Global symmetry violation from non-isometric codes

TL;DR

Baek and Choi propose that quantum gravity inherently violates global symmetries by modeling black holes with non-isometric codes that encode interior states carrying global charges into the fundamental description. They show that, while average inner products are preserved on the code, fluctuations are bounded and exponentially suppressed by the black hole entropy, and that the radiation's entropy obeys a QES-type formula with a symmetry-breaking interior contribution. By computing Renyi and sandwiched Renyi relative entropies between symmetry-transformed and untransformed radiation, they demonstrate nonzero, and in some regimes divergent, measures of global-symmetry violation, with fidelity decreasing as charge variance grows. The results provide a quantitative link between non-isometric encoding, the QES framework, and global-charge violation, and they discuss remnant contributions and extensions to other global symmetries. This work strengthens the no-global-symmetry conjecture in quantum gravity and offers a calculational path to explore symmetry-violation signatures in Hawking radiation and beyond.

Abstract

We study the no-global-symmetry conjecture in quantum gravity by modeling black holes as non-isometric codes that encode the interior states with global charges into the fundamental states. The fluctuation in the inner products of the charged states can be larger compared to the case without charges. The non-isometric map causes states with different charges to have non-zero overlaps, signaling symmetry violation. The Renyi entropies of the radiation with global charges are found to be consistent with the quantum extremal surface formula. We compute various forms of Renyi relative entropy, as well as the fidelity, to quantify the degree of a global symmetry violation in Hawking radiation, demonstrating that global symmetries are indeed violated. We also comment on the instability of the black hole remnant.

Figures (1)

• Figure 1: Holographic map $V$ acts with a typical unitary $U$ on $\ell$ and $r$ of the effective theory with some fixed state $|\psi_0\rangle_f$. It post-selects on an auxiliary system $P$ and produces a state in the fundamental description $B$. Similarly, $W$ maps the global charges $Q_\ell$, $Q_r$, and a fixed state $|\widetilde{\psi}_0\rangle_{f_G}$ to the fundamental charge ${C}$ by a random unitary $U_G$, which post-selects a state of another auxiliary system $P_G$.