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We study analytically the constraints of the conformal bootstrap on the low-lying spectrum of operators in field theories with global conformal symmetry in one and two spacetime dimensions. We introduce a new class of linear functionals…
In this paper, we study periodic linear systems on periodic time scales which include not only discrete and continuous dynamical systems but also systems with a mixture of discrete and continuous parts (e.g. hybrid dynamical systems). We…
The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general…
We explore the constraining power of OPE associativity in 4D Conformal Field Theory with a continuous global symmetry group. We give a general analysis of crossing symmetry constraints in the 4-point function <Phi Phi Phi* Phi*>, where Phi…
The recent emergence of the modern conformal bootstrap method for the study of conformal field theories (CFTs) has enabled the revisiting of old problems in classical critical phenomena described by three-dimensional CFTs. The study of such…
We extend the Ax-Katz theorem for a single polynomial from finite fields to the rings Z_m with m composite. This extension not only yields the analogous result, but gives significantly higher divisibility bounds. We conjecture what computer…
We continue the study of model-independent constraints on the unitary Conformal Field Theories in 4-Dimensions, initiated in arXiv:0807.0004. Our main result is an improved upper bound on the dimension \Delta of the leading scalar operator…
From the computation of three-point singlet correlators in the two-matrix model, we obtain an explicit expression for the macroscopic three-loop amplitudes having boundary lengths $\ell_{i}$ $(i = 1\sim 3)$ in the case of the unitary series…
We report on the first steps of an ongoing project to add gauge observables and gauge corrections to the well-studied strong coupling limit of staggered lattice QCD, which has been shown earlier to be amenable to numerical simulations by…
We use commutativity of null-integrated operators on the same null plane to construct dispersive CFT sum rules for spinning operators. The contribution of heavy blocks to these sum rules is dominated by a saddle configuration that we call…
We examine the precise connection between the exact renormalisation group with local couplings and the renormalisation of correlation functions of composite operators in scale-invariant theories. A geometric description of theory space…
A straightforward expansion of Edwards' functional integral representation of the grand partition function for a polymer liquid as an infinite set of Feynman diagrams is shown to yield a cluster expansion that is closely related to the…
This paper studies structured products of real matrices for which the top Lyapunov exponent can be accessed by reducing the dynamics to an amenable generalization of upper triangular matrices. Exploiting prescribed zero patterns (including…
We describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal…
Recently, Son and Stephanov have considered an "open moose" as a possible dual model of a QCD-like theory of chiral symmetry breaking. In this note we demonstrate that although the Weinberg sum rules are satisfied in any such model, the…
In their recent paper \cite{Alday:2009aq} Alday, Gaiotto and Tachikawa proposed a relation between $\mathcal{N}=2$ four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories. As part of their conjecture they…
The existence of an exactly marginal deformation in a conformal field theory is very special, but it is not well understood how this is reflected in the allowed dimensions and OPE coefficients of local operators. To shed light on this…
The coding theorem for Kolmogorov complexity states that any string sampled from a computable distribution has a description length close to its information content. A coding theorem for resource-bounded Kolmogorov complexity is the key to…
We argue that nonperturbative CFT correlation functions admit a Mellin amplitude representation. Perturbative Mellin representation readily follows. We discuss the main properties of nonperturbative CFT Mellin amplitudes: subtractions,…
We consider mixed four-point correlators of 1/2-BPS operators $\mathcal{O}_{k}$ in the maximally supersymmetric CFTs, i.e. the 3d $\mathcal{N}=8$, 4d $\mathcal{N}=4$, and 6d $\mathcal{N}=(2,0)$ theories. In arXiv:hep-th/0405180, Dolan,…