arXiv subjects

Alexander Berkovich

Publications and source records attributed to Alexander Berkovich.

60 records · Page 4Linked to original sources

arXiv1998

The perturbation $ϕ_{2,1}$ of the M(p,p+1) models of conformal field theory and related polynomial character identities

Using $q$-trinomial coefficients of Andrews and Baxter along with the technique of telescopic expansions, we propose and prove a complete set of polynomial identities of Rogers-Ramanujan type for M(p, p+1) models of conformal field theory perturbed by the operator $phi_{2,1}$. The bosonic form of our polynomials is closely related to corner transfer matrix sums which arise in the computation of the order parameter in the regime $1^+$ of $A_{p-1}$ dilute models. In the limit where the degree of the polynomials tends to infinity our identities provide new companion fermionic representations for all Virasoro characters of unitary minimal series.

math.QA↗

arXiv1997

Rogers-Schur-Ramanujan type identities for the $M(p,p')$ minimal models of conformal field theory

We present and prove Rogers-Schur-Ramanujan (Bose/Fermi) type identities for the Virasoro characters of the minimal model $M(p,p').$ The proof uses the continued fraction decomposition of $p'/p$ introduced by Takahashi and Suzuki for the study of the Bethe's Ansatz equations of the XXZ model and gives a general method to construct polynomial generalizations of the fermionic form of the characters which satisfy the same recursion relations as the bosonic polynomials of Forrester and Baxter. We use this method to get fermionic representations of the characters $χ_{r,s}^{(p,p')}$ for many classes of $r$ and $s.$

q-alg↗

arXiv1995

N=2 Supersymmetry and Bailey Pairs

We demonstrate that the Bailey pair formulation of Rogers-Ramanujan identities unifies the calculations of the characters of $N=1$ and $N=2$ supersymmetric conformal field theories with the counterpart theory with no supersymmetry. We illustrate this construction for the $M(3,4)$ (Ising) model where the Bailey pairs have been given by Slater. We then present the general unitary case. We demonstrate that the model $M(p,p+1)$ is derived from $M(p-1,p)$ by a Bailey renormalization flow and conclude by obtaining the $N=1$ model $SM(p,p+2)$ and the unitary $N=2$ model with central charge $c=3(1-2/p).$

hep-th↗

arXiv1995

Generalizations of the Andrews-Bressoud Identities for the $N=1$ Superconformal Model $SM(2,4ν)$

We present generalized Rogers-Ramanujan identities which relate the fermi and bose forms of all the characters of the superconformal model $SM(2,4ν).$ In particular we show that to each bosonic form of the character there is an infinite family of distinct fermionic $q-$ series representations.

hep-th↗

arXiv1995

Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4ν)

We prove polynomial identities for the N=1 superconformal model SM(2,4ν) which generalize and extend the known Fermi/Bose character identities. Our proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations for q-series on the fermionic side. We use these polynomials to demonstrate a dual relation under q \rightarrow q^{-1} between SM(2,4ν) and M(2ν-1,4ν). We also introduce a generalization of the Witten index which is expressible in terms of the Rogers false theta functions.

hep-th↗

arXiv1994

Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models

We present fermionic sum representations of the characters $χ^{(p,p')}_{r,s}$ of the minimal $M(p,p')$ models for all relatively prime integers $p'>p$ for some allowed values of $r$ and $s$. Our starting point is binomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin ${1\over 2}$ chain of anisotropy $-Δ=-\cos(π{p\over p'})$. We use the Takahashi-Suzuki method to express the allowed values of $r$ (and $s$) in terms of the continued fraction decomposition of $\{{p'\over p}\}$ (and ${p\over p'}$) where $\{x\}$ stands for the fractional part of $x.$ These values are, in fact, the dimensions of the hermitian irreducible representations of $SU_{q_{-}}(2)$ (and $SU_{q_{+}}(2)$) with $q_{-}=\exp (i π\{{p'\over p}\})$ (and $q_{+}=\exp ( i π{p\over p'})).$ We also establish the duality relation $M(p,p')\leftrightarrow M(p'-p,p')$ and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.

hep-th↗