A modular spectral triple for $\kappa$-Minkowski space

Understand

We present a spectral triple for $\kappa$-Minkowski space in two dimensions.

• Starting from an algebra naturally associated to this space, a Hilbert space is built using a weight which is invariant under the $\kappa$-Poincar\'e algebra.
• The weight satisfies a KMS condition and its associated modular operator plays an important role in the construction.
• This forces us to introduce two ingredients which have a modular flavor: the first is a twisted commutator, used to obtain a boundedness condition for the Dirac operator, the second is a weight replacing the usual operator trace, used to measure the growth of the resolvent of the Dirac operator.