arXiv 1602.021662016-02hep-th

最简串式钻头模型的数值研究

Numerical Study of the Simplest String Bit Model

Gaoli Chen, Songge Sun

备注：: 54 pages, 15 figures
发表信息：: Phys. Rev. D 93, 106004 (2016)
DOI：: 10.1103/PhysRevD.93.106004

摘要：

字符串位模型提供了一种可能的方法来制定一个字符串作为一个离散链的点状字符串位。当位数$M$较大时，链表现为连续字符串。我们研究的最简单的情况下，只有一个玻色子位和一个费米子位。创建和湮灭算子是$U\left(N\right)$色群的伴随表示。我们发现，超对称性减少了参数的哈密顿量从7到3，在$N=\infty$，确保连续的能谱，这意味着出现一个空间维度。构造哈密顿量$H_{0}$，使得在大的$N$极限下，它产生具有一个格拉斯曼世界片场的世界片谱。我们集中在有限$N$模型的数值研究。对于哈密顿量$H_{0}$，我们发现对于奇数$M\leq11$，可能的基态在$N=\left(M-1\right)/2$处消失。如果$H$有一个不影响$N=\infty$结果的附加项$ξΔH$，那么这样一个简单的模式就被破坏了。当$ξ$增加（减少）时，消失点移动到更高（更低）的$N$。特别是，$\pm\left(H_{0}-ΔH\right)$的情况下提出了一种可能性，基态可以生存在大$M$和$M\gg N$。我们的研究表明，该模型具有弦性行为：当$N$固定且足够大时，基态能量相对于$M$线性减小，激发能近似为$M^{-1}$阶.我们还验证了一个稳定的系统的哈密顿$\pm H_{0}+ξΔH$需要$ξ\geq\mp1$。

英文摘要：

String bit models provide a possible method to formulate a string as a discrete chain of pointlike string bits. When the bit number $M$ is large, a chain behaves as a continuous string. We study the simplest case that has only one bosonic bit and one fermionic bit. The creation and annihilation operators are adjoint representations of the $U\left(N\right)$ color group. We show that the supersymmetry reduces the parameter number of a Hamiltonian from 7 to 3 and, at $N=\infty$, ensures a continuous energy spectrum, which implies the emergence of one spatial dimension. The Hamiltonian $H_{0}$ is constructed so that in the large $N$ limit it produces a world sheet spectrum with one Grassmann world sheet field. We concentrate on numerical study of the model in finite $N$. For the Hamiltonian $H_{0}$, we find that the would-be ground energy states disappear at $N=\left(M-1\right)/2$ for odd $M\leq11$. Such a simple pattern is spoiled if $H$ has an additional term $ξΔH$ which does not affect the result of $N=\infty$. The disappearance point moves to higher (lower) $N$ when $ξ$ increases (decreases). Particularly, the $\pm\left(H_{0}-ΔH\right)$ cases suggest a possibility that the ground state could survive at large $M$ and $M\gg N$. Our study reveals that the model has stringy behavior: when $N$ is fixed and large enough, the ground energy decreases linearly with respect to $M$, and the excitation energy is roughly of order $M^{-1}$. We also verify that a stable system of Hamiltonian $\pm H_{0}+ξΔH$ requires $ξ\geq\mp1$.

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英文摘要：

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