具有多尺度动力学的全息级联理论中的复杂度度量
Complexity measures in holographic cascading theories with multiscale dynamics
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中文总结 AI 辅助
该研究通过引力对偶，在一类三维规范理论中考察两种复杂度概念，发现理论在不同参数极限下，复杂度对基态禁闭性质的响应存在差异，揭示了多尺度动力学下的相关特性。
中文摘要 AI 辅助
利用引力对偶，我们对一类具有丰富红外结构的三维规范理论中的两种复杂度概念开展系统研究。对于热场双态，我们采用复杂度=体积（complexity=volume）方案，将计算复杂度与对偶爱因斯坦-罗森桥（Einstein-Rosen bridge）的体积关联起来。对于通过在真空中插入定域算符产生的单粒子态，我们研究其在克雷洛夫（Krylov）空间中的扩散，该扩散由体激发的径向动量全息编码。我们在理论的整个参数空间中考察这两种复杂度概念，重点关注一个可调参数的两个极限值。在理论流向中间共形不动点附近的极限附近，两种复杂度均呈现出“行走”动力学的不同表现形式。在相反极限附近，计算复杂度对基态的禁闭性质基本不敏感，而由新兴红外标度设定的克雷洛夫扩散复杂度的振荡频率则对禁闭的存在敏感。
英文摘要
Using the gravitational duals, we perform a systematic study of two notions of complexity in a family of three-dimensional gauge theories with rich infrared structure. For thermofield double states, we employ the complexity=volume prescription, which relates computational complexity to the volume of the dual Einstein-Rosen bridge. For one particle states created by the insertion of a local operator on the vacuum, we study their spreading in Krylov space, encoded holographically by the radial momentum of bulk excitations. We investigate these two notions of complexity across the parameter space of the theories, focusing on the two limiting values of a tunable parameter. Near the limit where the theories flow close to an intermediate conformal fixed point, both notions reveal distinct manifestations of ``walking'' dynamics. Near the opposite limit, computational complexity is largely insensitive to the confining nature of the ground state, whereas the frequency of oscillations in the Krylov spread complexity -- set by the emerging infrared scale -- is sensitive to the presence of confinement.
