Irrelevant deformations of chiral bosons

We study $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ deformations of chiral bosons using the formalism due to Sen. For arbitrary numbers of left- and right-chiral bosons, we find that the $$ \mathrm{T}\overline{\mathrm{T}} $$ T 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 $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ coupling, the equations of motion of deformed theory exhibits chiral decoupling. We then turn to a discussion of $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ -deformed chiral fermions, and point out that the stress tensor of the $$ \mathrm{T}\overline{\mathrm{T}} $$ T 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 $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ deformation of multiple free fermions truncate at linear order. We conclude by discussing the possibility of an interplay between $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ deformations and bosonisation.

$$T\bar{T}$$ deformation of chiral bosons and Chern–Simons $$\hbox {AdS}_3$$ gravity

We study the $$T\bar{T}$$ T T ¯ deformation of the chiral bosons and show the equivalence between the chiral bosons of opposite chiralities and the scalar fields at the Hamiltonian level under the deformation. We also derive the deformed Lagrangian of more generic theories which contain an arbitrary number of chiral bosons to all orders. By using these results, we derive the $$T\bar{T}$$ T T ¯ deformed boundary action of the $$\hbox {AdS}_3$$ AdS 3 gravity theory in the Chern–Simons formulation. We compute the deformed one-loop torus partition function, which satisfies the $$T\bar{T}$$ T T ¯ flow equation up to the one-loop order. Finally, we calculate the deformed stress–energy tensor of a solution describing a BTZ black hole in the boundary theory, which coincides with the boundary stress–energy tensor derived from the BTZ black hole with a finite cutoff.

Variational tricomplex of a local gauge system, Lagrange structure and weak Poisson bracket

We introduce the concept of a variational tricomplex, which is applicable both to variational and nonvariational gauge systems. Assigning this tricomplex with an appropriate symplectic structure and a Cauchy foliation, we establish a general correspondence between the Lagrangian and Hamiltonian pictures of one and the same (not necessarily variational) dynamics. In practical terms, this correspondence allows one to construct the generating functional of a weak Poisson structure starting from that of a Lagrange structure. As a byproduct, a covariant procedure is proposed for deriving the classical BRST charge of the BFV formalism by a given BV master action. The general approach is illustrated by the examples of Maxwell’s electrodynamics and chiral bosons in two dimensions.