arXiv 1806.026912018-06hep-th

$D^8 R^4$亏格2弦不变量的渐近性

Asymptotics of the $D^8 R^4$ genus-two string invariant

Eric D'Hoker, Michael B. Green, Boris Pioline

备注：: 50+44 pages, 13 figures; v2: minor corrections, including an overall factor of 2 in Eq. 5.18, published version; v3: more factors of 2 corrected, see footnote 7
发表信息：: Comm. Num. Theo. Phys. 13 (2019) 351-462

摘要：

我们继续我们的调查模块图函数和字符串不变量，出现在genus-2作为系数的低能量有效的相互作用在II型超弦理论。在以前的工作中，证明了亏格为2的模图函数$w$的非分离退化是由退化参数$t$的次数为$(w,w)$的Laurent多项式给出的.该多项式的系数推广了亏格一模图函数，直到在$t$中被指数抑制为$t \to \infty$的项。在本文中，我们评估这种扩展明确的模块化图功能与$D^8 {\cal R}^4$有效的相互作用，劳伦多项式的程度$(2,2)$。我们还证明了分离退化是由一个多项式的退化参数$\ln (|v|)$的贡献是权力表现在$v$作为$v \to 0$。我们进一步提取完整的，或热带，退化，并将其与独立计算的费曼图，有助于两个环路II型超引力扩展到相同的顺序在低能量扩展的总和的被积函数进行比较。我们发现，热带极限的弦论被积函数再现超引力被积函数作为其主导项，但也包括子主导项成比例的奇zeta值是缺席的超引力，可以归因于更高的衍生弦相互作用。

英文摘要：

We continue our investigation of the modular graph functions and string invariants that arise at genus-two as coefficients of low energy effective interactions in Type II superstring theory. In previous work, the non-separating degeneration of a genus-two modular graph function of weight $w$ was shown to be given by a Laurent polynomial in the degeneration parameter $t$ of degree $(w,w)$. The coefficients of this polynomial generalize genus-one modular graph functions, up to terms which are exponentially suppressed in $t$ as $t \to \infty$. In this paper, we evaluate this expansion explicitly for the modular graph functions associated with the $D^8 {\cal R}^4$ effective interaction for which the Laurent polynomial has degree $(2,2)$. We also prove that the separating degeneration is given by a polynomial in the degeneration parameter $\ln (|v|)$ up to contributions which are power-behaved in $v$ as $v \to 0$. We further extract the complete, or tropical, degeneration and compare it with the independent calculation of the integrand of the sum of Feynman diagrams that contributes to two-loop type II supergravity expanded to the same order in the low energy expansion. We find that the tropical limit of the string theory integrand reproduces the supergravity integrand as its leading term, but also includes sub-leading terms proportional to odd zeta values that are absent in supergravity and can be ascribed to higher-derivative stringy interactions.

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