arXiv subjects

Doron Gepner

Publications and source records attributed to Doron Gepner.

At least 37 records · Page 2Linked to original sources

arXiv2015

The $\boldsymbol{SO(2r)_2}$ string functions as $\boldsymbol{q}$-diagrams

We discuss our conjecture for simply laced Lie algebras level two string functions of mark one fundamental weights and prove it for the $SO(2r)$ algebra. To prove our conjecture we introduce $q$-diagrams and examine the diagrammatic interpretations of known identities by Euler, Cauchy, Heine, Jacobi and Ramanujan. Interestingly, the diagrammatic approach implies these identities are related in the sense that they represent the first few terms in an infinite series of diagrammatic identities. Furthermore, these diagrammatic identities entail all the identities needed to prove our conjecture as well as generalise it to all $SO(2r)$ level two string functions. As such, our main objective is proving these series of diagrammatic identities thus extending the works mentioned and establishing our conjecture for the $SO(2r)$ level two string functions.

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arXiv2014

On The Characters of Parafermionic Field Theories

We study cosets of the type $H_l/U(1)^r$, where $H$ is any Lie algebra at level $l$ and rank $r$. These theories are parafermionic and their characters are related to the string functions, which are generating functions for the multiplicities of weights in the affine representations. An identity for the characters is described, which apply to all the algebras and all the levels. The expression is of the Rogers Ramanujan type. We verify this conjecture, for many algebras and levels, using Freudenthal Kac formula, which calculates the multiplicities in the affine representations, recursively, up to some grade. Our conjecture encapsulates all the known results about these string functions, along with giving a vast wealth of new ones.

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arXiv2014

New String Theories And Their Generation Number

New heterotic string theories in four dimensions are constructed by tensoring a nonstandard SCFT along with some minimal SCFT's. All such theories are identified and their particle generation number is found. We prove that from the infinite number of new heterotic string theories only the {6} theory predicts three generations as seen in nature which makes it an interesting candidate for further study.

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arXiv2013

On The Real Part of a Conformal Field Theory

Every conformal field theory has the symmetry of taking each field to its adjoint. We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. A general method for computing such quotients is developed using the coulomb gas representation. Examples of parafermions, $SU(2)$ current algebra and the $N=2$ minimal models are described explicitly. The partition functions and the dimensions of the disordered fields are given. This result is a tool for finding new theories.

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arXiv2012

Generalized Rogers Ramanujan Identities from AGT Correspondence

AGT correspondence and its generalizations attracted a great deal of attention recently. In particular it was suggested that $U(r)$ instantons on $R^4/Z_p$ describe the conformal blocks of the coset ${\cal A}(r,p)=U(1)\times sl(p)_r\times {sl(r)_p\times sl(r)_n\over sl(r)_{n+p}}$, where $n$ is a parameter. Our purpose here is to describe Generalized Rogers Ramanujan (GRR) identities for these cosets, which expresses the characters as certain $q$ series. We propose that such identities exist for the coset ${\cal A}(r,p)$ for all positive integers $n$ and all $r$ and $p$. We treat here the case of $n=1$ and $r=2$, finding GRR identities for all the characters.

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arXiv2011

Nonstandard Parafermions and String Compactification

Nonstandard parafermions are built and their central charges and dimensions are calculated. We then construct new N=2 superconformal field theories by tensoring the parafermions with a free boson. We study the spectrum and modular transformations of these theories. Superstring and heterotic strings in four dimensions are then obtained by tensoring the new superconformal field theories along with some minimal models. The generations and antigenerations are studied. We give an example of the $1^2(5,7)$ theory which is shown to have three net generations.

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arXiv2010

Nonabelian parafermions and their dimensions

We propose a generalization of the Zamolodchikov-Fateev parafermions which are abelian, to nonabelian groups. The fusion rules are given by the tensor product of representations of the group. Using Vafa equations we get the allowed dimensions of the parafermions. We find for simple groups that the dimensions are integers. For cover groups of simple groups, we find, for $n.G.m$, that the dimensions are the same as $Z_n$ parafermions. Examples of integral parafermionic systems are studied in detail.

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arXiv2009

Chiral algebras for superconformal interacting bosons

A sort of calculus is developed to find the chiral algebras of N=2 superconformal interacting bosonic models. Many examples are discussed. It is shown that the algebras share a common structure, which we call almost Landau Ginzburg. For one or two generators, the number of relations is equal to the number of generators and they are algebraically independent.

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arXiv2009

On conformal field theories with low number of primary fields

Using Verlinde formula and the symmetry of the modular matrix we describe an algorithm to find all conformal field theories with low number of primary fields. We employ the algorithm on up to eight primary fields. Four new conformal field theories are found which do not appear to come from current algebras. This supports evidence to the fact that rational conformal field theories are far richer than suspected before.

