比率的依赖性）。在弱耦合时，对这些方程的求解在梯子积分方面产生了八角形的已知序列表示。在强耦合时，我们在耦合常数的反向中发展了八角形的系统扩展，并通过分析伴随膨胀系数进行计算。我们研究了各个运动区域中相关函数的强耦合扩展，并观察到与OPE所决定的预期渐近行为以及数值评估的结果。我们发现，令人惊讶的是，强大的耦合扩展是可以总结的。应用Borel-Pade求和方法，我们表明，强耦合扩展正确地描述了'T Hooft耦合的广泛区域的相关函数。
We study a special class of four-point correlation functions of infinitely heavy half-BPS operators in planar N=4 SYM which admit factorization into a product of two octagon form factors. We demonstrate that these functions satisfy a system of nonlinear integro-differential equations which are powerful enough to fully determine their dependence on the 't Hooft coupling and two cross ratios. At weak coupling, solution to these equations yields a known series representation of the octagon in terms of ladder integrals. At strong coupling, we develop a systematic expansion of the octagon in the inverse powers of the coupling constant and calculate accompanying expansion coefficients analytically. We examine the strong coupling expansion of the correlation function in various kinematical regions and observe a perfect agreement both with the expected asymptotic behavior dictated by the OPE and with results of numerical evaluation. We find that, surprisingly enough, the strong coupling expansion is Borel summable. Applying the Borel-Pade summation method, we show that the strong coupling expansion correctly describes the correlation function over a wide region of the 't Hooft coupling.
