NS-NS部分中α'^3阶的杂弦耦合
Heterotic string couplings at order $α'^3$ in NS-NS sector
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中文总结 AI 辅助
该研究利用T对偶程序推导NS-NS部分杂弦理论α'^3阶经典有效作用量，确定耦合项并在两种方案下验证其与S矩阵结果及文献预期的一致性。
中文摘要 AI 辅助
我们利用标准T对偶程序推导NS-NS部分内杂弦理论在八导数阶的经典有效作用量，该部分包含度规、B场和伸缩子。从该阶由872个偶宇称耦合和477个奇宇称耦合组成的最小基出发，我们对圆周进行维数约化并施加T对偶变换下的不变性，具体为补充了高阶导数修正的Buscher规则。该不变性唯一确定了一部分耦合，使其与II型理论的对应耦合相差一个整体因子，其余耦合则由α'阶的系数确定。对于后一类耦合，我们同时采用Metsaev-Tseytlin方案和Meissner方案。随后，通过场重定义，我们将作用量重构为伸缩子仅通过整体因子e^{-2Φ}出现的正则形式。在Meissner方案中，纯引力部分精确重现了已知的S矩阵结果；在两种方案中，纯引力项均可表示为双重迹(Tr(R^2))^2，当与对应的杨-米尔斯项(Tr(F^2))^2结合时，呈现为文献中预期的统一形式(Tr(R^2-F^2))^2。
英文摘要
We utilize the standard T-duality procedure to derive the classical effective action of heterotic string theory at the eight-derivative order within the NS-NS sector, which comprises the metric, the \(B\)-field, and the dilaton. Starting from the minimal basis at this order, consisting of 872 even-parity and 477 odd-parity couplings, we perform a dimensional reduction on a circle and impose invariance under T-duality transformations, specifically the Buscher rules supplemented by higher-derivative corrections. This invariance uniquely fixes a subset of the couplings to match those of type II theory up to an overall factor, while the remaining couplings are determined in terms of the coefficients at order \(α'\). For these latter couplings, we adopt both the Metsaev-Tseytlin and Meissner schemes. Subsequently, through field redefinitions, we recast the action into a canonical form in which the dilaton appears solely through the overall factor \(e^{-2Φ}\). In the Meissner scheme, the pure gravity sector precisely reproduces the known S-matrix results. In both schemes, the pure gravity terms can be expressed as the double trace \((\Tr(R^2))^2\), and when combined with the corresponding Yang-Mills terms \((\Tr(F^2))^2\), they take the unified form \((\Tr(R^2-F^2))^2\), as anticipated in the literature.
