The authors consider a constrained fermionic model in a non-trivial topological sector and compute the conformal charge showing its dependence on the topological charge.
Abstract We study N N = 2 supersymmetric Sachdev-Ye-Kitaev (SYK) models with com- plex fermions at non-zero background charge. Motivated by multi-charge supersymmetric black holes, we propose a new N N = 2 SYK model with multiple U(1) symmetries, integer charges, and a non-vanishing supersymmetric index, realizing features not present in known SYK models. In both models, a conformal solution with a super-Schwarzian mode emerges at low temperatures, signalling the appearance of nearly AdS2/BPS physics. However, in contrast to complex SYK, the fermion scaling dimension depends on the background charge in the conformal limit. For a critical charge, we find a high to low entropy phase transition in which the conformal solution ceases to be valid. This transition has a simple interpretation– the fermion scaling dimension violates the unitarity bound. We offer some comments on a holographic interpretation for supersymmetric black holes.
In one dimension, strongly correlated gapless systems are highly constrained due to conformal invariance, leading to the decoupling of low energy degrees of freedom corresponding to different symmetry sectors. The most familiar example of this is spin-charge separation. Here, we extend this mechanism to the non-Hermitian realm by demonstrating that skin effects corresponding to different symmetry sectors exhibit an emergent decoupling. We establish this for N flavor fermions and demonstrate it numerically for the special case of the Hubbard model, in which spin and charge skin effects separate at low energies. Finally, we construct an interaction-enabled E8 skin effect with no free fermion counterpart.