论文标题
朝着封闭的字符串作为单价值的单字符串
Towards closed strings as single-valued open strings at genus one
论文作者
论文摘要
我们关联了开放式和封闭式状态属属中世界表积分的低能扩展。相应的膨胀系数是开弦情况中的椭圆形多重Zeta值，而非晶状模块化模块化形式则称为“模块化图形”，用于封闭字符串。通过检查适当生成一系列属的积分的微分方程和变性限制，我们确定了形式的替换规则，将开放字符串的椭圆形多个Zeta值映射到封闭字符串的模块化图形形式。基于这些规则的属性，我们将其称为椭圆形单值地图，该映射概括了作用于开放式和封闭字符串之间的树级关系中的多个Zeta值的单值映射属属概念。
We relate the low-energy expansions of world-sheet integrals in genus-one amplitudes of open- and closed-string states. The respective expansion coefficients are elliptic multiple zeta values in the open-string case and non-holomorphic modular forms dubbed "modular graph forms" for closed strings. By inspecting the differential equations and degeneration limits of suitable generating series of genus-one integrals, we identify formal substitution rules mapping the elliptic multiple zeta values of open strings to the modular graph forms of closed strings. Based on the properties of these rules, we refer to them as an elliptic single-valued map which generalizes the genus-zero notion of a single-valued map acting on multiple zeta values seen in tree-level relations between the open and closed string.
