<p>We study correlators in two-dimensional <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( T\overline{T} \)</EquationSource> </InlineEquation>-deformed conformal field theories by interpreting the <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( T\overline{T} \)</EquationSource> </InlineEquation> deformation as a coupling to two-dimensional gravity. To demonstrate the utility of the massive gravity framework as a particular realization of the gravitational interpretation, we show how the <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( T\overline{T} \)</EquationSource> </InlineEquation>-deformed correlators at finite coupling can be computed by adopting a judicious parametrization of the 2D metric and a preferred choice of zweibeins. To illustrate how this method works in practice, we compute the leading logarithmic contributions to two- and three-point functions to all orders in the <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( T\overline{T} \)</EquationSource> </InlineEquation> coupling, reproducing a known result while producing new findings. This framework generalizes the random geometry approach to finite coupling.</p>

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\( T\overline{T} \)-deformed correlators from a 2D gravity description

  • Shinji Hirano,
  • Vinayak Raj

摘要

We study correlators in two-dimensional T T ¯ \( T\overline{T} \) -deformed conformal field theories by interpreting the T T ¯ \( T\overline{T} \) deformation as a coupling to two-dimensional gravity. To demonstrate the utility of the massive gravity framework as a particular realization of the gravitational interpretation, we show how the T T ¯ \( T\overline{T} \) -deformed correlators at finite coupling can be computed by adopting a judicious parametrization of the 2D metric and a preferred choice of zweibeins. To illustrate how this method works in practice, we compute the leading logarithmic contributions to two- and three-point functions to all orders in the T T ¯ \( T\overline{T} \) coupling, reproducing a known result while producing new findings. This framework generalizes the random geometry approach to finite coupling.