Related papers: Classical Codes and Chiral CFTs at Higher Genus
A classical result from analytic number theory by Rademacher gives an exact formula for the Fourier coefficients of modular forms of non-positive weight. We apply similar techniques to study the spectrum of two-dimensional unitary conformal…
The goal of this paper is to propose a new way to generalize the Weierstrass sigma-function to higher genus Riemann surfaces. Our definition of the odd higher genus sigma-function is based on a generalization of the classical representation…
We propose conformal polynomial coordinates for 2D closed high-order cages, which consist of polynomial curves of any order. The coordinates enable the transformation of the input polynomial curves into polynomial curves of any order. We…
We present an analytic study of conformal field theories on the real projective space $\mathbb{RP}^d$, focusing on the two-point functions of scalar operators. Due to the partially broken conformal symmetry, these are non-trivial functions…
Certain integrable models are described by pairs (X,Y) of ADET Dynkin diagrams. At high energy these models are expected to have a conformally invariant limit. The S-matrix of the model determines algebraic equations, whose solutions are…
In this study, we examine the modular transformations of the (root-)$\text{T}\overline{\text{T}}$ deformed torus partition function of a two-dimensional CFT (with a gravitational anomaly) from the holographic perspective by computing the…
Two-dimensional conformal field theory is a powerful tool to understand the geometry of surfaces. Here, we study Liouville conformal field theory in the classical (large central charge) limit, where it encodes the geometry of the moduli…
Idempotent Boolean functions form a highly structured subclass of Boolean functions that is closely related to rotation symmetry under a normal-basis representation and to invariance under a fixed linear map in a polynomial basis. These…
Chordal and factor-width decomposition methods for semidefinite programming and polynomial optimization have recently enabled the analysis and control of large-scale linear systems and medium-scale nonlinear systems. Chordal decomposition…
The coefficient $C_T$ of the conformal energy-momentum tensor two-point function is determined for the non-unitary scalar CFTs with four- and six-derivative kinetic terms. The results match those expected from large-$N$ calculations for the…
The analytic contribution to the low energy expansion of Type II string amplitudes at genus-one is a power series in space-time derivatives with coefficients that are determined by integrals of modular functions over the complex structure…
We study symmetric products of the chiral 'Monster' conformal field theory with c=24 in the grand canonical ensemble by introducing a complex parameter \rho, whose imaginary part represents the chemical potential \mu conjugate to the number…
We consider the problem of computing (irregular) conformal blocks in 2d CFTs whose chiral symmetry algebra is the N=2 superconformal algebra. Our construction uses two ingredients: (i) the relation between the representation theories of the…
We present an analytic way of writing simple crossing symmetric expressions and use them to search for unitary 4-point functions in 2D CFTs. We've applied our method for a class of functions we called generalized polynomials to achieve…
We show how to construct a large class of quantum error correcting codes, known as CSS codes, from highly entangled cluster states. This becomes a primitive in a protocol that foliates a series of such cluster states into a much larger…
We identify Narain conformal field theories (CFTs) that correspond to code lattices for quantum error-correcting codes (QECC) over integers of cyclotomic fields $Q(\zeta_p)$ $(\zeta_p=e^{\frac{2\pi i}p})$ for general prime $p\geq 3$. This…
In the path integral formulation of the superstring, the chiral measure acquires a phase under the modular transformation of a Riemann surface. This motivated the use of anomaly inflow to define the superstring chiral measure by a path…
Conformal field theories (CFTs) are associated with critical phenomena and phase transitions and also play an essential role in string theory. Solving a CFT is an extremely constrained problem due to conformal invariance -- the task…
The dependence of the Virasoro-$N$-point function on the moduli of the Riemann surface is investigated. We propose an algebraic geometric approach that applies to any hyperelliptic Riemann surface.
Lyubashenko's construction associates representations of mapping class groups Map_{g,n} of Riemann surfaces of any genus g with any number n of holes to a factorizable ribbon category. We consider this construction as applied to the…