论文标题
海森贝格自旋链作为量化弦的世界表格坐标
Heisenberg spin chain as a worldsheet coordinate for lightcone quantized string
论文作者
论文摘要
虽然Heisenberg自旋链的能量谱在一个圆上定义为$ h = \ frac {1} {4} {4} \ sum_ {k = 1}^m（σ_k^xσ_{k+1}^x+σ_k^yt y yesive y noir the boundary conditions vary according to whether $M\in 4\mathbb{N}+r$, where $r=-1,0,1,2$, and also according to the parity of the number of overturned spins in the state, In string theory all these cases must be allowed because interactions involve a string with $M$ spins breaking into strings with $M_1<M$ and $M-M_1$ spins (or vice versa).我们在$δ= 0 $的情况下组织了$ h $的能源谱和变性，其中该系统等同于自由费米子系统。尽管有多种特殊情况，但在限制$ m \至\ infty $的情况下，频谱是一个免费的压缩世界表字段。这样的字段可以解释为紧凑的横弦坐标$ x（σ）\ equiv x（σ）+r_0 $。我们在所有单独的情况下明确构建玻体化公式，并且每个部门都在费莫斯和骨气配方中均给出了Virasoro保形发电机。此外，从文献中的精选类别的激发态的计算中，有强有力的证据表明，$δ\ neq0 $的唯一变化是压实半径$ r_0 \ tor_Δ$的变化。由于$δ\ to-1 $此半径归功于无穷大，从而给出了一个从离散动力学系统中出现的非划界空间的具体示例。最后，我们将工作应用于构造由该机制从骨气坐标出现的字符串所隐含的三个字符串顶点。
Although the energy spectrum of the Heisenberg spin chain on a circle defined by $H=\frac{1}{4}\sum_{k=1}^M(σ_k^xσ_{k+1}^x+σ_k^yσ_{k+1}^y +Δσ_k^zσ_{k+1}^z)$ is well known for any fixed $M$, the boundary conditions vary according to whether $M\in 4\mathbb{N}+r$, where $r=-1,0,1,2$, and also according to the parity of the number of overturned spins in the state, In string theory all these cases must be allowed because interactions involve a string with $M$ spins breaking into strings with $M_1<M$ and $M-M_1$ spins (or vice versa). We organize the energy spectrum and degeneracies of $H$ in the case $Δ=0$ where the system is equivalent to a system of free fermions. In spite of the multiplicity of special cases, in the limit $M\to\infty$ the spectrum is that of a free compactified worldsheet field. Such a field can be interpreted as a compact transverse string coordinate $x(σ)\equiv x(σ)+R_0$. We construct the bosonization formulas explicitly in all separate cases, and for each sector give the Virasoro conformal generators in both fermionic and bosonic formulations. Furthermore from calculations in the literature for selected classes of excited states, there is strong evidence that the only change for $Δ\neq0$ is a change in the compactification radius $R_0\to R_Δ$. As $Δ\to-1$ this radius goes to infinity, giving a concrete example of noncompact space emerging from a discrete dynamical system. Finally we apply our work to construct the three string vertex implied by a string whose bosonic coordinates emerge from this mechanism.
