Related papers: The Analytic Functional Bootstrap I: 1D CFTs and 2…
We consider the conformal bootstrap for spacetime dimension $1<d<2$. We determine bounds on operator dimensions and compare our results with various theoretical and numerical models, in particular with resummed $\epsilon$-expansion and…
Capillarity functionals are parameter invariant functionals defined on classes of two-dimensionals parametric surfaces in R3 as the sum of the area integral with an anisotropic term of suitable form. In the class of parametric surfaces with…
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 review the recent developments in the study of conformal field theories in generic space time dimensions using the methods of the conformal bootstrap, in its analytic aspect. These techniques are based solely on symmetries, in particular…
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.…
We investigate the holographic description of CFTs defined on the cylinder and on AdS, which include an operator saturating the unitarity bound. The standard Klein-Gordon field with the corresponding mass and boundary conditions on global…
We elaborate on the symmetry breaking pattern involved in the Penrose limit of $AdS_{d+1} \times S^{d+1}$ spacetimes and the corresponding limit of the CFT dual. For d=2 we examine in detail how the symmetries contract to products of…
We study the conformal bootstrap constraints for 4D $\mathcal{N}=1$ superconformal field theories containing a chiral operator $\phi$ and the chiral ring relation $\phi^2=0$. Hints for a minimal interacting SCFT in this class have appeared…
We explore the Mellin representation of conformal correlation functions recently proposed by Mack. Examples in the AdS/CFT context reinforce the analogy between Mellin amplitudes and scattering amplitudes. We conjecture a simple formula…
Gravity solutions dual to d-dimensional field theories at finite charge density have a near-horizon region which is AdS_2 x R^{d-1}. The scale invariance of the AdS_2 region implies that at low energies the dual field theory exhibits…
In this work we initiate the conformal bootstrap program for ${\mathcal N}=2$ superconformal field theories in four dimensions. We promote an abstract operator-algebraic viewpoint in order to unify the description of Lagrangian and…
We test the AdS/CFT correspondence in the case of a d=4 N=2 SCFT by comparing chiral anomalies which are of order N in the 't Hooft large N limit. These include corrections of order 1/N to the conformal anomaly, thus testing the…
We generalize Regge theory to correlation functions in conformal field theories. This is done by exploring the analogy between Mellin amplitudes in AdS/CFT and S-matrix elements. In the process, we develop the conformal partial wave…
We study three prominent diagnostics of chaos and scrambling in the context of two-dimensional conformal field theory: the spectral form factor, out-of-time-ordered correlators, and unitary operator entanglement. With the observation that…
We formulate the conformal bootstrap approach to four--fermion theory at its strong coupling fixed point in dimensions $2<d<4$. We present a solution of the bootstrap equations in the five--vertex approximation. We show that the bootstrap…
Simplest examples of AdS/CFT duality correspond to free CFTs in d dimensions with fields in vector or adjoint representation of an internal symmetry group dual in the large N limit to a theory of massless or massless plus massive higher…
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…
The Gross-Neveu model defines a unitary CFT of interacting fermions in $2<d<4$ which has perturbative descriptions in the $1/N$ expansion and in the epsilon-expansion near two and four dimensions. In each of these descriptions, the CFT has…
We study scalar conformal field theories whose large $N$ spectrum is fixed by the operator dimensions of either Ising model or Lee-Yang edge singularity. Using numerical bootstrap to study CFTs with $S_N\otimes Z_2$ symmetry, we find a…
We study the ratio of the entropy to the total energy in conformal field theories at finite temperature. For the free field realizations of {\cal N}=4 super Yang-Mills theory in D=4 and the (2,0) tensor multiplet in D=6, the ratio is…