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Friedan–Janik boundary states as endpoints of bulk RG flow

Determine whether Friedan–Janik boundary states in the compact free boson conformal field theory at irrational radius can arise as infrared boundary conditions that are the endpoint of a bulk renormalization group flow starting from a boundary conformal field theory with central charge c>1, taking into account that boundary entropy g can increase under bulk RG flows even though it decreases under boundary RG flows.

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Background

The paper studies the one-parameter family of Friedan–Janik boundary states in the compact free boson CFT at irrational radius. These states exhibit pathologies, including a continuous open-string spectrum and a divergent g-function (boundary entropy), and they do not correspond to simple Dirichlet or Neumann boundary conditions.

Because g decreases monotonically under boundary RG flows, Friedan–Janik states cannot be obtained by boundary perturbations of standard Dirichlet or Neumann states (or such states with finitely many added degrees of freedom). However, prior work shows that g can increase under bulk RG flows, opening the possibility that Friedan–Janik states might be accessible as endpoints of bulk flows starting from theories with c>1.

The authors explicitly raise the question of whether such a bulk RG mechanism can produce these boundary conditions, highlighting a concrete unresolved issue about the dynamical origin and realizability of Friedan–Janik states in physical settings.

References

Since $g$ decreases monotonically under boundary RG flows , we can not hope to obtain FJ states from a boundary perturbation of a Neumann or Dirichlet state, or even from a Neumann or Dirichlet state dressed with finitely many additional degrees of freedom (e.g.~Chan-Paton factors), however it is an interesting open question whether these states could arise as the end-point of a bulk RG flow from a boundary conformal field theory with $c>1$, since it is known that $g$ can increase under such flows .

— Constraining boundary conditions in non-rational CFTs (2504.00367 - Cai et al., 1 Apr 2025) in Conclusions and future directions (Section: Conclusions and future directions)