A bstract There is a rich connection between classical errorcorrecting codes, Euclidean lattices, and chiral conformal field theories. Here we show that quantum errorcorrecting codes, those of the stabilizer type, are related to Lorentzian lattices and nonchiral CFTs. More specifically, real selfdual stabilizer codes can be associated with even selfdual Lorentzian lattices, and thus define Narain CFTs. We dub the resulting theories code CFTs and study their properties. Tduality transformations of a code CFT, at the level of the underlying code, reduce to code equivalences. By means of such equivalences, any stabilizer code can be reduced to a graph code. We can therefore represent code CFTs by graphs. We study code CFTs with small central charge c = n ≤ 12, and find many interesting examples. Among them is a nonchiral E 8 theory, which is based on the root lattice of E 8 understood as an even selfdual Lorentzian lattice. By analyzing all graphs with n ≤ 8 nodes we find many pairs and triples of physically distinct isospectral theories. We also construct numerous modular invariant functions satisfying all the basic properties expected of the CFT partition function, yet which are not partition functions of any known CFTs. Wemore »
Universal dynamics of heavy operators in CFT2
A bstract We obtain an asymptotic formula for the average value of the operator product expansion coefficients of any unitary, compact two dimensional CFT with c > 1. This formula is valid when one or more of the operators has large dimension or — in the presence of a twist gap — has large spin. Our formula is universal in the sense that it depends only on the central charge and not on any other details of the theory. This result unifies all previous asymptotic formulas for CFT2 structure constants, including those derived from crossing symmetry of four point functions, modular covariance of torus correlation functions, and higher genus modular invariance. We determine this formula at finite central charge by deriving crossing kernels for higher genus crossing equations, which give analytic control over the structure constants even in the absence of exact knowledge of the conformal blocks. The higher genus modular kernels are obtained by sewing together the elementary kernels for fourpoint crossing and modular transforms of torus onepoint functions. Our asymptotic formula is related to the DOZZ formula for the structure constants of Liouville theory, and makes precise the sense in which Liouville theory governs the universal dynamics of more »
 Award ID(s):
 1801805
 Publication Date:
 NSFPAR ID:
 10293124
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2020
 Issue:
 7
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
More Like this


A bstract It is a longstanding conjecture that any CFT with a large central charge and a large gap ∆ gap in the spectrum of higherspin singletrace operators must be dual to a local effective field theory in AdS. We prove a sharp form of this conjecture by deriving numerical bounds on bulk Wilson coefficients in terms of ∆ gap using the conformal bootstrap. Our bounds exhibit the scaling in ∆ gap expected from dimensional analysis in the bulk. Our main tools are dispersive sum rules that provide a dictionary between CFT dispersion relations and Smatrix dispersion relations in appropriate limits. This dictionary allows us to apply recentlydeveloped flatspace methods to construct positive CFT functionals. We show how AdS 4 naturally resolves the infrared divergences present in 4D flatspace bounds. Our results imply the validity of twicesubtracted dispersion relations for any Smatrix arising from the flatspace limit of AdS/CFT.

The monster sporadic group is the automorphism group of a central charge $c=24$ vertex operator algebra (VOA) or meromorphic conformal field theory (CFT). In addition to its $c=24$ stress tensor $T(z)$, this theory contains many other conformal vectors of smaller central charge; for example, it admits $48$ commuting $c=\frac12$ conformal vectors whose sum is $T(z)$. Such decompositions of the stress tensor allow one to construct new CFTs from the monster CFT in a manner analogous to the GoddardKentOlive (GKO) coset method for affine Lie algebras. We use this procedure to produce evidence for the existence of a number of CFTs with sporadic symmetry groups and employ a variety of techniques, including Hecke operators and modular linear differential equations, to compute the characters of these CFTs. Our examples include (extensions of) nine of the sporadic groups appearing as subquotients of the monster, as well as the simple groups ${}^2\tsl{E}_6(2)$ and $\tsl{F}_4(2)$ of Lie type. Many of these examples are naturally associated to McKay's $\widehat{E_8}$ correspondence, and we use the structure of Norton's monstralizer pairs more generally to organize our presentation.

A bstract We develop a new technique for computing a class of fourpoint correlation functions of heavy halfBPS operators in planar $$ \mathcal{N} $$ N = 4 SYM theory which admit factorization into a product of two octagon form factors with an arbitrary bridge length. We show that the octagon can be expressed as the Fredholm determinant of the integrable Bessel operator and demonstrate that this representation is very efficient in finding the octagons both at weak and strong coupling. At weak coupling, in the limit when the four halfBPS operators become null separated in a sequential manner, the octagon obeys the Toda lattice equations and can be found in a closed form. At strong coupling, we exploit the strong Szegő limit theorem to derive the leading asymptotic behavior of the octagon and, then, apply the method of differential equations to determine the remaining subleading terms of the strong coupling expansion to any order in the inverse coupling. To achieve this goal, we generalize results available in the literature for the asymptotic behavior of the determinant of the Bessel operator. As a byproduct of our analysis, we formulate a SzegőAkhiezerKac formula for the determinant of the Bessel operator with amore »

A bstract Using the fact that flat space with a boundary is related by a Weyl transformation to antide Sitter (AdS) space, one may study observables in boundary conformal field theory (BCFT) by placing a CFT in AdS. In addition to correlation functions of local operators, a quantity of interest is the free energy of the CFT computed on the AdS space with hyperbolic ball metric, i.e. with a spherical boundary. It is natural to expect that the AdS free energy can be used to define a quantity that decreases under boundary renormalization group flows. We test this idea by discussing in detail the case of the large N critical O ( N ) model in general dimension d , as well as its perturbative descriptions in the epsilonexpansion. Using the AdS approach, we recover the various known boundary critical behaviors of the model, and we compute the free energy for each boundary fixed point, finding results which are consistent with the conjectured F theorem in a continuous range of dimensions. Finally, we also use the AdS setup to compute correlation functions and extract some of the BCFT data. In particular, we show that using the bulk equations of motion,more »