ISSN:
1573-0530
Keywords:
81T10
;
conformal field theory
;
fermionic sum representations
;
continued fractions
;
Andrews-Bailey transformations
;
Rogers-Ramanujan identities
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract We present fermionic sum representations of the characters χ τ, s (p, p′) 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 biomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin 1/2 chain of anisotropy −Δ=−cos(π(p/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/p′} (and p/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(iπ{p/p}) (and q+=exp(iπ(p/p′))). We also establish the duality relation M(p,p′) ↔ 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00400138
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