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arXiv · 2312.17056

Inequivalent light-cone gauge-fixings of strings on $AdS_n \times S^n$ backgrounds

Riccardo Borsato·Sibylle Driezen·Ben Hoare·Ana L. Retore·Fiona K. Seibold
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Abstract

Light-cone gauge-fixed sigma-models on $AdS_n\times S^n$ backgrounds play an important role in the integrability formulation of the AdS/CFT correspondence. The string spectrum of the sigma-model is gauge-independent, however the Hamiltonian and scattering matrix of the transverse worldsheet fields are not. We study how these change for a large family of inequivalent light-cone gauges, which are interpreted as $T\bar{T}$, $\tilde{J}T_\tau$, $JT_\sigma$ and $J^\tau$ deformations. We investigate the moduli space of equivalent light-cone gauges and, specialising to $AdS_5 \times S^5$, compute the different light-cone gauge symmetry algebras, well-known to be $\mathfrak{psu}(2|2)^{\oplus 2} \oplus \mathfrak{u}(1)^{\oplus 2}$ for the standard gauge-fixing. Many integrable deformations require a non-standard light-cone gauge, hence our classification and analysis of inequivalent gauges will be important for analysing such models.

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Riccardo Borsato, Sibylle Driezen, Ben Hoare, Ana L. Retore, Fiona K. Seibold. 2023-12-28. Inequivalent light-cone gauge-fixings of strings on $AdS_n \times S^n$ backgrounds. https://arxiv.org/abs/2312.17056

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