Infinite $\mathrm{T\bar T}$-like symmetries of compactified LST

Abstract

We show that the three-dimensional asymptotically linear dilaton background that arises in the near-horizon decoupling region of NS5-branes compactified on T^4 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>T</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> admits boundary conditions that lead to an infinite set of symmetries. The associated conserved charges, which implement field-dependent coordinate transformations, are found to be identical to the corresponding generators in a symmetric product orbifold of T\bar T <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo accent="true">‾</mml:mo> </mml:mover> </mml:mrow> </mml:math> - deformed CFTs. Their algebra is a non-linear modification of the Virasoro × Virasoro algebra, which precisely coincides with the algebra of the “unrescaled” symmetry generators in T\bar T <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo accent="true">‾</mml:mo> </mml:mover> </mml:mrow> </mml:math> -deformed CFTs. This further strengthens a previously proposed link between the single-trace T\bar T <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo accent="true">‾</mml:mo> </mml:mover> </mml:mrow> </mml:math> deformation and compactified little string theory.

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