Item

Abstract

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.