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

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)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)O(a) improved is then derived.