Speaker
Kirill Krasnov
Description
Any field theory is renormalisable once all terms compatible
with the symmetries are added to the Lagrangian. One can
then in principle attempt to compute the arising
renormalisation group flow, and search for fixed points
realising the asymptotic safety scenario. However, in
practice the terms one needs to add to the Lagrangian
contain higher derivatives, and the necessary computation,
even at one loop, becomes unrealistic. I report on a
one-loop computation where the salting point is taken to be
the family of Lagrangians given by an arbitrary function of
the self-dual part of the Yang-Mills curvature tensor. All
such Lagrangians lead to just second order in derivatives
field equations, and so seem to be clearly insufficient to
renormalise the arising divergences. However, as I will
show, the magic of self-duality makes this family of
theories one-loop renormalisable. I will explicitly describe
the arising renormalisation group flow in the
infinite-dimensional space of coupling constants.