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arXiv2006

Galois groups in rational conformal field theory II. The discriminant

We express the discriminant of the polynomial relations of the fusion ring, in any conformal field theory, as the product of the rows of the modular matrix to the power -2. The discriminant is shown to be an integer, always, which is a product of primes which divide the level. Detailed formulas for the discriminant are given for all WZW conformal field theories.

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arXiv2006

Galois Groups in Rational Conformal Field Theory

It was established before that fusion rings in a rational conformal field theory (RCFT) can be described as rings of polynomials, with integer coefficients, modulo some relations. We use the Galois group of these relations to obtain a local set of equation for the points of the fusion variety. These equations are sufficient to classify all the RCFT, Galois group by Galois group. It is shown that the Galois group is equivalent to the pseudo RCFT group. We prove that the Galois groups encountered in RCFT are all abelian, implying solvability by radicals of the modular matrix.

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arXiv2005

Monte--Carlo Thermodynamic Bethe Ansatz

We introduce a Monte--Carlo simulation approach to thermodynamic Bethe ansatz (TBA). We exemplify the method on one particle integrable models, which include a free boson and a free fermions systems along with the scaling Lee--Yang model (SLYM). It is confirmed that the central charges and energies are correct to a very good precision, typically 0.1% or so. The advantage of the method is that it enables the calculation of all the dimensions and even the particular partition function.

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arXiv2005

On the distribution of prime numbers (II)

Recently, I have defined the so called PDF's (prime distribution factors) which govern the distribution of prime numbers of the type $p,p+a_i$ being all primes up to some number $n$. It was shown that the PDF's are expressible in terms of the basic PDF's which are defined as $a_i-a_j$ or $a_i$ being composed of primes which are less or equal to the number of primes. For example, $p,p+2$ (twin primes), or $p,p+2,p+6$ being all primes (basic triplets). We give here a conjecture for the number of basic prime PDF's in terms of Hardy-Littlewood numbers, thus completing the determination of PDF's. These conjectures are supported by extensive calculations.

math.NT↗

arXiv2003

On the distribution of prime multiplets

The probability of finding a prime multiplet, i.e., a sequence of primes $p$ and $p+a_i$, $i=1... m$, being all primes where $p$ is some prime less than the integer $n$ is naively $1/log(n)^{m+1}$. It is shown that, in reality, it is proportional to this probability by a constant factor which depends on $a_i$ and $m$ but not on $n$, for large $n$. These constants are appellated as PDF (prime distribution factors). Moreover, it is argued that the PDF depend on the $a_i$ in a "week" way, only on the prime factors of the differences $a_i-a_j$ and not on their exponents. For example $p$ and $p+2^s$ will have the exact same probability for all integer $s>0$. The exact formulae for the PDF ratios are given. Moreover, the actual 'basic' PDF's are calculated exactly and are shown to be bigger than 1, which indicates that primes 'repel' each other. An exact asymptotic formula for the number of basic multiplets is given.

math.NT↗

arXiv2002

Field Identifications for Interacting Bosonic Models in N=2 Superconformal Field Theory

We study a family of interacting bosonic representations of the N=2 superconformal algebra. These models can be tensored with a conjugate theory to give the free theory. We explain how to use free fields to study interacting fields and their dimensions, and how we may identify different free fields as representing the same interacting field. We show how a lattice of identifying fields may be built up and how every free field may be reduced to a standard form, thus permitting the resolution of the spectrum. We explain how to build the extended algebra and show that there are a finite number of primary fields for this algebra for any of the models. We illustrate this by studying an example.

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arXiv2001

Unitary representations of SW(3/2,2) superconformal algebra

SW(3/2,2) superconformal algebra is W algebra with two Virasoro operators. The Kac determinant is calculated and the complete list of unitary representations is determined. Two types of extensions of SW(3/2,2) algebra are discussed. A new approach to construction of W algebras from rational conformal field theories is proposed.

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arXiv2001

Pseudoconformal field theory at the "wrong level"

Pseudoaffine theories are characterized by formal replacement of the level to the fractional number: $k\to\frac{k}{q}$, where $q$ is integer strange to $k(g+k)$ ($g$ - dual Coxeter number). An example of "forbidden" $q$ is considered (SU(2), $q=2$). The fusions of obtained theory are similar to the affine ones. Spectra of minimal models are calculated.

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arXiv1999

On New Conformal Field Theories with Affine Fusion Rules

Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have an extended $W$ algebras which are close analogues of affine algebras. Exact character formulae is given, and the realizations are shown to be full fledged unitary conformal field theories.

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