More on $$ T\overline{T} $$-like deformations in higher dimensions

A

bstract

We investigate several possible generalisations of

deformations to three- and higher-dimensional field theories. Starting from the two-dimensional

$$ T\overline{T} $$ T T ¯

flow, we work out its higher-dimensional uplift, which results in a non-local and non-isotropic three-dimensional theory. Starting instead from the relation between the Nambu-Goto action and

$$ T\overline{T} $$ T T ¯

in d = 2, we study the flow equation obeyed by the Dirac-Nambu-Goto actions in d > 2 dimensions, written in terms of the stress-energy tensor only. Similarly, we derive the stress-tensor flow obeyed by the Born-Infeld actions in d dimensions and by the Dirac-Born-Infeld actions in d = 2 and d = 3.