c-theorem of the entanglement entropy

We holographically investigate the renormalization group flow in a two-dimensional conformal field theory deformed by a relevant operator. If the relevant operator allows another fixed point, the UV conformal field theory smoothly flows to a new IR conformal field theory. From the holographic point of view, such a renormalization group flow can be realized as a dual geometry interpolating two different AdS boundaries. On this interpolating geometry, we investigate how the c-function of the entanglement entropy behaves along the RG flow analyt- ically and numerically, which reproduces the expected central charges of UV and IR. We also show that the c-function monotonically decreases from UV to IR without any phase transition.Comment: 24 pages, 8 figure

Quantum correlation in quark-gluon medium

We study thermodynamics and quantum correlations of the string cloud geometry whose field theory dual is the quark-gluon medium. We found the novel universality of the entanglement entropy first law in the high quark density limit. We also showed that a correlation function generally decreases as the entanglement entropy of the background medium increases due to the screening effect of the background. We study the UV and IR effects of the medium on phase transition behaviour observed in the holographic mutual information using both perturbative and numerical computations. Moreover, by numerical computation, we show that in the IR region the critical length obtained from the mutual information behaves similar to the correlation length of the two-point function.Comment: 18 pages, 2 figures, reference added, minor change

Holographic Entanglement Entropy with Momentum Relaxation

We studied the holographic entanglement entropy for a strip and sharp wedge entangling regions in momentum relaxation systems. In the case of strips, we found analytic and numerical results for the entanglement entropy and showed the effect on the minimal surface by the electric field. We also studied the entanglement entropy of wedges and confirmed that there is a linear change in the electric field. This change is proportional to the thermoelectric conductivity, $\bar\alpha$, that can be measured.Comment: 22 pages and 15 figures, enlarged version with clarifications, references adde

End of the World Perspective to BCFT

In this work, we study the end-of-the-world (EOW) branes anchored to the boundaries of BCFT${}_2$ dual to the BTZ black hole. First, we explore the thermodynamics of the boundary system consisting of the conformal boundary and two EOW branes. This thermodynamics is extended by the tension appearing as the effective cosmological constant of JT black holes on the EOW branes. The tension contribution is identified with the shadow entropy equivalent to the boundary entropy of the BCFT${}_2$. The thermodynamics of the JT black holes and the bulk of BCFT${}_2$ can be combined into a novel grafted thermodynamics based on the first law. Second, we focus on the observer's view of the EOW branes by lowering the temperature. We show that the EOW branes generate a scale called ``reefs" inside the horizon. This scale also appears in the grafted thermodynamics. At high temperatures, observers on the EOW branes see their respective event horizons. The reef starts to grow relatively to the horizon size at the temperature, $T_{grow}$. As the temperature cools down the reef area fills the entire interior of the JT black holes at the temperature $T_{out}$. Then, the observers recognize their horizons disappear and see the large density of the energy flux. At this temperature, the two JT regions become causally connected. This connected spacetime has two asymptotic $AdS_2$ boundaries with a conformal matter. Also, we comment on the grafted thermodynamics to higher dimensions in Appendix B.Comment: 29 pages, 9 figure

Self-supervised debiasing using low rank regularization

Spurious correlations can cause strong biases in deep neural networks, impairing generalization ability. While most existing debiasing methods require full supervision on either spurious attributes or target labels, training a debiased model from a limited amount of both annotations is still an open question. To address this issue, we investigate an interesting phenomenon using the spectral analysis of latent representations: spuriously correlated attributes make neural networks inductively biased towards encoding lower effective rank representations. We also show that a rank regularization can amplify this bias in a way that encourages highly correlated features. Leveraging these findings, we propose a self-supervised debiasing framework potentially compatible with unlabeled samples. Specifically, we first pretrain a biased encoder in a self-supervised manner with the rank regularization, serving as a semantic bottleneck to enforce the encoder to learn the spuriously correlated attributes. This biased encoder is then used to discover and upweight bias-conflicting samples in a downstream task, serving as a boosting to effectively debias the main model. Remarkably, the proposed debiasing framework significantly improves the generalization performance of self-supervised learning baselines and, in some cases, even outperforms state-of-the-art supervised debiasing approaches