$$ \mathcal{PT} $$ breaking and RG flows between multicritical Yang-Lee fixed points

Abstract

We study a novel class of Renormalization Group flows which connect multicritical versions of the two-dimensional Yang-Lee edge singularity described by the conformal minimal models $$ \mathcal{M} $$ M (2, 2n + 3). The absence in these models of an order parameter implies that the flows towards and between Yang-Lee edge singularities are all related to the spontaneous breaking of $$ \mathcal{PT} $$ PT symmetry and comprise a pattern of flows in the space of $$ \mathcal{PT} $$ PT symmetric theories consistent with the c-theorem and the counting of relevant directions. Additionally, we find that while in a part of the phase diagram the domains of unbroken and broken $$ \mathcal{PT} $$ PT symmetry are separated by critical manifolds of class $$ \mathcal{M} $$ M (2, 2n + 3), other parts of the boundary between the two domains are not critical.

Hamiltonian truncation crafted for UV-divergent QFTs

“…where E i = (∆ i − c Ising /12)/R are the energy levels of the Ising on the cylinder. The last equation was obtained by applying tree-level perturbation theory on (30). This equation was used in Ref.…”

“…On the right boundary, the first gap remains nonvanishing even for large radius, disfavoring a CFT interpretation. Evidence for critical and non-critical PT -breaking-transitions have been recently studied using TCSA [29,30].…”

“…The Tricritical Ising operator ε ′ is even under a global 2 and is also invariant under the Kramers-Wannier self-duality of the CFT. These two symmetries explain the absence of EFT scalar operators in the σ and ε family of the Ising CFT in(30).…”