CERN Lattice Coffee

Sneaking up on chiral lattice gauge theories?

by Simon Catterall (Syracuse University)

4/2-037 - TH meeting room (CERN)

4/2-037 - TH meeting room


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I will show how Kaehler-Dirac fermions suffer from an anomaly in a U(1) symmetry that can be computed exactly on a finite lattice contradicting the usual folklore. This anomaly is connected to an ambiguity in the path integral measure for a reduced lattice Kaehler fermion that is an analog of the measure problem for chiral lattice fermions. In the Kaehler case it can be explicitly solved using a mirror fermion construction. 
To gap the mirror fermions requires all 't Hooft anomalies vanish which then determines the fermion content.
We show that the minimal anomaly free theory has a continuum limit that corresponds to the Pati-Salam GUT - a chiral gauge theory containing the Standard Model. Because of the close connection between the lattice Kaehler fermion and staggered fermions this suggests an alternative approach to at least a class of lattice chiral gauge theory.
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Elena Gianolio
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Tobias Tsang, Mattia Dallabrida, Andreas Juttner, Simon Kuberski, Matteo Di Carlo, Felix Benjamin Erben, Pascal Pignereau
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