Related papers: Cosets of Meromorphic CFTs and Modular Differentia…
We investigate the admissible vector-valued modular forms having three independent characters and vanishing Wronskian index and determine which ones correspond to genuine 2d conformal field theories. This is done by finding bilinear…
In recent years it has been understood that new rational CFTs can be discovered by applying the coset construction to meromorphic CFTs. Here we turn this approach around and show that the coset construction, together with the classification…
Quasi-characters are vector-valued modular functions having an integral, but not necessarily positive, q-expansion. Using modular differential equations, a complete classification has been provided in arXiv:1810.09472 for the case of two…
Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the coefficient functions (in monic form) have no poles, or poles at special points of moduli…
In the Mathur-Mukhi-Sen (MMS) classification scheme for rational conformal field theories (RCFTs), a RCFT is identified by a pair of non-negative integers $\mathbf{[n, \ell]}$, with $\mathbf{n}$ being the number of characters and…
The coset construction is the most important tool to construct rational conformal field theories with known chiral data. For some cosets at small level, so-called maverick cosets, the familiar analysis using selection and identification…
We provide a simple and general construction of infinite families of consistent, modular-covariant pairs of characters satisfying the basic requirements to describe two-character RCFT. These correspond to solutions of generic second-order…
Two-dimensional rational CFT are characterised by an integer $\ell$, related to the number of zeroes of the Wronskian of the characters. For two-character RCFT's with $\ell<6$ there is a finite number of theories and most of these are…
Modular invariance imposes rigid constrains on the partition functions of two-dimensional conformal field theories. Many fundamental results follow strictly from modular invariance, giving rise to the numerical modular bootstrap program.…
For any root system corresponding to a semisimple simply-laced Lie algebra a logarithmic CFT is constructed. Characters of irreducible representations were calculated in terms of theta functions.
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…
Using the method of modular-invariant differential equations, we classify a family of Rational Conformal Field Theories with two and three characters having no Kac-Moody algebra. In addition to unitary and non-unitary minimal models, we…
In this short note, we present a simple and elementary proof that meromorphic conformal field theories (CFTs) have central charges of the form: $c=8N$ with $N\in\mathbb{N}$ (the set of natural numbers) using the modular linear differential…
Code CFTs are 2d conformal field theories defined by error-correcting codes. Recently, Dymarsky and Shapere generalized the construction of code CFTs to include quantum error-correcting codes. In this paper, we explore this connection at…
We study one-character CFTs obtained as one-character extensions of the tensor products of a single CFT $\mathcal{C}$. The motivation comes from the fact that $28$ of the $71$ CFTs in the Schelleken's list of $c = 24$ CFTs are such CFTs. We…
This book describes some computational methods to deal with modular characters of finite groups. It is the theoretical background of the MOC system of the same authors. This system was, and is still used, to compute the modular character…
Various relations between conformal quantum field theories in one, two and four dimensions are explored. The intention is to obtain a better understanding of 4D CFT with the help of methods from lower dimensional CFT.
We systemically study the Hecke relations and the $c=8k$ coset relations among 2d rational conformal field theories (RCFTs) with up to seven characters. We propose that the characters of any 2d RCFT -- unitary or non-unitary -- satisfying a…
Higher genus modular invariance of two-dimensional conformal field theories (CFTs) is a largely unexplored area. In this paper, we derive explicit expressions for the higher genus partition functions of a specific class of CFTs: code CFTs,…
CFTs are naturally defined on Riemann surfaces. The rational ones can be solved using methods from algebraic geometry. One particular feature is the covariance of the partition function under the mapping class group. In genus $g=1$, this…