N=2 Supersymmetry and Bailey Pairs

Abstract

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 $c=3(1-2/p).$

32 pages in harvmac, no figures

References in corpus (10)

• Fermionic Sum Representations for Conformal Field Theory Characters
• Fermionic counting of RSOS-states and Virasoro character formulas for the unitary minimal series M(ν,ν+1). Exact results
• Extended N=2 Superconformal Structure of Gravity and W-Gravity Coupled to Matter
• Fermionic Character Sums and the Corner Transfer Matrix
• d\leq1\bigcup d\geq25$andConstrainedKPHierarchyfromBRSTInvarianceinthe$c\neq3$ Topological Algebra
• A BRST Operator for non-critical W-Strings
• Polynomial identities of the Rogers--Ramanujan type
• Multinomials and Polynomial Bosonic Forms for the Branching Functions of the $\widehat{su}(2{)}_M\times \widehat{su}(2{)}_N/\widehat{su}(2{)}_{M+N}$ Conformal Coset Models
• Polynomial Fermionic Forms for the Branching Functions of the Rational Coset Conformal Field Theories $\widehat{su}(2{)}_M\times \widehat{su}(2{)}_N/\widehat{su}(2{)}_{M+N}$}
• RG Flows of Non-Unitary Minimal CFTs

Cited by in corpus (6)

• Bailey flows and Bose-Fermi identities for the conformal coset models $(A_1^{(1)}{)}_N\times (A_1^{(1)}{)}_{N^{\prime }}/(A_1^{(1)}{)}_{N+N^{\prime }}$
• A Higher-level Bailey Lemma
• The universal chiral partition function for exclusion statistics
• Conjugate Bailey pairs
• A Higher-Level Bailey Lemma: Proof and Application
• Central Charge and the Andrews-Bailey Construction