User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse




Journal Article

Resolving modular flow: a toolkit for free fermions


Reyes,  Ignacio
Gravity, Quantum Fields and Information, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

External Ressource
No external resources are shared
Fulltext (public)
Supplementary Material (public)
There is no public supplementary material available

Erdmenger, J., Fries, P., Reyes, I., & Simon, C. P. (2020). Resolving modular flow: a toolkit for free fermions. Journal of High Energy Physics, 2020(12): 126. Retrieved from http://arxiv.org/abs/2008.07532.

Cite as: http://hdl.handle.net/21.11116/0000-0006-F2CF-0
Modular flow is a symmetry of the algebra of observables associated to spacetime regions. Being closely related to entanglement, it has played a key role in recent connections between information theory, QFT and gravity. However, little is known about its action beyond highly symmetric cases. The key idea of this work is to introduce a new formula for modular flows for free chiral fermions in $1+1$ dimensions, working directly from the \textit{resolvent}, a standard technique in complex analysis. We present novel results -- not fixed by conformal symmetry -- for disjoint regions on the plane, cylinder and torus. Depending on temperature and boundary conditions, these display different behaviour ranging from purely local to non-local in relation to the mixing of operators at spacelike separation. We find the modular two-point function, whose analytic structure is in precise agreement with the KMS condition that governs modular evolution. Our ready-to-use formulae may provide new ingredients to explore the connection between spacetime and entanglement.