AI 中文总结
研究构建NS - NS和杂化超引力的卡罗尔极限，通过场的超相对论展开及对伸缩子缩放等方法，纳入规范场和机制扩展到杂化超引力，研究卡罗尔运动方程，表明\(\alpha'\)修正贡献有限，还探讨与卡罗尔弦理论世界面形式主义的联系。
AI 中文摘要
我们通过对场进行超相对论展开来构建NS - NS和杂化超引力的卡罗尔极限。对伸缩子进行适当缩放使测度有限，并补偿NS - NS超引力拉格朗日量产生的发散，在\(w\rightarrow\infty\)时给出有限作用量。通过纳入非阿贝尔规范场和格林 - 施瓦茨机制将此构建扩展到杂化超引力（忽略费米子）。所得理论包含与引力一致耦合的有限规范部分，卡罗尔1 - 形式场的格林 - 施瓦茨机制可通过场重定义平凡化。通过展开相对论方程和从变分原理推导来研究卡罗尔运动方程。我们还表明，在弦参数\(\alpha'\rightarrow\frac{\alpha'_c}{w^2}\)的重标度下，领先的\(\alpha'\)修正的\(\hat{\rm Riem}^2\)贡献保持有限，为全四导数有效作用量的进一步研究开辟了道路。最后，我们讨论了与卡罗尔弦理论的世界面形式主义的潜在联系。
英文摘要
We construct the Carrollian limit of NS--NS and heterotic supergravity through an ultra-relativistic expansion of the fields. An appropriate scaling of the dilaton renders the measure finite and compensates the divergences arising from the NS-NS supergravity Lagrangian, giving a finite action as $w\rightarrow\infty$. We then extend the construction to heterotic supergravity (neglecting fermions) by incorporating the non-Abelian gauge field together with the Green--Schwarz (GS) mechanism. The resulting theory contains a finite gauge sector consistently coupled to gravity, and the GS mechanism for the Carrollian 1-form field can be trivialized imposing field redefinitions. Then, we investigate the Carrollian equations of motion by both expanding the relativistic equations and deriving them from a variational principle. We also show that the leading $α'$-corrected $\hat{\rm Riem}^2$ contribution remains finite under a rescaling of the string parameter $α'\rightarrow \frac{α'_c}{w^2}$, opening further research towards the full four-derivative effective action. Finally, we discuss the potential connection with the worldsheet formalism of the Carrollian string theory.
CommentsV1: 25 pages + appendix + references. V2: typos fixed and references updated
