Jordanian spin chains for twisted strings in $AdS_5\times S^5$
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| Format: | Preprint |
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2025
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| author | Driezen, Sibylle Molines, Adrien |
| author_facet | Driezen, Sibylle Molines, Adrien |
| contents | We study the proposed integrable spin chain formulation of Jordanian deformations of the $AdS_5\times S^5$ superstring, realised via Drinfel'd twists. Among these models, we first identify a unique supergravity deformation confined to an $SL(2,\mathbb{R})$ sector and with constant dilaton. We then develop a general framework for closed Drinfel'd twisted spin chains and construct an explicit map to undeformed models with twisted-boundary conditions. Applied to the non-compact $\mathrm{XXX}_{-1/2}$ spin chain, the Jordanian twist breaks the Cartan generator labelling magnon excitations, obstructing the standard Bethe methods. Instead, using the twisted-boundary formulation, we initiate the spectral problem based on a residual root generator both in the continuum limit and for short chains. We find that the ground state is non-trivially deformed, and is in agreement with the classical string result, while our analysis does not capture higher-spin excited states. We also study the asymptotics of the associated $Q$-system, which is well-behaved and compatible with the boundary-twist. While a full understanding of the spectrum remains open, our work provides concrete steps toward a spectral description of non-abelian twisted integrable models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_13911 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Jordanian spin chains for twisted strings in $AdS_5\times S^5$ Driezen, Sibylle Molines, Adrien High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems We study the proposed integrable spin chain formulation of Jordanian deformations of the $AdS_5\times S^5$ superstring, realised via Drinfel'd twists. Among these models, we first identify a unique supergravity deformation confined to an $SL(2,\mathbb{R})$ sector and with constant dilaton. We then develop a general framework for closed Drinfel'd twisted spin chains and construct an explicit map to undeformed models with twisted-boundary conditions. Applied to the non-compact $\mathrm{XXX}_{-1/2}$ spin chain, the Jordanian twist breaks the Cartan generator labelling magnon excitations, obstructing the standard Bethe methods. Instead, using the twisted-boundary formulation, we initiate the spectral problem based on a residual root generator both in the continuum limit and for short chains. We find that the ground state is non-trivially deformed, and is in agreement with the classical string result, while our analysis does not capture higher-spin excited states. We also study the asymptotics of the associated $Q$-system, which is well-behaved and compatible with the boundary-twist. While a full understanding of the spectrum remains open, our work provides concrete steps toward a spectral description of non-abelian twisted integrable models. |
| title | Jordanian spin chains for twisted strings in $AdS_5\times S^5$ |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2507.13911 |