Natalie M. Paquette

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.

Twining Genera of (0,4) Supersymmetric Sigma Models on K3

A bstractConformal field theories with (0,4) worldsheet supersymmetry and K3 target can be used to compactify the E8 × E8 heterotic string to six dimensions in a supersymmetric manner. The data specifying such a model includes an appropriate configuration of 24 gauge instantons in the E8 × E8 gauge group to satisfy the constraints of anomaly cancellation. In this note, we compute twining genera — elliptic genera with appropriate insertions of discrete symmetry generators in the trace — for (0,4) theories with various instanton embeddings. We do this by constructing linear sigma models which flow to the desired conformal field theories, and using the techniques of localization. We present several examples of such twining genera which are consistent with a moonshine relating these (0,4) models to the finite simple sporadic group M24.

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.

Towards a holographic Bose-Hubbard model

A bstractWe present a holographic construction of the large-N Bose-Hubbard model. The model is based on Maxwell fields coupled to charged scalar fields on the AdS2 hard wall. We realize the lobe-shaped phase structure of the Bose-Hubbard model and find that the model admits Mott insulator ground states in the limit of large Coulomb repulsion. In the Mott insulator phases, the bosons are localized on each site. At zero hopping we find that the transitions between Mott insulating phases with different fillings correspond to first order level-crossing phase transitions. At finite hopping we find a holographic phase transition between the Mott phase and a non-homogeneous phase. We then analyze the perturbations of fields around both the Mott insulator phase and inhomogeneous phase. We find almost zero modes in the non-homogeneous phase.

No more walls! A tale of modularity, symmetry, and wall crossing for 1/4 BPS dyons

A bstractWe determine the generating functions of 1/4 BPS dyons in a class of 4d N

Landau-Ginzburg orbifolds and symmetries of K3 CFTs

\mathcal{N}

T^8

= 4 string vacua arising as CHL orbifolds of K3 × T2, a classification of which has been recently completed. We show that all such generating functions obey some simple physical consistency conditions that are very often sufficient to fix them uniquely. The main constraint we impose is the absence of unphysical walls of marginal stability: discontinuities of 1/4 BPS degeneracies can only occur when 1/4 BPS dyons decay into pairs of 1/2 BPS states. Formally, these generating functions in spacetime can be described as multiplicative lifts of certain supersymmetric indices (twining genera) on the worldsheet of the corresponding nonlinear sigma model on K3. As a consequence, our procedure also leads to an explicit derivation of almost all of these twining genera. The worldsheet indices singled out in this way match precisely a set of functions of interest in moonshine, as predicted by a recent conjecture.

and the Borcherds automorphic form

The simplest string theory compactifications to 3D with 16 supercharges -- the heterotic string on