5 papers
Anomaly cancellation for two factors
Ben Gripaios, Khoi Le Nguyen Nguyen
We show that solving the abelian part of the local anomaly cancellation conditions for a 4-d gauge theory whose gauge Lie algebra has an abelian summand with rank is equ…
TQFTs do not detect the Milnor sphere
Ben Gripaios, Oscar Randal-Williams
We show that, under very general hypotheses, topological quantum field theories (TQFTs) cannot detect homotopy spheres bounding parallelisable manifolds, such as Milnor's exotic 7-…
Anomaly cancellation for a factor
Ben Gripaios, Khoi Le Nguyen Nguyen
We use methods of arithmetic geometry to find solutions to the abelian local anomaly cancellation equations for a four-dimensional gauge theory whose Lie algebra has a single $\mat…
The asymptotically-free gauge theories
Ben Gripaios, Khoi Le Nguyen Nguyen
We show how to classify the asymptotically-free gauge theories in four spacetime dimensions, focussing here on the case of purely fermionic matter. The classification depends on th…
More varieties of 4-d gauge theories: product representations
Ben Gripaios, Khoi Le Nguyen Nguyen
Recently, we used methods of arithmetic geometry to study the anomaly-free irreducible representations of an arbitrary gauge Lie algebra. Here we generalize to the case of products…