Quantum flux operators for Carrollian diffeomorphism in general dimensions

TL;DR

This paper develops Carrollian scalar field theories in various dimensions, demonstrating that their quantum flux operators realize Carrollian diffeomorphisms with a central charge, and linking supertranslations to modular Hamiltonians, with implications for quantum information and gravitational physics.

Contribution

It constructs Carrollian scalar field theories with flux operators representing Carrollian diffeomorphisms and connects supertranslations to modular Hamiltonians, offering new insights into null hypersurfaces and entanglement entropy.

Findings

Flux operators form faithful representations of Carrollian diffeomorphisms.

Central charge can be regularized to be finite using spectral methods.

Zero mode of supertranslation identified as modular Hamiltonian.

Abstract

We construct Carrollian scalar field theories in general dimensions, mainly focusing on the boundaries of Minkowski and Rindler spacetime, whose quantum flux operators form a faithful representation of Carrollian diffeomorphism up to a central charge, respectively. At future/past null infinity, the fluxes are physically observable and encode rich information of the radiation. The central charge may be regularized to be finite by the spectral zeta function or heat kernel method on the unit sphere. For the theory at the Rindler horizon, the effective central charge is proportional to the area of the bifurcation surface after regularization. Moreover, the zero mode of supertranslation is identified as the modular Hamiltonian, linking Carrollian diffeomorphism to quantum information theory. Our results may hold for general null hypersurfaces and provide new insight in the study of the Carrollian field theory, asymptotic symmetry group and entanglement entropy.