Siegel paramodular forms and sparseness in AdS3/CFT2

Abstract

We discuss the application of Siegel paramodular forms to the counting of polar states in symmetric product orbifold CFTs. We present five special examples and provide exact analytic counting formulas for their polar states. The first example reproduces the known result for type IIB supergravity on AdS 3 ×S 3 ×K3, whereas the other four examples give new counting formulas. Their crucial feature is that the low energy spectrum is very sparse, which suggests the existence of a suitable dual supergravity theory. These examples open a path to novel realizations of AdS 3 /CFT 2 .

$\mathcal{N}=2$ minimal models: A holographic needle in a symmetric orbifold haystack

“…To deal with the first hurdle, we simply concentrate on CFTs with c ≤ 6. To deal with the second hurdle, we use the fact that [22][23][24] found mathematical exceptions to the generic behavior established in [21]: that is, there are specific so-called weak Jacobi forms, which could describe the elliptic genus of a CFT, whose symmetric orbifold exhibits a slow, supergravity-like growth. In this paper we build on these observations to find explicit CFTs that pass both diagnostics: N = 2 minimal models.…”

Symmetries in A-type little string theories. Part I. Reduced free energy and paramodular groups

“…The generator V N extends Σ N to a subgroup of Sp(4, R), which we denote by Σ * N . As was discussed in [30], the partition functions of symmetric orbifold CFTs have Σ * N as symmetry group. This agrees with the conclusion of [18] as we have the following relation,…”

Sphere packing and quantum gravity

“…These universal properties follow from modular invariance in the large-c limit and the assumption of a sparse lowlying spectrum [29]. For other applications and extensions of the modular bootstrap, see, e.g., [30][31][32][33][34][35][36][37][38][39][40].…”