Related papers: Fake Z

We use holomorphic factorization to find the partition functions of an abelian two-form chiral gauge-field on a flat six-torus. We prove that exactly one of these partition functions is modular invariant. It turns out to be the one that…

Recently, the construction of Narain CFT from a certain class of quantum error correcting codes has been discovered. In particular, the spectral gap of Narain CFT corresponds to the binary distance of the code, not the genuine Hamming…

In this work, we investigate the partition function of 2d CFT under root-$T\bar{T}$ deformation. We demonstrate that the deformed partition function satisfies a flow equation. At large central charge sector, the deformed partition function…

In modular invariant models of flavor, observables must be modular invariant. The observables discussed so far in the literature are functions of the modulus $\tau$ and its conjugate, $\bar\tau$. We point out that certain combinations of…

In this work, we consider a new type of Fourier-like representation of Boolean function $f\colon\{+1,-1\}^n\to\{+1,-1\}$ \[ f(x) = \cos\left(\pi\sum_{S\subseteq[n]}\phi_S \prod_{i\in S} x_i\right). \] This representation, which we call the…

Recently, Mertens, Ono, and the third author studied mock modular analogues of Eisenstein series. Their coefficients are given by small divisor functions, and have shadows given by classical Shimura theta functions. Here, we construct a…

In this paper, we provide a solution to the open problem of computing the Fourier transform of a binary function defined over $n$-bit vectors taking $m$-bit vector values. In particular, we introduce the two-modular Fourier transform (TMFT)…

We prove that any function with real-valued coefficients, whose input is 4 binary variables and whose output is a real number, is perfectly equivalent to a quadratic function whose input is 5 binary variables and is minimized over the new…

The type $\tau$($\alpha$) of an irrational number $\alpha$ measures the extent to which rational numbers can closely approximate $\alpha$. More precisely, $\tau$($\alpha$) is the infimum over those t$\in$R for which…

We calculate the torus partition sum of a general $CFT_2$ with left and right moving conserved currents $J$ and $\bar J$, perturbed by a combination of the irrelevant operators $T\bar T$, $J\bar T$ and $T\bar J$. We use string theory…

We consider the problem of isolating the real roots of a square-free polynomial with integer coefficients using (variants of) the continued fraction algorithm (CF). We introduce a novel way to compute a lower bound on the positive real…

Let $K[x]$ be a polynomial algebra in a variable $x$ over a commutative $\Q$-algebra $K$, and $\G'$ be the monoid of $K$-algebra monomorphisms of $K[x]$ of the type $\s : x\mapsto x+\l_2x^2+... +\l_nx^n$, $\l_i\in K$, $\l_n$ is a unit of…

We discuss the problem to develop a mathematical theory of a certain class of nonrational conformal field theories (CFT) which contain the unitary CFT. A variant of the concept of a modular functor is proposed that appears to be suitable…

Quantifier-free nonlinear arithmetic (QF_NRA) appears in many applications of satisfiability modulo theories solving (SMT). Accordingly, efficient reasoning for corresponding constraints in SMT theory solvers is highly relevant. We propose…

A variant of the Archimedean Positivstellensatz is proved which is based on Archimedean semirings or quadratic modules of generating subalgebras. It allows one to obtain representations of strictly positive polynomials on compact…

We establish a theory of scalar Fourier coefficients for a class of non-holomorphic, automorphic forms on the quaternionic real Lie group $\mathrm{U}(2,n)$. By studying the theta lifts of holomorphic modular forms from $\mathrm{U}(1,1)$, we…

Study of the matrix-level affine algebra $U_{m,K}$ is motivated by conformal field theory and the fractional quantum Hall effect. Gannon completed the classification of $U_{m,K}$ modular-invariant partition functions. Here we connect the…

We introduce a purely Lie algebraic formalization of the Feigin--Tipunin's geometric construction of logarithmic CFTs/VOAs. After reformulating the geometric representation theory of FT construction under this new setting, within this…

We consider chiral fermionic conformal field theories (CFTs) constructed from lattices and investigate their orbifolds under reflection and shift $\mathbb{Z}_2$ symmetries. For lattices based on binary error-correcting codes, we show the…

We investigate the gauging of a $\mathbb{Z}_2$ symmetry in Narain conformal field theories (CFTs) constructed from qudit stabilizer codes. Considering both orbifold and fermionization, we establish a connection between $\mathbb{Z}_2$…