Resummation of MultiStress Tensors in Higher Dimensions
Abstract
In the context of holographic conformal field theories (CFTs), a system of linear partial differential equations was recently proposed to be the higherdimensional analog of the nullstate equations in $d=2$ CFTs at large central charge. Solving these equations in a nearlightcone expansion yields solutions that match the minimaltwist multistress tensor contributions to a heavylight fourpoint correlator (or a thermal twopoint correlator) computed using holography, the conformal bootstrap, and other methods. This note explores the exact solutions to these equations. We begin by observing that, in an expansion in terms of the ratio between the heavy operator's dimension and the central charge, the $d=2$ correlator involving the leveltwo degenerate scalars at each order can be represented as a Bessel function; the resummation yields the Virasoro vacuum block. We next observe a relation between the $d=2$ correlator and the $d=4$ nearlightcone correlator involving light scalars with the same conformal dimension. The resummed $d=4$ correlator takes a simple form in the complex frequency domain. Unlike the Virasoro vacuum block, the resummation in $d=4$ leads to essential singularities. Similar expressions are also obtained when the light scalar's dimension takes other finite values. These CFT results correspond to a holographic computation with a spherical black hole. In addition, using the differential equations, we demonstrate that the correlators can be reconstructed via certain modes. In $d=2$, these modes are related to the Virasoro algebra.
 Publication:

arXiv eprints
 Pub Date:
 June 2024
 DOI:
 10.48550/arXiv.2406.07458
 arXiv:
 arXiv:2406.07458
 Bibcode:
 2024arXiv240607458H
 Keywords:

 High Energy Physics  Theory
 EPrint:
 39 pages, v2: notation improved