The $$ T\overline{T} $$ deformation of quantum field theory as random geometry Article Swipe
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· 2018
· Open Access
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· DOI: https://doi.org/10.1007/jhep10(2018)186
· OA: W2890626725
A bstract We revisit the results of Zamolodchikov and others on the deformation of two-dimensional quantum field theory by the determinant det T of the stress tensor, commonly referred to as $$ T\overline{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> . Infinitesimally this is equivalent to a random coordinate transformation, with a local action which is, however, a total derivative and therefore gives a contribution only from boundaries or nontrivial topology. We discuss in detail the examples of a torus, a finite cylinder, a disk and a more general simply connected domain. In all cases the partition function evolves according to a linear diffusion-type equation, and the deformation may be viewed as a kind of random walk in moduli space. We also discuss possible generalizations to higher dimensions.
