Universal lowest-twist in CFTs from holography
Fitzpatrick, A. Liam; Huang, Kuo-Wei
We probe the conformal block structure of a scalar four-point function in d ≥ 2
conformal field theories by including higher-order derivative terms in a bulk gravitational
action. We consider a heavy-light four-point function as the boundary correlator at large
central charge. Such a four-point function can be computed, on the gravity side, as a
two-point function of the light operator in a black hole geometry created by the heavy
operator. We consider analytically solving the corresponding scalar field equation in a nearboundary expansion and find that the multi-stress tensor conformal blocks are insensitive
to the horizon boundary condition. The main result of this paper is that the lowest-twist
operator product expansion (OPE) coefficients of the multi-stress tensor conformal blocks
are universal: they are fixed by the dimension of the light operators and the ratio between
the dimension of the heavy operator and the central charge CT . Neither supersymmetry
nor unitary is assumed. Higher-twist coefficients, on the other hand, generally are not
protected. A recursion relation allows us to efficiently compute universal lowest-twist
coefficients. The universality result hints at the potential existence of a higher-dimensional
Virasoro-like symmetry near the lightcone. While we largely focus on the planar black hole
limit in this paper, we include some preliminary analysis of the spherical black hole case
in an appendix.
↧