Two-particle spectrum of tensor multiplets coupled to $Ad{S}_3\times S^3$ gravity

Abstract

We study the spectrum of certain two-particle operators in the supergravity regime of the D1-D5 system, focussing on the four-point correlators of tensor multiplets on $Ad{S}_3\times S^3$ at tree level. In Mellin space, these are nicely determined by a single amplitude, which makes manifest the large $p$ limit, the connection with the flat space S-matrix, and the six dimensional conformal symmetry. We compute the $(1,1)\times \overline{(1,1)}$ superconformal blocks for the two-dimensional $\mathcal{N}=(4,4)$ conformal theory at the boundary, and then we obtain a formula for the anomalous dimensions of the operators exchanged in the symmetric and anti-symmetric flavor channels. These anomalous dimensions solve an unmixing problem which is analogous to the one in $Ad{S}_5\times S^5$, with interesting modifications. Along the way we show how the $(1,1)\times \overline{(1,1)}$ superconformal blocks relate to those in $\mathcal{N}=4$ SYM in four dimensions, and we provide new intuition on the known data for $Ad{S}_5\times S^5$.

arXiv commentv1 5 pages; v2 some typos fixed, extended version, match PRD version

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Cited by in corpus (8)

• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• BCJ relations in ${AdS}_5\times S^3$ and the double-trace spectrum of super gluons
• Higher-Dimensional Symmetry of AdS${}_2\times$S${}^2$ Correlators
• Holographic S-fold theories at one loop
• One-loop string amplitudes in AdS${}_5\times$S${}^5$: Mellin space and sphere splitting
• Mellin amplitudes for $Ad{S}_3\times S^3$
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry
• Hexagonalization in $Ad{S}_3\times S^3\times T^4$: Mirror Corrections