Conformal Bootstrap with Duality-Inspired Fusion Rule

2025/11/01 by Nakayama, Yu, Onagi, Toshiki
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2511.00386

Abstract

We present the first systematic exploration of conformal field theories (CFTs) possessing fusion rules inspired by categorical (non-invertible) symmetries, using the conformal bootstrap. Specifically, we impose a selection rule motivated by Kramers-Wannier duality and derive bounds on the conformal dimensions (Δ_σ, Δ_ε) of the lowest-lying ℤ₂-odd scalar σ and ℤ₂-even scalar ε in dimensions d=2 through d=7. Our bounds correctly allow the d=2 Ising model while excluding the d=3 Ising model, demonstrating the effectiveness of the imposed condition. Furthermore, we observe a distinct feature in d=2 corresponding to the M(8,7) minimal model and find non-trivial constraints in d=3 (Δ_σ\gtrsim 0.85), relevant for theories like QED₃. This work opens a new avenue for non-perturbatively probing the vast landscape of CFTs constrained by non-invertible symmetries.

Citations

• Spurion Analysis for Non-Invertible Selection Rules from Near-Group Fusions
• Bootstrapping the Simplest Deconfined Quantum Critical Point
• Redundancy Channels in the Conformal Bootstrap
• On discrete gauging and non-invertible selection rules
• Non-invertible symmetry as an axion-less solution to the strong CP problem
• Coupling Selection Rules in Heterotic Calabi-Yau Compactifications
• Phenomenological implications of a class of non-invertible selection rules
• More about quark Yukawa textures from selection rules without group actions
• An Atlas for 3d Conformal Field Theories with a U(1) Global Symmetry
• Bootstrapping the 3d Ising stress tensor
• Selection rules of topological solitons from non-invertible symmetries in axion electrodynamics
• Non-invertible defects on the worldsheet
• Who told you magnetization is a vector in 4-ε dimensions?
• Particle-Soliton Degeneracies from Spontaneously Broken Non-Invertible Symmetry
• Non-Abelian currents bootstrap
• Upper critical dimension of the 3-state Potts model
• The Hybrid Bootstrap
• Exploring SU(N) adjoint correlators in 3d
• Scaling the semidefinite program solver SDPB
• Weizmann Lectures on the Numerical Conformal Bootstrap
• A Semidefinite Program Solver for the Conformal Bootstrap
• Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions
• Monopole Taxonomy in Three-Dimensional Conformal Field Theories

Cited by

• Irrational CFTs from coupled anyon chains with non-invertible symmetries?

Related

• Conformal bootstrap in two-dimensional conformal field theories with non-diagonal spectrums
• The old conformal bootstrap revisited
• Two applications of the analytic conformal bootstrap: A quick tour guide
• Conformal field theory on the plane
• The Bootstrap of Points and Lines