Related papers: Holomorphic modular bootstrap revisited
In this paper we deploy for the first time Reinforcement-Learning algorithms in the context of the conformal-bootstrap programme to obtain numerical solutions of conformal field theories (CFTs). As an illustration, we use a soft…
We prove existence and uniqueness of complex Hodge structures on modular functors. The proof is based on the non-Abelian Hodge correspondence and Ocneanu rigidity. Given a modular functor, we explain how its Hodge numbers fit into a…
We find the Holographic Renormalization Group equations for the holographic duals of generic gravity theories coupled to form fields and spin-1/2 fermions. Using Hamilton-Jacobi theory we discuss the structure of Ward identities, anomalies,…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…
We provide and discuss complex analytic methods for overcoming the formal character of formal deformation quantization. This is a necessity for returning to physically meaningful statements, and accounts for the fact that the formal…
We consider a two-dimensional conformal field theory which contains two kinds of the bosonic degrees of freedom. Two linear dilaton fields enable us to study a more general case. Various properties of the model such as OPEs, central charge,…
We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising…
Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the $\varepsilon$ expansion. In an earlier…
We present a method for classifying conformal field theories based on Coulomb gases (bosonic free-field construction). Given a particular geometric configuration of the screening charges, we give necessary conditions for the existence of…
We consider the problems of determining the feasibility of a linear congruence, producing a solution to a linear congruence, and finding a spanning set for the nullspace of an integer matrix, where each problem is considered modulo an…
Let K be a subfield of the complex numbers, and let D be the Weyl algebra of K-linear differential operators on K[x_1,...,x_n]. If M and N are holonomic left D-modules we present an algorithm that computes explicit generators for the finite…
Planar holomorphic systems $\dot{x}=u(x,y)$, $\dot{y}=v(x,y)$ are those that $u=\operatorname{Re}(f)$ and $v=\operatorname{Im}(f)$ for some holomorphic function $f(z)$. They have important dynamical properties, highlighting, for example,…
In this paper we express certain multiplicities in modular representation-theoretic categories of type A in terms of affine p-Kazhdan-Lusztig polynomials. The representation-theoretic categories we deal with include the categories of…
I investigate modal group theory for arbitrary homomorphisms. Possibility is interpreted by the existence of a group homomorphism out of the given group, so the semantics is governed by the possibility of collapse: elements may be…
In a recent paper Flohr, Grabow and Koehn conjectured that the characters of the logarithmic conformal field theory c_{k,1}, of central charge c=1-6(k-1)^2/k, admit fermionic representations labelled by the Lie algebra D_k. In this note we…
This paper focuses on the analysis of $4d$ $\mathcal{N}=4$ superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is…
We review the relations between Jordan cells in various branches of physics, ranging from quantum mechanics to massive gravity theories. Our main focus is on holographic correspondences between critically tuned gravity theories in Anti-de…
Relaxed highest-weight modules play a central role in the study of many important vertex operator (super)algebras and their associated (logarithmic) conformal field theories, including the admissible-level affine models. Indeed, their…
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…
Assuming the existence of a field theory in D dimensions dual to (D+1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review…