Integrable Spherical Brane Model at Large $N$

Mohsen Gheisarieha; Ramtin M. Yazdi; Arash Arabi Ardehali

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arXiv · 2509.23869

Integrable Spherical Brane Model at Large $N$

Mohsen Gheisarieha·Ramtin M. Yazdi·Arash Arabi Ardehali

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Abstract

We study one of the simplest integrable two-dimensional quantum field theories with a boundary: $N$ free non-compact scalars in the bulk, constrained non-linearly on the boundary to lie on an $(N-1)$-sphere of radius $1/\sqrt{g}$. The $N=1$ case reduces to the single-channel Kondo problem, for $N=2$ the model describes dissipative Coulomb charging in quantum dots, and larger $N$ is analogous to higher-spin impurity or multi-channel scenarios. Adding a boundary magnetic field -- a linear boundary coupling to the scalars -- enriches the model's structure while preserving integrability. Lukyanov and Zamolodchikov (2004) conjectured an expansion for the boundary free energy on the infinite half-cylinder in powers of the magnetic field. Using large-$N$ saddle-point techniques, we confirm their conjecture to next-to-leading order in $1/N$. Renormalization of the subleading solution turns out to be highly instructive, and we connect it to the RG running of $g$ studied by Giombi and Khanchandani (2020).

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Mohsen Gheisarieha, Ramtin M. Yazdi, Arash Arabi Ardehali. 2025-09-28. Integrable Spherical Brane Model at Large $N$. https://arxiv.org/abs/2509.23869

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