"Characters of superconformal algebra and mock theta functions"의 두 판 사이의 차이

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==introduction==
 
==introduction==
  
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==$\mathcal{N}=4$ superconformal algebra==
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===$c=6k$ with $k=1$ case===
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* non-BPS characters : $h>k/4,\ell=1/2$
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$$
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\operatorname{ch}^{\tilde R}_{h=1/4+n,\ell=0}
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$$
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* BPS characters : $h=1/4,\ell=0,1/2$
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$$
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\operatorname{ch}^{\tilde R}_{h=1/4,\ell=0}=\frac{[\theta_{11}(z;\tau)]^2}{\eta^3}\mu(z;\tau)\\
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\operatorname{ch}^{\tilde R}_{h=1/4,\ell=1/2}
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$$
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where $\mu(z;\tau)$ is the [[Appell-Lerch sums]] which is a holomorphic part of a mock modular form
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* this is related to [[Mathieu moonshine]] and the elliptic genus of K3 surface
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===$k\geq 2$ case===
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* this is related to [[Umbral moonshine]] and elliptic genus of hyperKahler manifolds of complex dimension $2k$
  
  

2013년 7월 26일 (금) 09:32 판

introduction

$\mathcal{N}=4$ superconformal algebra

$c=6k$ with $k=1$ case

  • non-BPS characters : $h>k/4,\ell=1/2$

$$ \operatorname{ch}^{\tilde R}_{h=1/4+n,\ell=0} $$

  • BPS characters : $h=1/4,\ell=0,1/2$

$$ \operatorname{ch}^{\tilde R}_{h=1/4,\ell=0}=\frac{[\theta_{11}(z;\tau)]^2}{\eta^3}\mu(z;\tau)\\ \operatorname{ch}^{\tilde R}_{h=1/4,\ell=1/2} $$ where $\mu(z;\tau)$ is the Appell-Lerch sums which is a holomorphic part of a mock modular form


$k\geq 2$ case

  • this is related to Umbral moonshine and elliptic genus of hyperKahler manifolds of complex dimension $2k$




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