Replica transitions and universal behavior in higher-dimensional measurement-altered criticality

Determine whether replica transitions occur at the physical replica limit Q=1 in 2+1-dimensional measurement-altered critical systems, and characterize the universal behavior captured by their entropies and correlators.

Background

The paper develops a boundary conformal field theory description of a replica transition at Q=1 for projectively measured critical Ising systems in 1+1 dimensions. The mechanism relies on boundary-condition-changing operators and the availability of well-developed conformal and boundary-conformal methods in that setting.

The authors identify higher spatial dimensions as an open direction because conformal field theories and boundary conformal field theories are less developed in 2+1 dimensions. They specifically leave unresolved whether the Q=1 replica transition persists there and what universal information is encoded in measurement-record entropies and measurement-averaged correlators.

References

A broader open direction is to investigate measurement-altered criticality in higher spatial dimensions, where CFTs (and BCFTs) are less developed than in $1+1$ dimensions. In particular, it would be interesting to determine whether replica transitions occur at $Q=1$ in $2+1$ dimensions, and what universal behavior is captured by entropies and correlators.

— Replica Transition at Measurement-Altered Ising Criticality  (2610.13802 - Khanna et al., 9 Oct 2026) in Summary