Triality in minimal model holography

Theory of minimal updates in holography

Consider two quantum critical HamiltoniansH and H̃ on a d-dimensional lattice that only differ in some region R. We study the relation between holographic representations, obtained through real-space renormalization, of their corresponding ground states |ψ〉 and |ψ̃〉. We observe that, even though |ψ〉 and |ψ̃〉 disagree significantly both inside and outside region R, they still admit holographic desc...

Holography in the EPRL Model

In this research announcement, we propose a new interpretation of the Engle Pereira Rovelli (EPR) quantization of the Barrett-Crane (BC) model using a functor we call the time functor, which is the first example of a co-lax, amply renormalizable (claren) functor. Under the hypothesis that the universe is in the Kodama state, we construct a holographic version of the model. Generalisations to ot...

Migdal’s model and Holography

More than 30 years ago Migdal proposed a model for hadronic resonances based on rational approximants [1]. The final aim was to determine the spectrum of vector mesons in the large-Nc limit which best fulfills quarkhadron duality. The strategy was to start from the short distance behavior of the vector vacuum polarization function < V V > and build the Padé approximant thereof. Migdal further s...

Hopf Algebras with Triality

In this paper we revisit and extend the constructions of Glauberman and Doro on groups with triality and Moufang loops to Hopf algebras. We prove that the universal enveloping algebra of any Lie algebra with triality is a Hopf algebra with triality. This allows us to give a new construction of the universal enveloping algebras of Malcev algebras. Our work relies on the approach of Grishkov and ...

Lie Algebras with Triality