Related papers: Free partition functions and an averaged holograph…
We revisit the proposal that the ensemble average over free boson CFTs in two dimensions - parameterized by Narain's moduli space - is dual to an exotic theory of gravity in three dimensions dubbed $U(1)$ gravity. We consider flavored…
Recent developments involving JT gravity in two dimensions indicate that under some conditions, a gravitational path integral is dual to an average over an ensemble of boundary theories, rather than to a specific boundary theory. For an…
We apply the theory of harmonic analysis on the fundamental domain of $SL(2,\mathbb{Z})$ to partition functions of two-dimensional conformal field theories. We decompose the partition function of $c$ free bosons on a Narain lattice into…
We study simple examples of ensemble-averaged holography in free compact boson CFTs with rational values of the radius squared. These well-known rational CFTs have an extended chiral algebra generated by three currents. We consider the…
We define a normalizable measure on the space of two-dimensional conformal field theories, which we interpret as a maximum ignorance ensemble. We test whether pure quantum gravity in AdS$_3$ is dual to the average over this ensemble. We…
It has been recently argued that the averaging of free CFT's over the Narain lattice can be holographically described through a Chern-Simons theory for $U\left(1\right)^{D}\times U\left(1\right)^{D}$ with a precise prescription to sum over…
We consider the weighted average of a two dimensional CFT, whose target space is $T^2$, over its Narain moduli space. We take as the weighing function the integral kernel which gives rise to $T \bar T$ deformation when applied to the world…
We introduce a framework for two-dimensional conformal field theory (CFT) in the language of analytic number theory. Attached to the torus partition function of every two-dimensional CFT is a self-dual, degree-4 $L$-function of root number…
In recent work we computed the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. Here we employ a modular bootstrap to show that the amplitude is…
We discuss the holographic correspondence between 3d "Chern-Simons gravity" and an ensemble of 2d Narain code CFTs. Starting from 3d abelian Chern-Simons theory, we construct an ensemble of boundary CFTs defined by gauging all possible…
In this paper, we study the logarithmic terms in the partition functions of CFTs with boundaries (BCFTs). In three dimensions, their coefficients give the boundary central charges, which are conjectured to be monotonically decreasing…
We outline a general derivation of holographic duality between "TQFT gravity" - the path integral of a 3d TQFT summed over different topologies - and an ensemble of boundary 2d CFTs. The key idea is to place the boundary ensemble on a…
In this paper, we attempt to explore the landscape of two-dimensional conformal field theories (2d CFTs) by efficiently searching for numerical solutions to the modular bootstrap equation using machine-learning-style optimization. The torus…
The partition function of the W_N minimal model CFT is computed in the large N 't Hooft limit and compared to the spectrum of the proposed holographic dual, a 3d higher spin gravity theory coupled to massive scalar fields. At finite N, the…
In this work we study families of $\mathbb{Z}_2$ orbifolds of toroidal conformal field theories based on both factorizable and non-factorizable target space tori. For these classes of theories, we analyze their moduli spaces, and compute…
We consider the ensemble average of two dimensional symmetric product orbifold CFTs $\text{Sym}^N(\mathbb{T}^D)$ over the Narain moduli space. We argue for a bulk dual given by $N$ copies of an abelian Chern-Simons theory coupled to…
We provide a precise relation between an ensemble of Narain conformal field theories (CFTs) with central charge $c=n$, and a sum of $(U(1) \times U(1))^n$ Chern-Simons theories on different handlebody topologies. We begin by reviewing the…
We compute the ${\cal N}=2$ supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the K\"ahler form with jumps…
We propose a SymTFT interpretation of ensemble averaging in low-dimensional holography. The central operation is to keep fixed both the SymTFT and the physical boundary condition, while averaging over topological boundary conditions at the…
We extend the holographic duality between 3d pure gravity and the 2d Ising CFT proposed in [Phys. Rev. D 85 (2012) 024032] to CFTs with boundaries. Besides the usual asymptotic boundary, the dual bulk spacetime now has a real cutoff, on…