On non-linear chiral 4-form theories in D = 10

A bstract We consider properties of non-linear theories of a chiral 4-form gauge field A 4 in ten space-time dimensions with an emphasis on a subclass of these theories which are invariant under the D = 10 conformal symmetry. We show that general results regarding a peculiar structure of duality-invariant abelian gauge theories in four and six space-time dimensions do not extend to non-linear chiral 4-form theories in ten dimensions. This discrepancy arises primarily from the large number 81 of independent invariants constructible from the self-dual part of the five-form field strength F 5 = dA 4 in D = 10, in stark contrast to the single independent (fourth-order) invariants which are building blocks of the actions in the lower dimensional cases. In particular, unlike the D = 4 and D = 6 cases, where non-linear duality-invariant theories can be viewed as stress-tensor ( TT̄ T T ¯ -like) deformations of seed theories, the flow equations in D = 10 generally involve both stress-tensor invariants and additional higher-order structures constructed from F 5 . In passing, we prove the equivalence of three Lagrangian formulations of non-linear duality-invariant p -form theories: the PST, the Ivanov-Nurmagambetov-Zupnik and the “clone” one.