Nathan Benjamin

Elliptic Genera and 3d Gravity

We describe general constraints on the elliptic genus of a 2d supersymmetric conformal field theory which has a gravity dual with large radius in Planck units. We give examples of theories which do and do not satisfy the bounds we derive, by describing the elliptic genera of symmetric product orbifolds of K3, product manifolds, certain simple families of Calabi–Yau hypersurfaces, and symmetric products of the “Monster CFT”. We discuss the distinction between theories with supergravity duals and those whose duals have strings at the scale set by the AdS curvature. Under natural assumptions, we attempt to quantify the fraction of (2,2) supersymmetric conformal theories which admit a weakly curved gravity description, at large central charge.

Universal Bounds on Charged States in 2d CFT and 3d Gravity

A bstractWe derive an explicit bound on the dimension of the lightest charged state in two dimensional conformal field theories with a global abelian symmetry. We find that the bound scales with c and provide examples that parametrically saturate this bound. We also prove that any such theory must contain a state with charge-to-mass ratio above a minimal lower bound. We comment on the implications for charged states in three dimensional theories of gravity.

Emergent space-time and the supersymmetric index

A bstractIt is of interest to find criteria on a 2d CFT which indicate that it gives rise to emergent gravity in a macroscopic 3d AdS space via holography. Symmetric orbifolds in the large N limit have partition functions which are consistent with an emergent space-time string theory with Lstring ∼ LAdS. For supersymmetric CFTs, the elliptic genus can serve as a sensitive probe of whether the SCFT admits a large radius gravity description with Lstring ≪ LAdS after one deforms away from the symmetric orbifold point in moduli space. We discuss several classes of constructions whose elliptic genera strongly hint that gravity with LPlanck ≪ Lstring ≪ LAdS can emerge at suitable points in moduli space.

Small black holes and near-extremal CFTs

A bstractPure theories of AdS3 quantum gravity are conjectured to be dual to CFTs with sparse spectra of light primary operators. The sparsest possible spectrum consistent with modular invariance includes only black hole states above the vacuum. Witten conjectured the existence of a family of extremal CFTs, which realize this spectrum for all admissible values of the central charge. We consider the quantum corrections to the classical spectrum, and propose a specific modification of Witten’s conjecture which takes into account the existence of “small” black hole states. These have zero classical horizon area, with a calculable entropy attributed solely to loop effects. Our conjecture passes various consistency checks, especially when generalized to include theories with supersymmetry. In theories with N

An Extremal N=2 Superconformal Field Theory

\mathcal{N}

{\mathcal{N}}=2

= 2 supersymmetry, this “near-extremal CFT” proposal precisely evades the no-go results of Gaberdiel et al.

superconformal field theory

A bstractWe examine the low-lying quarter BPS spectrum of a 2d conformal field theory with target SymN (K3) at various points in the moduli space, and look at a more refined count than the ordinary elliptic genus. We compute growth of the spectrum at both the symmetric orbifold point, as well as at the supergravity point in the moduli space. Finally we do a decomposition of the spectra into N=4