Non-linear p-form gauge theories and their deformations

The so-called TTbar deformation of field theories, originally introduced by Zamolodchikov in two-dimensional conformal field theories, provides a rare example of an irrelevant deformation that preserves remarkable features such as integrability and supersymmetry. Motivated by a recent interest in a new type of stress-tensor deformation called ''Root-TTbar'', we study TTbar-like deformations of chiral p-form theories in d=2p+2 dimensions with p even. Focusing on self-interacting chiral 4-form theories in ten dimensions, we analyze perturbatively the flow equations associated with both the T^2 and Root-TTbar deformations. Lorentz covariance is implemented by making use of the Ivanov-Nurmagambetov-Zupnik (INZ) approach which is closely related to the Pasti-Sorokin-Tonin (PST) formulation. We determine the deformed Lagrangian up to the third order in the deformation parameter and extract the invariant structures that enter at fifth order for the Root-TTbar case. Our results highlight a qualitative difference with the six-dimensional counterpart: in 10d the branch controlled by the square-root of the unique fourth order invariant of the field strength \sqrt{I_4} does not exhibit, at the orders considered, the simple hyperbolic resummation found in 6d.