Nonperturbative effects in T T ¯ -deformed conformal field theories: A toy model for Planckian physics

We propose a nonperturbative completion of two-point correlators in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>T</a:mi> <a:mover accent="true"> <a:mi>T</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> </a:math> -deformed conformal field theories (CFTs) and analyze their behavior at distance scales shorter than the fundamental length scale set by the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>T</e:mi> <e:mover accent="true"> <e:mi>T</e:mi> <e:mo stretchy="false">¯</e:mo> </e:mover> </e:math> deformation. Building on the interpretation of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>T</i:mi> <i:mover accent="true"> <i:mi>T</i:mi> <i:mo stretchy="false">¯</i:mo> </i:mover> </i:math> deformation as a coupling to two-dimensional quantum gravity with a unique built-in length scale, we advance the study of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>T</m:mi> <m:mover accent="true"> <m:mi>T</m:mi> <m:mo stretchy="false">¯</m:mo> </m:mover> </m:math> -deformed CFTs as a toy model for Planckian physics. As we probe shorter distances, trans-Planckian oscillations are followed by a super-Planckian regime in which correlations are typically suppressed by geometric randomness, in contrast to the power-law growth characteristic of CFTs. Moreover, their dependence on distance becomes exponentially weaker, suggesting that the underlying geometric structure has been largely erased—a behavior broadly consistent with expectations for quantum spacetime in this regime.