The Anti-de Sitter/Conformal field theory (AdS/CFT) correspondence is a conjecture that was first proposed in 1997 by Juan Maldacena in the framework of string theory, which has been developed as a consistent theory to combine gravity and quantum mechanics. The conjecture equates two seemingly very different theories to each other: a 4+1 dimensional weakly coupled gravity theory and a 3+1 dimensional strongly coupled conformal field theory. Soon after string theorists found more and more evidence to support this conjecture, they started to discover that AdS/CFT correspondence has a lot of implications and applications in various areas of physics and connects many unrelated theories together, e.g. quantum gravity, quantum field theory, hydrodynamics, nuclear physics, QCD, quantum information etc. In 2007, physicists (both high energy and condensed matter theorists) started to use AdS/CFT correspondence to solve strongly coupled condensed matter problems. AdS/CFT correspondence is a strong-weak duality, i.e. weakly coupled gravity theory in the classical limit corresponds to strongly coupled quantum field theory at the boundary. This allows us to look at difficult strongly coupled problems using the language of weakly coupled gravity theory. AdS/CFT correspondence also provides a useful tool to study the real time propagators compared to the conventional methods in condensed matter physics. AdS/CMT (applications of AdS/CFT to condensed matter (CM) theories) has been a very fruitful research area during the last ten years and has become more closely related to experiments in condensed matter physics.
However, there has been a missing piece in the AdS/CMT realm, which is the dual of topologically nontrivial CM systems. In the CM community, there has been a lot of interest in various topological CM systems recently. The concept of topology in CM systems has been developed in the weakly coupled limit and an immediate question that arises is whether nontrivial topological systems still exist at strong coupling. Does there exist a duality between a certain geometry in weakly coupled gravity theory and topologically nontrivial state? If it exists, is there any novel prediction or hint from the gravity side for the dual topological system? As a first step to answer these question, the objective of the first part of the project is to build a holographic model for a topological gapless Weyl semimetal (WSM) state and study possible implications of the holographic model to the transport behavior of a topological WSM system.
Besides the topological nature of WSM systems, there is another important feature that a WSM possesses, the chiral anomaly, which qualitatively affects the transport behavior of not only the WSM but also other systems which have chiral anomaly. For these systems, there is a special transport behavior called negative magnetoresistivity (NMR). Since the year 2013, there has been a lot of observation of NMR for many different kinds of materials in laboratories. The behavior of NMR could be calculated in the weakly coupled kinetic theory and the result shows that at small magnetic field (B), the DC longitudinal magnetoconductivity has a squared behavior in the magnetic field while at large B, it grows linearly in B. However, in different materials different scaling in B behavior has been found, which could be different from the weakly coupled prediction. There is also evidence showing that the real Dirac/Weyl semimetal systems might be strongly coupled. Thus studying the behavior of NMR for strongly coupled chiral anomalous systems would be very important. The objective of the second part of the project is to study the NMR in strongly coupled holographic chiral anomalous systems, especially its scaling behavior in the magnetic field B and compare with the experimental observations.
These questions lie at the intersection of high energy physics and CM physics, and are important to both CM physics and the better understanding of holography. The importance of the development in CM physics to the society is more straightforward. Better understanding of the transport behavior of novel materials will very likely result in new developments in daily life technologies in the future. In summary, the overall objectives of the project are to build and study the holographic dual of topological nontrivial states, e.g. Weyl semimetals, which are gapless topologically nontrivial states, as well as to study the transport behavior.
Conclusions: we showed that the topological states that are protected from perturbations still exist in the strongly coupled theory. We further showed that the odd viscosities in the strongly coupled holographic WSM are nonvanishing in the quantum critical region due to the existence of mixed axial gravity anomaly. This is a prediction to a transport coefficient induced by the mixed axial gravity anomaly in the quantum critical region of a WSM from holography and can be tested in laboratories.
