Related papers: Updating the holomorphic modular bootstrap

The modular properties of fractional level affine sl(2)-theories and, in particular, the application of the Verlinde formula, have a long and checkered history in conformal field theory. Recent advances in logarithmic conformal field theory…

We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…

We consider integrable models of the Haldane-Shastry type with open boundary conditions. We define monodromy matrices, obeying the reflection equation, which generate the symmetries of these models. Using a map to the Calogero-Sutherland…

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 observe that every self-dual ternary code determines a holomorphic N=1 superconformal field theory. This provides ternary constructions of some well-known holomorphic N=1 SCFTs, including Duncan's "supermoonshine" model and the fermionic…

Rational CFT's are classified by an integer $\ell$, the number of zeroes of the Wronskian of their characters in moduli space. For $\ell=0$ they satisfy non-singular modular-invariant differential equations, while for $\ell>0$ the…

A formula is presented for the modular transformation matrix S for any simple current extension of the chiral algebra of a conformal field theory. This provides in particular an algorithm for resolving arbitrary simple current fixed points,…

We study the conformal bootstrap of 1D CFTs on the straight Maldacena-Wilson line in 4D ${\cal N}=4$ super-Yang-Mills theory. We introduce an improved truncation scheme with an 'OPE tail' approximation and use it to reproduce the…

For a finite tensor category $\mathcal C$ and a Hopf monad $T:\mathcal C\to \mathcal C$ satisfying certain conditions we describe exact indecomposable left $\mathcal C^T$-module categories in terms of left $\mathcal C$-module categories and…

Bootstrap equations for conformal correlators that mimic the early theory of conformal bootstrap are written down in frames of the AdS/CFT approach. The simplified version of these equations, that may be justified if Schwinger-Keldysh…

We use the numerical bootstrap to study conformal line defects with $O(2)$ global symmetry. Our results are very general and capture in particular conformal line defects originating from bulk CFTs with a continuous global symmetry, which…

Modular linear differential equations (MLDE) play a significant role in the classification of two-dimensional CFTs, where the modular forms in the equations belonged to the space of $\text{SL}(2,\mathbb{Z})$. A systematic study of the…

We study the constraints of crossing symmetry and unitarity for conformal field theories in the presence of a boundary, with a focus on the Ising model in various dimensions. We show that an analytic approach to the bootstrap is feasible…

Let $\mathscr{C}$ be a modular tensor category over an algebraically closed field $k$ of characteristic 0. Then there is the ubiquitous notion of the S-matrix $S(\mathscr{C})$ associated with the modular category. The matrix…

We propose a new approach towards analytically solving for the dynamical content of Conformal Field Theories (CFTs) using the bootstrap philosophy. This combines the original bootstrap idea of Polyakov with the modern technology of the…

Given two two-dimensional conformal field theories, a domain wall -- or defect line -- between them is called invertible if there is another defect with which it fuses to the identity defect. A defect is called topological if it is…

We continue our study of the defect CFT on a Maldacena-Wilson line in N=4 Super-Yang-Mills theory using Bootstrability -- the conformal bootstrap supplemented with exact integrability data. In this paper, we extend this program to charged…

We implement methods that efficiently impose integrality -- i.e., the condition that the coefficients of characters in the partition function must be integers -- into numerical modular bootstrap. We demonstrate the method with a number of…

We study the computational complexity of satisfiability problems for classes of simple finite height (ortho)complemented modular lattices $L$. For single finite $L$, these problems are shown tobe $\mc{NP}$-complete; for $L$ of height at…

We calculate the fusion rules among $\mathbb{Z}_2$-twisted modules $L_{\mathfrak{sl}_2}(\ell,0)$ at admissible levels. We derive a series MLDEs for normalized characters of ordinary twisted modules of quasi-lisse vertex algebras. Examples…