论文标题
双杨 - 巴克斯特旋转字符串变形
Double Yang-Baxter deformation of spinning strings
论文作者
论文摘要
我们研究了在$ \ hbox {ads} _3 \ times \ hbox {s}^3 \ times \ times \ hbox {t \ hbox {t}^4 $背景的$ \ hbox {ads} _3 \ times \ hbox {s} _3 \ times \ hbox {s}^3 \ hbox {ads} _3 \ times \ hbox {ads} _3 \ times \ hbox {ads} _3 \ times \ hbox {ads}^4 $背景中的经典弦的减少。通用旋转的ANSATZ的使用导致Neumann-Rosochatius系统的整合变形。该系统的整合性源于以下事实：Uhlenbeck常数的通常约束适用于尊重三个球体的等距坐标的任何变形。我们根据基础椭圆形坐标为系统构建解决方案。解决方案取决于变形参数的域以及第四阶多项式的根的现实条件。当根部变性时，我们会获得恒定的-dradii，巨麦农和三角溶液，并在未构造的极限中分析可能的溶液。如果变形参数纯粹是虚构的，并且多项式涉及两个复杂偶联的根，则我们找到了一类新的溶液。新类别在无限时期的退化极限中与双重巨型马格农溶液相连。
We study the reduction of classical strings rotating in the deformed three-sphere truncation of the double Yang-Baxter deformation of the $\hbox{AdS}_3 \times \hbox{S}^3 \times \hbox{T}^4$ background to an integrable mechanical model. The use of the generalized spinning-string ansatz leads to an integrable deformation of the Neumann-Rosochatius system. Integrability of this system follows from the fact that the usual constraints for the Uhlenbeck constants apply to any deformation that respects the isometric coordinates of the three-sphere. We construct solutions to the system in terms of the underlying ellipsoidal coordinate. The solutions depend on the domain of the deformation parameters and the reality conditions of the roots of a fourth order polynomial. We obtain constant-radii, giant-magnon and trigonometric solutions when the roots degenerate, and analyze the possible solutions in the undeformed limit. In the case where the deformation parameters are purely imaginary and the polynomial involves two complex-conjugated roots, we find a new class of solutions. The new class is connected with twofold giant-magnon solutions in the degenerate limit of infinite period.
