磁化复杂度与磁简化
Complexity of Magnetization and Magnetic Simplification
AI总结：
采用复杂度=体积规则研究磁场对两种引力模型对偶规范理论中态复杂度的影响，发现磁场直接增加复杂度，但可通过减少非零标量自由度间接降低复杂度，并比较了5D与10D背景下的结果。
摘要：
我们采用复杂度=体积（CV）规则，研究了磁场对两种不同引力模型对偶的规范理论中态的计算复杂度的影响。在其中一个理论中，复杂度随磁场强度增加而增大，而在另一个理论中，我们发现了更有趣的行为，从而产生了一种我们称之为磁简化的现象。这两种理论之间的关键区别在于，第二种理论包含一个具有非零真空期望值的标量算子。这使我们得出结论：磁场的直接影响是增加态的复杂度，但当额外自由度在空间中不为零时，磁场可以通过减少与这些额外自由度相关的复杂度来间接降低复杂度。此外，我们比较了在完整十维背景及其有效五维截断中所得结果，表明在CV规则中应使用哪个曲面（是5D极值曲面的提升还是10D中的极值曲面）这一问题仍然悬而未决。
英文摘要：
We use the complexity=volume (CV) prescription to study the effect of a magnetic field on the computational complexity for states in the gauge theories dual to two different gravitational models. In one of these theories the complexity increases with the intensity of the magnetic field, while in the other a more interesting behavior is discovered, resulting in a phenomenon that we term magnetic simplification. The relevant difference between the two theories is that the content of the second includes a scalar operator with a nonvanishing vacuum expectation value. This leads us to conclude that the direct impact of the magnetic field is to increase the complexity of a state, but it can indirectly lower it by diminishing the complexity associated to additional degrees of freedom when these do not vanish across the space. We additionally compare the results obtained working in the full ten-dimensional backgrounds and in their effective five-dimensional truncations, exhibiting that the question is still current about which surface, whether the uplift of the 5D extremal hypersurface or the extremal surface in 10D, should be used in the CV prescription.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
