Integrable perturbation of Yang-Lee model

수학노트
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introduction

  • S-matrix describes the infrared data of the model
  • it is important to check that the UV limit of the model coincides with the conformal field theory that was originally perturbed
  • TBA is a method which provides such a check


perturbed action

  • \(\mathcal{A}_{SLYM}=\mathcal{A}_{M_{2,5}}+i \lambda \int d^2x \varphi(x)\)
  • \(M=(2.642944662\cdots) \lambda^{5/12}\) where \(M\) is the single particle mass
  • http://www.wolframalpha.com/input/?i=2.642944662
  • spin of conserved charges : 1,5,7,11,13,17,19, ...


S-matrix

  • 1 particle
  • S-matrix

\[ S_{11}(\theta)=\tanh \left(\frac{1}{2} \left(\theta -\frac{2 i \pi }{3}\right)\right) \coth \left(\frac{1}{2} \left(\theta +\frac{2 i \pi }{3}\right)\right) \]

  • 커널

\[ \phi_{11}(\theta)=-i\frac{d}{d\theta}\log S_{11}(\theta)=\sqrt{3} \left(\frac{1}{2 \cosh (\theta )+1}+\frac{1}{2 \cosh (\theta )-1}\right) \]


TBA analysis

\[ N=\frac{1}{2\pi}\int_{-\infty}^{\infty}\phi_{11}(\theta)=1 \]


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