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arXiv · 1801.06895

The $T\overline T$ deformation of quantum field theory as random geometry

John Cardy
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Abstract

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 $T\overline T$. 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.

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John Cardy. 2018-01-21. The $T\overline T$ deformation of quantum field theory as random geometry. https://doi.org/10.1007/jhep10(2018)186

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