$AdS_3 \times S^3$ Virasoro-Shapiro amplitude with KK modes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916887426760704 |
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| author | Jiang, Hongliang Zhong, De-liang |
| author_facet | Jiang, Hongliang Zhong, De-liang |
| contents | We study the first curvature correction to the string amplitude of four Kaluza--Klein (KK) modes on $AdS_3 \times S^3 \times M_4$, with $M_4=K3$ or $T^4$, in type IIB string theory, which is holographically dual to the four--point correlator $\langle \mathcal{O}_{p_1} \mathcal{O}_{p_2} \mathcal{O}_{p_3} \mathcal{O}_{p_4} \rangle$ of certain half--BPS operators in the boundary D1--D5 CFT. The result takes the form of an integral over the Riemann sphere, analogous to the flat-space Virasoro--Shapiro amplitude, but with insertions of single-valued multiple polylogarithms of weight three. Our results are obtained in two steps. First, we derive the $AdS_3 \times S^3$ Virasoro--Shapiro amplitude in the special case $\langle \mathcal{O}_{p} \mathcal{O}_{p} \mathcal{O}_{1} \mathcal{O}_{1} \rangle$, by matching the CFT block expansion with an ansatz based on single-valued multiple polylogarithms. We then employ the $AdS \times S$ Mellin formalism to generalize the result to the general case of four arbitrary KK modes $\langle \mathcal{O}_{p_1} \mathcal{O}_{p_2} \mathcal{O}_{p_3} \mathcal{O}_{p_4} \rangle$. Our analysis yields an infinite set of results for operator anomalous dimensions and OPE data in D1--D5 CFT at strong coupling. In particular, the resulting scaling dimensions of certain operators are shown to be consistent with classical string theory computations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_06039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $AdS_3 \times S^3$ Virasoro-Shapiro amplitude with KK modes Jiang, Hongliang Zhong, De-liang High Energy Physics - Theory We study the first curvature correction to the string amplitude of four Kaluza--Klein (KK) modes on $AdS_3 \times S^3 \times M_4$, with $M_4=K3$ or $T^4$, in type IIB string theory, which is holographically dual to the four--point correlator $\langle \mathcal{O}_{p_1} \mathcal{O}_{p_2} \mathcal{O}_{p_3} \mathcal{O}_{p_4} \rangle$ of certain half--BPS operators in the boundary D1--D5 CFT. The result takes the form of an integral over the Riemann sphere, analogous to the flat-space Virasoro--Shapiro amplitude, but with insertions of single-valued multiple polylogarithms of weight three. Our results are obtained in two steps. First, we derive the $AdS_3 \times S^3$ Virasoro--Shapiro amplitude in the special case $\langle \mathcal{O}_{p} \mathcal{O}_{p} \mathcal{O}_{1} \mathcal{O}_{1} \rangle$, by matching the CFT block expansion with an ansatz based on single-valued multiple polylogarithms. We then employ the $AdS \times S$ Mellin formalism to generalize the result to the general case of four arbitrary KK modes $\langle \mathcal{O}_{p_1} \mathcal{O}_{p_2} \mathcal{O}_{p_3} \mathcal{O}_{p_4} \rangle$. Our analysis yields an infinite set of results for operator anomalous dimensions and OPE data in D1--D5 CFT at strong coupling. In particular, the resulting scaling dimensions of certain operators are shown to be consistent with classical string theory computations. |
| title | $AdS_3 \times S^3$ Virasoro-Shapiro amplitude with KK modes |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.06039 |