来自凝聚态的跨级数
Trans-series from condensates
AI总结：
本文利用Gross-Neveu模型费米子自能的精确大N跨级数，对SVZ求和规则进行精确检验，证明其可全圈重现双夸克与四夸克凝聚态对应的幂级数。
摘要：
Shifman-Vainshtein-Zakharov（SVZ）求和规则提供了一种在许多量子场论中获得跨级数展开的方法，其中指数小修正是通过将算符乘积展开与真空凝聚态假设相结合来计算的。在某些可解模型中，可以从非微扰结果获得跨级数的精确表达式，这使得通过将SVZ方法的预测与这些精确跨级数进行比较来检验该方法成为可能。本文以Gross-Neveu模型中的费米子自能为例，进行了这样的精确检验。其精确跨级数展开可以从大N解中在1/N的第一个非平凡阶提取。它由指数小修正的无穷级数给出，涉及't Hooft参数中因子阶发散的幂级数。我们表明前两个修正与双夸克和四夸克凝聚态相关，并使用SVZ方法在所有圈阶精确重现了相应的幂级数。此外，凝聚态的数值可以从精确结果中提取，精确到1/N阶。
英文摘要：
The Shifman-Vainshtein-Zakharov (SVZ) sum rules provide a method to obtain trans-series expansions in many quantum field theories, in which exponentially small corrections are calculated by combining the operator product expansion with the assumption of vacuum condensates. In some solvable models, exact expressions for trans-series can be obtained from non-perturbative results, and this makes it possible to test the SVZ method by comparing its predictions to these exact trans-series. In this paper we perform such a precision test in the example of the fermion self-energy in the Gross-Neveu model. Its exact trans-series expansion can be extracted from the large $N$ solution, at the first non-trivial order in $1/N$. It is given by an infinite series of exponentially small corrections involving factorially divergent power series in the 't Hooft parameter. We show that the first two corrections are associated to two-quark and four-quark condensates, and we reproduce the corresponding power series exactly, and at all loops, by using the SVZ method. In addition, the numerical values of the condensates can be extracted from the exact result, up to order $1/N$.
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