Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs
A. Liam Fitzpatrick, Kuo-Wei Huang, David Meltzer, Eric Perlmutter, David Simmons-Duffin
Abstract
A bstract Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge C T , we clarify the properties of stress tensor composite primary operators of minimal twist, [ T m ], using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling $$ \left\langle {\mathcal{O}}_L{\mathcal{O}}_L\left[{T}^m\right]\right\rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>L</mml:mi> </mml:msub> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>L</mml:mi> </mml:msub> <mml:mfenced> <mml:msup> <mml:mi>T</mml:mi> <mml:mi>m</mml:mi> </mml:msup> </mml:mfenced> </mml:mrow> </mml:mfenced> </mml:math> , where $$ {\mathcal{O}}_L $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:math> is any light primary operator, is independent of the purely gravitational action. Next, we consider corrections to this coupling due to additional interactions in AdS effective field theory and the corresponding dual CFT. When the CFT contains a non-zero three-point coupling $$ \left\langle TT{\mathcal{O}}_L\right\rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mrow> <mml:mi>TT</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:mrow> </mml:mfenced> </mml:math> , the three-point coupling $$ \left\langle {\mathcal{O}}_L{\mathcal{O}}_L\left[{T}^2\right]\right\rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>L</mml:mi> </mml:msub> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>L</mml:mi> </mml:msub> <mml:mfenced> <mml:msup> <mml:mi>T</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mfenced> </mml:mrow> </mml:mfenced> </mml:math> is modified at large C T if $$ \left\langle TT{\mathcal{O}}_L\right\rangle \sim \sqrt{C_T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mrow> <mml:mi>TT</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:mrow> </mml:mfenced> <mml:mo>∼</mml:mo> <mml:msqrt> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>T</mml:mi> </mml:msub> </mml:msqrt> </mml:math> . This scaling is obeyed by the dilaton, by Kaluza-Klein modes of prototypical supergravity compactifications, and by scalars in stress tensor multiplets of supersymmetric CFTs. Quartic derivative interactions involving the graviton and the light probe field dual to $$ {\mathcal{O}}_L $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:math> can also modify the minimal-twist couplings; these local interactions may be generated by integrating out a spin- ℓ ≥ 2 bulk field at tree level, or any spin ℓ at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively.