arXiv 2103.093122021-03-21hep-th

关于大R荷下${\cal N} = 2$超共形关联函数的指数小修正

On the exponentially small corrections to ${\cal N} = 2$ superconformal correlators at large R-charge

Simeon Hellerman

备注：: 87 pages, 4 figures, 2 photographs

摘要：

本文研究了具有规范群$SU(2)$的${\cal N} = 2$超共形QCD中的库仑支手征主关联函数，在手征主算符$[{\cal O}(x)]^ n$的大R荷${\cal J} = 2n$极限下，逆规范耦合$τ$保持不变.在以前的工作中，这些相关函数被确定为$n$中的所有阶数，直到未知的指数小修正。在本文中，我们确定的前几个订单的渐近展开的指数小的修正本身。为此，我们用途：物理解释的指数小校正作为虚拟传播的大规模BPS粒子，以固定的领先项的扩展;超对称递归关系，以获得微分方程的耦合依赖的subleading条款;和双标度限制，以固定待定系数的微分方程的解决方案。我们计算的指数小项的扩展，并包括相对顺序$n^{-{5\over 2}}$。我们还使用的递归关系来计算subleading大${\cal J}$修正的指数小的修正在双标度限制，并包括相对顺序$n^{-5}$在固定的双标度耦合$λ$。我们比较的扩展，从超对称本地化的耦合$τ= {{25}\over π} i$，$n=150$的确切结果。在值$n\sim 100-150$处，我们发现固定耦合和双尺度大R电荷展开分别精确到$10^ 6$和$10^ 8$中的一个部分内，指数小校正本身的大小。相对于包含主要EFT贡献的全相关器，这些估计给出的结果分别精确到$10^{15}$和$10^{17}$中的一部分。

英文摘要：

In this note we consider Coulomb-branch chiral primary correlation functions in ${\cal N} = 2$ superconformal QCD with gauge group $SU(2)$, in the limit of large R-charge ${\cal J} = 2n$ for the chiral primary operators $[{\cal O}(x)]^ n$ with the inverse gauge coupling $τ$ held fixed. In previous work, these correlation functions were determined to all orders in $n$, up to unknown exponentially small corrections. In this paper we determine the first several orders of the asymptotic expansion of the exponentially small correction itself. To do this we use: the physical interpretation of the exponentially small correction as the virtual propagation of a massive BPS particle, to fix the leading term in the expansion; the supersymmetric recursion relations to derive differential equations for the coupling-dependence of the subleading terms; and the double-scaling limit, to fix undetermined coefficients in the solution of the differential equation. We calculate the expansion of the exponentially small term up to and including relative order $n^{-{5\over 2}}$. We also use the recursion relations to calculate the subleading large-${\cal J}$ corrections to the exponentially small correction in the double-scaling limit, up to and including relative order $n^{-5}$ at fixed double-scaled coupling $λ$. We compare the expansion to exact results from supersymmetric localization at the coupling $τ= {{25}\over π} i$, up to $n=150$. At values $n\sim 100-150$, we find the fixed-coupling and double-scaled large-R-charge expansions are accurate to within one part in $10^ 6$ and $10^ 8$, respectively, of the size of the exponentially small correction itself. Relative to the full correlator including the dominant EFT contribution, these estimates give results accuracte to one part in $10^{15}$ and $10^{17}$, respectively.

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