AdS $N$-body problem at large spin
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914096478158848 |
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| author | Kravchuk, Petr Mann, Jeremy A. |
| author_facet | Kravchuk, Petr Mann, Jeremy A. |
| contents | Motivated by the problem of multi-twist operators in general CFTs, we study the leading-twist states of the $N$-body problem in AdS at large spin $J$. We find that for the majority of states the effective quantum-mechanical problem becomes semiclassical with $\hbar=1/J$. The classical system at $J=\infty$ has $N-2$ degrees of freedom, and the classical phase space is identified with the positive Grassmannian $\mathrm{Gr}_{+}(2,N)$. The quantum problem is recovered via a Berezin-Toeplitz quantization of a classical Hamiltonian, which we describe explicitly. For $N=3$ the classical system has one degree of freedom and a detailed structure of the spectrum can be obtained from Bohr-Sommerfeld conditions. For all $N$, we show that the lowest excited states are approximated by a harmonic oscillator and find explicit expressions for their energies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12328 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | AdS $N$-body problem at large spin Kravchuk, Petr Mann, Jeremy A. High Energy Physics - Theory Mathematical Physics Motivated by the problem of multi-twist operators in general CFTs, we study the leading-twist states of the $N$-body problem in AdS at large spin $J$. We find that for the majority of states the effective quantum-mechanical problem becomes semiclassical with $\hbar=1/J$. The classical system at $J=\infty$ has $N-2$ degrees of freedom, and the classical phase space is identified with the positive Grassmannian $\mathrm{Gr}_{+}(2,N)$. The quantum problem is recovered via a Berezin-Toeplitz quantization of a classical Hamiltonian, which we describe explicitly. For $N=3$ the classical system has one degree of freedom and a detailed structure of the spectrum can be obtained from Bohr-Sommerfeld conditions. For all $N$, we show that the lowest excited states are approximated by a harmonic oscillator and find explicit expressions for their energies. |
| title | AdS $N$-body problem at large spin |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2412.12328 |