Toshiki Onagi

We present a systematic exploration of conformal field theories (CFTs) constrained by duality-inspired fusion rules using the conformal bootstrap. We classify the operator spectrum into three sectors: [ σ ], [ ε ], and [ 1 ] . The [ σ ] sector consists of all Z 2 -odd operators. The Z 2 -even operators are further divided into the [ ε ] sector, which contains only the operators that change sign under duality, and the [ 1 ] sector, which encompasses all remaining operators. We impose a selection rule motivated by Kramers-Wannier duality, specifically forbidding the appearance of the [ ε ] sector in the [ ε ] × [ ε ] operator product expansion. By applying this constraint to the lowest-lying relevant scalars, we derive bounds on their conformal dimensions ( Δ σ , Δ 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 nontrivial constraints in d = 3 ( Δ σ ≳ 0.85 ), relevant for theories like QED 3 . This work opens a new avenue for nonperturbatively probing the landscape of CFTs constrained by fusion rules.

A representative quantity that characterizes the dynamics of conformal interfaces is the transmission coefficient, which is defined through correlation functions of the stress tensor. Typically, this coefficient is complicated and highly dependent on its details. In this work, we introduce a new perspective based on the notion of a “phantom current”. We have shown that a spin-2 phantom current arising from the folding trick determines the transmission coefficient. As a result, our framework provides a unified explanation of known results in minimal models and the free boson, while also yielding concrete predictions for previously unexplored interfaces.