The chiral central charge is a number attached to a gapped (2+1)-dimensional phase of matter that characterizes the conformal field theory living on its edge, specifically the imbalance between left-moving and right-moving gapless edge modes. A phase with a nonzero chiral central charge — such as most fractional quantum Hall states — breaks time-reversal symmetry and supports edge transport, including a quantized contribution to thermal Hall conductance, that has no counterpart in a non-chiral phase.
Because it is a property of the edge, the chiral central charge was traditionally computed from an edge theory or a family of ground states on different geometries. More recent bulk-only diagnostics, such as the modular commutator, instead extract it directly from a single ground-state wave function’s entanglement structure, without reference to the edge at all.
Related papers
- Kim, Shi, Kato, and Albert, “Chiral central charge from a single bulk wave function”, Phys. Rev. Lett. 128, 176402 (2022) — introduces the modular-commutator diagnostic discussed above.
- Kim et al., “Chiral Virasoro algebra from a single wavefunction” (2024) — extends the same bulk-only approach to extract the full chiral Virasoro algebra, not just its central charge.