Determine the origin and consistency of the additional energy bands

Determine whether the nonperturbative additional energy bands in the spectrum of the fixed-$\rho_b$ theory correspond to actual physical states, and if so identify the bulk geometries that describe those states.

Background

For generalized boundary conditions, the spectral equation is periodic in the deformed energy and produces an infinite sequence of possible energy bands. The additional bands are separated from the black-hole band by an amount scaling nonperturbatively with the inverse gravitational coupling, so they would require new bulk geometries rather than perturbative excitations. The paper does not establish whether these states exist or what their bulk interpretation is.

References

It is an interesting question what these potential new states correspond to in the bulk. Since their energy differs from that of black holes by an amount that goes like $1/g2$, they must correspond to new geometries. It would be nice to determine if these states are really there, and if so to identify them.

— Interpolating between single and double trace $T\bar T$ by moving LST into the bulk  (2609.10823 - Chu et al., 9 Sep 2026) in Section 4.3, Fixed $\rho_b$

The spectrum we found in that case exhibits hints of discretization of spacetime. This raises a number of questions, like if the spacetime is indeed discrete, what happens to energy and momentum conservation, what features of the boundary conditions are responsible for the discrete structure we observe, and how common is the appearance of this discrete structure in the space of $F(\Phi_b)$.

— Interpolating between single and double trace $T\bar T$ by moving LST into the bulk  (2609.10823 - Chu et al., 9 Sep 2026) in Section 5, Discussion