Exact integrability of strings in D-dimensional de Sitter spacetime.
Exact integrability of strings in D-dimensional de Sitter spacetime.
复制标题
D 维德西特时空中弦的精确可积性。
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
Sánchez
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文献类型：
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作者：
de Vega HJ;Sánchez
我们证明了在D维de Sitter时空中弦传播的完全可积性。我们发现弦的运动方程，对应于一个非紧O（[italD]，1）-对称[sigma]模型，加上弦的约束，等价于一个广义的sinh-Gordon方程.在[ital D]=2时，这是Liouville方程，在[ital D]=3时，这是标准sinh-Gordon方程，在[ital D]=4时，这个方程与[ital B][sub 2]户田模型有关。我们表明，不稳定性的存在是一个一般的精确功能的弦在德西特空间，作为一个直接后果的强不稳定性的广义sinh-戈登哈密顿量（这是从下面无界），无论任何近似的计划。我们展示了这个广义的sinh-戈登方程，其中涉及扩大和收缩弦的解决方案的Baecklund变换。我们发现所有经典的解决方案在[ital D]=2和物理分析。在[italD]=3和[italD]=4时，我们发现了解在不稳定区域的渐近行为。精确解渐近地展示了弦不稳定性的所有特征：即宇宙时间[itu]对世界表时间[tau]的对数依赖性，[itu][r箭头][+-][无穷大]，弦的伸长（或收缩）更多>>，[tau]与共形时间成比例。«少
We show the complete integrability of the string propagation in [ital D]-dimensional de Sitter spacetime. We find that the string equations of motion, which correspond to a noncompact O([ital D],1)-symmetric [sigma] model, plus the string constraints, are equivalent to a generalized sinh-Gordon equation. In [ital D]=2 this is the Liouville equation, in [ital D]=3 this is the standard sinh-Gordon equation, and in [ital D]=4 this equation is related to the [ital B][sub 2] Toda model. We show that the presence of instability is a general exact feature of strings in de Sitter space, as a direct consequence of the strong instability of the generalized sinh-Gordon Hamiltonian (which is unbounded from below), irrespective of any approximative scheme. We exhibit Baecklund transformations for this generalized sinh-Gordon equation, which relate expanding and shrinking string solutions. We find all classical solutions in [ital D]=2 and physically analyze them. In [ital D]=3 and [ital D]=4, we find the asymptotic behaviors of the solutions in the instability regime. The exact solutions exhibit asymptotically all the characteristic features of string instability: namely, the logarithmic dependence of the cosmic time [ital u] on the world sheet time [tau] for [ital u][r arrow][plus minus][infinity], the stretching (or the shrinking)more » of the proper string size, and the proportionality between [tau] and the conformal time.« less