The TT* deformation at large central charge

TL;DR

This work investigates Zamolodchikov's TT* deformation of two-dimensional QFTs in a large central charge ($c$) regime with an 't Hooft-like scaling where $tc$ is held fixed. The authors show that, in this limit and to leading order in $1/c$, correlation functions become exact, local in space, and expressible as polynomials in $t$, with the large-$t$ regime governed by undeformed two-point functions and energies probed at $E\sim 1/\sqrt{|t|c}$. They develop a nonlocal reformulation via a Hubbard–Stratonovich field and leverage Ward identities to reduce $n$-point correlators to lower-point functions, yielding a differential equation for $t$-dependence. In the large-$c$ limit, they prove that two-point functions are $t$-independent, three-point functions are linear in $t$, and higher-point functions are polynomials of degree $(n-2)$ in $t$, consistent with a gravity dual description as a double-trace deformation that modifies boundary conditions for the graviton. As an explicit check, they compute all ten TT*-deformed three-point functions for a free scalar CFT, obtaining universal Ward-identity contributions and explicit nonuniversal terms proportional to $t$ and $c^2$, and showing OPE-like structures such as $T(x)\Theta(0)\sim (t c\overline T(0))/x_+^4$, clarifying locality properties and the UV behavior of the deformation.

Abstract

We study Zamolodchikov's TT* deformation of two dimensional quantum field theories in a 't Hooft-like limit, in which we scale the number of degrees of freedom c to infinity and the deformation parameter t to zero, keeping their product t*c fixed (more precisely, we keep energies and distances fixed in units of t*c). In this limit the Hagedorn temperature remains fixed, but other non-local aspects of the theory disappear. We show that in this limit correlation functions may be computed exactly, and they are local in space and polynomials in t. We compute explicitly the deformed three-point functions of the energy-momentum tensor for a TT*-deformed conformal field theory.