Chiral Ward identities, automatic O(a) improvement and the gradient flow

Understand

Non-singlet chiral Ward identities for fermionic operators at positive flow-time are derived using standard techniques based on local chiral variations of the action and of local operators.

• The gradient flow formalism is applied to twisted mass fermions and it is shown that automatic O(a) improvement for Wilson twisted mass fermions at maximal twist is a property valid also at positive flow-time.
• A definition of the chiral condensate that is multiplicatively renormalizable and automatically O(a) improved is then derived.