Irrelevant Deformations of Chiral Bosons

Abstract: We study $ \text{T}\overline{\text{T}} $ deformations of chiral bosons using the formalism due to Sen. For arbitrary numbers of left- and right-chiral bosons, we find that the $ \text{T}\overline{\text{T}} $-deformed Lagrangian can be computed in closed form, giving rise to a novel non-local action in Sen's formalism. We establish that at the limit of infinite $ \text{T}\overline{\text{T}} $ coupling, the equations of motion of deformed theory exhibits chiral decoupling. We then turn to a discussion of $ \text{T}\overline{\text{T}} $-deformed chiral fermions, and point out that the stress tensor of the $ \text{T}\overline{\text{T}} $-deformed free fermion coincides with the undeformed seed theory. We explain this behaviour of the stress tensor by noting that the deformation term in the action is purely topological in nature and closely resembles the fermionic Wess-Zumino term in the Green-Schwarz formalism. In turn, this observation also explains a puzzle in the literature, viz. why the $ \text{T}\overline{\text{T}} $ deformation of multiple free fermions truncate at linear order. We conclude by discussing the possibility of an interplay between $ \text{T}\overline{\text{T}} $ deformations and bosonisation.