论文标题
非权益主义领域理论和复杂性的发展
Developments in non-relativistic field theory and complexity
论文作者
论文摘要
本论文重点介绍了两个研究领域：非权威主义的现场理论和复杂性。在第一部分中，我们回顾了与牛顿 - 卡丹背景相连的2+1维场理论的痕量异常的一般分类，并应用热核法来计算特定理论的痕量异常。我们发现了与3+1维相对论对应物的共形异常的关系，这表明存在A Theorem的非相关版本。我们考虑一个模型，以实现$ \ Mathcal {n} = 2 $在2+1个维度中使用非散发性超电势的Bargmann组的超对称性扩展，这是通过无效减少相对性的Wess-Zumino模型获得的。我们检查超电势是否受到量子校正的保护，如相对论的父理论，从而找到了非赋予性化定理的非相关版本。我们发现证据表明该理论是一环准确的，这是由于非权利主义繁殖者的因果结构以及群众保护。在论文的第二部分中，我们回顾了Susskind提出的全息猜想来描述重力中爱因斯坦 - 罗森桥的时间进化：复杂性=体积和复杂性=动作。我们研究了生活在扭曲的$ \ mathrm {ads} _3 $ spacetime中的黑洞的卷和动作。当来自田间理论方面的双重状态混合在一起时，提案的扩展存在。然后，我们通过分析计算BTZ黑洞背景中边界上的一般段的子区域动作复杂性，发现它等于与子区域大小成比例的线性发散期限和与纠缠熵成比例的术语的总和。我们还发现，与相互信息相比，相互全息复杂性具有不同的内容。这意味着熵还不够！
This thesis focuses on two research areas: non-relativistic field theories and complexity. In the first part we review the general classification of the trace anomaly for 2+1 dimensional field theories coupled to a Newton-Cartan background and we apply the heat kernel method to compute the trace anomaly for specific theories. We find a relation with the conformal anomaly of the 3+1 dimensional relativistic counterpart which suggests the existence of a non-relativistic version of the a-theorem. We consider a model realizing a $\mathcal{N}=2$ supersymmetric extension of the Bargmann group in 2+1 dimensions with non-vanishing superpotential, obtained by null reduction of a relativistic Wess-Zumino model. We check that the superpotential is protected against quantum corrections as in the relativistic parent theory, thus finding a non-relativistic version of the non-renormalization theorem. We find evidence that the theory is one-loop exact, due to the causal structure of the non-relativistic propagator together with mass conservation. In the second part of the thesis we review the holographic conjectures proposed by Susskind to describe the time-evolution of the Einstein-Rosen bridge in gravity: the complexity=volume and complexity=action. We investigate both the volume and the action for black holes living in warped $\mathrm{AdS}_3$ spacetime. There exist extensions of the proposals when the dual state from the field theory side is mixed; we then analytically compute the subregion action complexity for a general segment on the boundary in the BTZ black hole background, finding that it is equal to the sum of a linearly divergent term proportional to the size of the subregion and of a term proportional to the entanglement entropy. We also find that mutual holographic complexity carries a different content compared to mutual information. This means that entropy is not enough!
