Monster symmetry and Extremal CFTs

TL;DR

This work tests conjectures about extremal self-dual CFTs and their potential Monster symmetry as holographic duals of pure gravity in AdS$_3$. It analyzes twisted partition functions $Z_g$ and their modular transforms to constrain the symmetry structure, applying the same logic to both $k=2$ ECFTs and $k^*=4$ ESCFTs via twisted Hecke transforms. The main results prove there is no Monster-symmetric $c=48$ ECFT or SCFT, and no Monster-symmetric $k=2$ ECFT or $k^*=4$ ESCFT, while a constructed counterexample to a size-differential conjecture shows ECFTs with larger $k$ are not ruled out by such arguments. Together, these findings constrain possible Monster-symmetric extremal theories and illuminate methods to generate consistent twisted data, informing future bootstrap and holographic analyses of AdS$_3$ gravity duals.

Abstract

We test some recent conjectures about extremal selfdual CFTs, which are the candidate holographic duals of pure gravity in $AdS_3$. We prove that no $c=48$ extremal selfdual CFT or SCFT may possess Monster symmetry. Furthermore, we disprove a recent argument against the existence of extremal selfdual CFTs of large central charge.