The gradient flow: a renormalisable probe for gauge theories

Gauge-invariant nonperturbative renormalisation has been a long-standing and challenging problem for lattice gauge theories. Perhaps the most widely-used nonperturbative procedure, the regularisation-independent momentum subtraction scheme, breaks gauge invariance, which introduces significant issues for composite operators of gauge fields. Other methods, such as the use of Ward identities, are generally not widely applicable to composite operators. The gradient flow, in which the boundary theory is classically evolved in a new half-dimension (the flow time), provides a nonperturbative, gauge-invariant probe of gauge theories. I will introduce the gradient flow in the context of lattice gauge theories and discuss some of the applications to the problem of nonperturbative renormalisation in lattice QCD.