arXiv subjects

Noé Suchel

Publications and source records attributed to Noé Suchel.

4 recordsLinked to original sources

arXiv2026

Taxonomy of coupled minimal models from finite groups

Fixed points of $N$ coupled Virasoro minimal models have recently been argued to provide large classes of compact unitary CFTs with $c>1$ and only Virasoro chiral symmetry. In this paper, we vastly increase the set of such potential irrational fixed points by considering couplings that break the maximal $G=S_N$ symmetry into various subgroups $H\subset G$. We rigorously classify all the fixed points with $N=4,5$ and do an extensive search for solutions of the beta function equations with $N\geq6$. In particular, we find non-trivial fixed points with $H=\mathbb{Z}_{N-1} \rtimes \mathbb{Z}_2, \, S_{M}\times S_{N-M}$ and rigorously prove that real fixed points with $H=(S_{N/2}\times S_{N/2})\rtimes \mathbb{Z}_2$ exist for all even $N\geq6$. We also identify fixed points with finite Lie-type symmetry $H=\rm{PSL}_2(N)\subset S_N$ where $N=7,11,13$ and uncover a non-unitary fixed point with $H=M_{22}\subset S_{22}$, a sporadic Mathieu group. Along the way, we encounter conformal manifolds at leading order in perturbation theory which we resolve at sub-leading order.

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arXiv2026

Super Sum rules for Long-Range Models

We study sum rules that control the Regge limit of one-dimensional conformal field theory (CFT) correlators and relate them to dual bulk scattering processes at high energies in $\mathrm{AdS}_2$. By imposing the condition that no scattering takes place in the bulk, these sum rules single out special solutions to crossing symmetry that describe long-range models, which can be understood as free fields in AdS with boundary interactions tuned to criticality. We test these sum rules perturbatively in several distinct theories, namely the 1d long-range versions of the Ising, $O(N)$ and Lee--Yang models, and find that they correctly predict the CFT data characterising these theories. Along the way we compute for the first time the leading contributions of quadruple-twist operators to the long range Ising correlator and analyse their role in the new sum rules. Finally, we explore the consequences of imposing these sum rules in a numerical bootstrap framework and find that they lead to substantial reductions in the allowed parameter space.

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arXiv2025

Solving 1D crossing and QFT$_2$/CFT$_1$

We provide an effective solution of the 1D crossing equation. We begin by arguing that crossing constraints can be recast in terms of bases of sum rules associated to special sets of CFT data -- extremal solutions -- which solve these constraints in a minimal way and naturally saturate positivity bounds on the space of CFTs. We conjecture, argue and check extensively that any extremal solution behaves as a generalized free field in the UV. This allows us to reconstruct the entirety of their CFT data using a rapidly convergent ``hybrid bootstrap'' method, which combines numerics and analytics. Strikingly, as we approach special corners in the space of extremal solutions we find that their CFT data can present non-trivial structure up to arbitrarily large energies. We interpret these corners as flat space limits of QFTs in AdS$_2$, which extremal solutions naturally describe. This picture allows us to bootstrap their CFT data in these limits in terms of 2d S-matrices, and conversely provide a microscopic CFT construction of the latter. Further evidence for this QFT in AdS description of extremal solutions comes from an explicit construction of bulk QFT operators solving an AdS locality problem. Concretly we show that it is possible to canonically associate one or more such operators to any extremal solution by explicitly solving for their BOE data. In the special case where this operator is the bulk stress-tensor we combine crossing and bulk locality constraints to derive stronger bounds on the OPE and BOE data, including an exact bootstrap lower bound on the central charge $C_T\geq 1/2$.

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arXiv2024

Gravity from quantum mechanics of finite matrices

We revisit the Berenstein-Maldacena-Nastase (BMN) conjecture relating M-theory on a PP-wave background and Matrix Quantum Mechanics (MQM) of $N\times N$ matrices. In particular, we study the BMN MQM at strong coupling and finite $N$ and derive an effective Hamiltonian that describes non-relativistic free particles in a harmonic trap. The energy spectrum predicted by this Hamiltonian matches the supergravity excitation spectrum around the PP-wave background, if we further assume the existence of bound states. Our derivation is based on the strong coupling expansion of the wavefunction and supersedes the naive path integral approach that can lead to incorrect results, as we demonstrate in a simple toy model. We conclude with open questions about various regimes of the theory when we vary the size of the matrices, the coupling and the temperature.

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