Brown Augustus, Heslop Paul, Wen Congkao, Xie Haitian
Centre for Theoretical Physics, Department of Physics and Astronomy, Queen Mary University of London, London E1 4NS, United Kingdom.
Centre for Particle Theory and Department of Mathematical Sciences, Durham University, Durham DH1 3LE, United Kingdom.
Phys Rev Lett. 2024 Mar 8;132(10):101602. doi: 10.1103/PhysRevLett.132.101602.
We study integrated correlators of four superconformal primaries O_{p} with arbitrary charges p in N=4 super Yang-Mills theory. The ⟨O_{2}O_{2}O_{p}O_{p}⟩ integrated correlators can be computed by supersymmetric localization, whereas correlators with more general charges are currently not accessible from this method and, in general, contain complicated multiple zeta values. Nevertheless, we observe that, if one sums over the contributions from all different channels in a given correlator, then all the multiple zeta values (and products of ζ's) cancel, leaving only ζ(2ℓ+1) at ℓ loops. We then propose an exact expression of such integrated correlators in the planar limit, valid for arbitrary 't Hooft coupling. The expression matches with the known exact localization-based results for specific charges, as well as with all existing perturbative and strong-coupling results in the literature for more general charges. As an application, our result is used to determine certain seven-loop Feynman integral periods and fix previously unknown coefficients in the correlators at strong coupling.
我们研究了(N = 4)超杨-米尔斯理论中具有任意电荷(p)的四个超共形原初算子(O_{p})的积分关联函数。(\langle O_{2}O_{2}O_{p}O_{p}\rangle)积分关联函数可通过超对称局域化来计算，而具有更一般电荷的关联函数目前无法通过此方法得到，并且通常包含复杂的多重zeta值。然而，我们观察到，如果对给定关联函数中所有不同通道的贡献进行求和，那么所有的多重zeta值（以及(\zeta)的乘积）都会相互抵消，在(\ell)圈时仅留下(\zeta(2\ell + 1))。然后我们提出了这种积分关联函数在平面极限下的精确表达式，该表达式对任意的't Hooft耦合均有效。该表达式与特定电荷下基于局域化的已知精确结果相匹配，也与文献中针对更一般电荷的所有现有微扰和强耦合结果相匹配。作为一个应用，我们的结果被用于确定某些七圈费曼积分周期，并确定强耦合下关联函数中先前未知的系数。
