Cappelli-Itzykson-Zuber A-D-E Classification

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Author: Dr. Andrea Cappelli, Istituto Nazionale Fisica Nucleare, Via G. Sansone, 1, I-50019 Sesto F.no (FI), Italy
Author: Dr. Jean-Bernard Zuber, LPTHE, Université Pierre et Marie Curie,FRANCE

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Cappelli-Itzykson-Zuber A-D-E Classification refers to the classification of modular invariant partition functions of two-dimensional conformal field theories related to the sl(2) affine algebra.

In equation (1)

(1)
\mathcal{H}=...

where\mathcal{H} is the Hilbert space of all ...

Moreover equation (2)

x^2
(2)
\frac{\mathrm{d}}{\mathrm{d}t}\left(x^{y^{z^t}}\right)
(3)


In figure 1 we can see....

As shown by Albero and Bocca (2001)...

Table 1: list of modular...
k\ge 0 \sum_{\lambda=1}^{k+1}|\chi_\lambda|^2 (A_{k+1})
k=4\rho\ge 4 \sum_{\lambda=1}^{k+1}|\chi_\lambda|^2 (A_{k+1})
k=4\rho-2\ge 6 \sum_{\lambda=1}^{k+1}|\chi_\lambda|^2 (A_{k+1})
k= 10 \sum_{\lambda=1}^{k+1}|\chi_\lambda|^2 (A_{k+1})
k= 16 \sum_{\lambda=1}^{k+1}|\chi_\lambda|^2 (A_{k+1})
k=28 \sum_{\lambda=1}^{k+1}|\chi_\lambda|^2 (A_{k+1})

blablablablablabla blabla blabla blabla blabla blabla

Table 2: ADE
h exponents
A_n
n+1 1,2,\cdots,n
A_n
n+1 1,2,\cdots,n


References

  • Albero, Antonio and Bocca, Bill (2001). Pizza Capricciosa. Journal of pizza eaters 27: 121-127. arXiv:0808.000

Further reading

See also

Conformal field theories in two dimensions, Verlinde formula

Invited by: Dr. Riccardo Guida, Institut de Physique Théorique; CEA, IPhT; CNRS; Gif-sur-Yvette, France
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