Related papers: The Analytic Functional Bootstrap II: Natural Base…
Infrared fixed points of gauge theories provide intriguing targets for the modern conformal bootstrap program. In this work we provide some preliminary evidence that a family of gauged fermionic CFTs saturate bootstrap bounds and can…
We consider the correlation functions of Coulomb branch operators in four-dimensional N=2 Superconformal Field Theories (SCFTs) involving exactly one anti-chiral operator. These extremal correlators are the "minimal" non-holomorphic local…
In this paper, we give a geometric interpretation of optimal functionals in the context of intersection of symmetry planes and cyclic polytopes. For 1D CFTs, we demonstrate that at given derivative order, the functional is given by a…
We investigate the constraints of crossing symmetry on CFT correlation functions. Four point conformal blocks are naturally viewed as functions on the upper-half plane, on which crossing symmetry acts by PSL(2,Z) modular transformations.…
Recently, boundary conformal field theories (BCFTs) have attracted much attention in the context of quantum gravity. This is because a BCFT can be dual to gravity coupled to a heat bath CFT, known as the island model. On this background, it…
We consider Deep Inelastic Scattering (DIS) thought experiments in unitary Conformal Field Theories (CFTs). We explore the implications of the standard dispersion relations for the OPE data. We derive positivity constraints on the OPE…
We give a differentially closed description of the uniformizing representation to the analytical apparatus on Riemann surfaces and orbifolds of finite analytic type. Apart from well-known automorphic functions and Abelian differentials it…
Correlation functions of local operators in Quantum Field Theory (QFT) on hyperbolic space can be fully characterized by the set of QFT data $\lbrace \Delta_i,C_{ijk},b^{\hat{\mathcal{O}}}_j\rbrace$. These are the scaling dimensions of…
The non-renormalization of the 3-point functions $tr X^{k_1} tr X^{k_2} tr X^{k_3}$ of chiral primary operators in N=4 super-Yang-Mills theory is one of the most striking facts to emerge from the AdS/CFT correspondence. A two-fold puzzle…
We explore extreme value phenomena in spatial scale-free random graphs in a continuum setting based on a homogeneous Poisson point process in $\mathbb{R}^d$. Vertices carry i.i.d. weights $(W_x)$ and, conditionally on the vertex set and the…
We continue to investigate planar four point worldsheet correlators of string theories which are conjectured to be duals of free gauge theories. We focus on the extremal correlators <Tr(Z^{J_1}(x)) Tr(Z^{J_2}(y)) Tr(Z^{J_3}(z))…
We develop an analytic approach to the four-point crossing equation in CFT, for general spacetime dimension. In a unitary CFT, the crossing equation (for, say, the s- and t-channel expansions) can be thought of as a vector equation in an…
It is expected that conformal symmetry is an emergent property of many systems at their critical point. This imposes strong constraints on the critical behavior of a given system. Taking them into account in theoretical approaches can lead…
We show that extremal correlators in all Lagrangian ${\cal N}=2$ superconformal field theories with a simple gauge group are governed by the same universal Toda system of equations, which dictates the structure of extremal correlators to…
We develop the analytic bootstrap in several directions. First, we discuss the appearance of nonperturbative effects in the Lorentzian inversion formula, which are exponentially suppressed at large spin but important at finite spin. We show…
We review some aspects of harmonic analysis for the Euclidean conformal group, including conformally-invariant pairings, the Plancherel measure, and the shadow transform. We introduce two efficient methods for computing these quantities:…
We give an introductory account of the recent hyperdensity functional theory for the equilibrium statistical mechanics of soft matter systems [F. Samm\"uller et al., Phys. Rev. Lett. 133, 098201 (2024); 10.1103/PhysRevLett.133.098201].…
We study correlation functions of spectrally-flowed vertex operators in bosonic string theory on $\text{AdS}_3\times X$ in the path integral formalism. By restricting the path integral to only include worldsheets which live near the…
We study the operator product expansion (OPE) of identical scalars in a conformal four-point correlator as a Stieltjes moment problem, and use Riemann-Liouville type fractional differential operators to generate classical moments from the…
It is shown explicitly that the correlation functions of Conformal Field Theories (CFT) with the logarithmic operators are invariant under the differential realization of Borel subalgebra of $\W_\infty$-algebra. This algebra is constructed…