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arXiv 0803.4323hep-th
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弦束缚态的S矩阵

The S-matrix of String Bound States

Gleb Arutyunov, Sergey Frolov

摘要:

我们找到了描述光锥弦西格玛模型在AdS 5 xS 5上两粒子束缚态散射的S矩阵。我们实现了中心扩展SU(2)的M粒子束缚态表象|2)依赖于两个玻色子变量和两个费米子变量的M次齐次(超)对称多项式空间上的代数。M粒子和N粒子束缚态的散射矩阵S^{MN}是作用于相应多项式的乘积的M+N次微分算子。我们要求该算子服从不变条件和Yang-Baxter方程,并在M=1,N=2和M=N=2两种情况下确定了它.我们证明了所得到的S-矩阵满足广义物理幺正性、CPT不变性、宇称变换规则和交叉对称性。虽然dressing因子作为四个参数x_1^+,x_1 ^-,x_2 ^+,x_2 ^-的函数对任何束缚态散射都是普适的,但它服从一个依赖于M和N的交叉对称方程。

英文摘要:

We find the S-matrix which describes the scattering of two-particle bound states of the light-cone string sigma model on AdS5xS5. We realize the M-particle bound state representation of the centrally extended su(2|2) algebra on the space of homogeneous (super)symmetric polynomials of degree M depending on two bosonic and two fermionic variables. The scattering matrix S^{MN} of M- and N-particle bound states is a differential operator of degree M+N acting on the product of the corresponding polynomials. We require this operator to obey the invariance condition and the Yang-Baxter equation, and we determine it for the two cases M=1,N=2 and M=N=2. We show that the S-matrices found satisfy generalized physical unitarity, CPT invariance, parity transformation rule and crossing symmetry. Although the dressing factor as a function of four parameters x_1^+,x_1^-,x_2^+,x_2^- is universal for scattering of any bound states, it obeys a crossing symmetry equation which depends on M and N.

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