Instituto de Física Teórica UAM-CSIC UNIVERSIDAD AUTÓNOMA DE MADRID TESIS DOCTORAL Anomalous Transport in Hydrodynamics and Gauge/Gravity Duality Out of Equilibrium Autor: Director: Jorge FERNÁNDEZ PENDÁS Dr. Karl LANDSTEINER 9 de octubre de 2019 iii Many things can happen in four years, but none of them has as much of an impact on you as the people you meet along the way. I would like to start thanking Miguel Ángel Ramos Osorio, who acted as a guide in the first days of my scientific career. Miguel Ángel, I learned from you the impor- tance of professional honesty and excellence. You left us too early, but will always be remembered. Much of this thesis would not be the same without my supervisor, Karl Landsteiner. My way of understanding physics has been forever altered by our dis- cussions. Karl, I know how lucky I am by having you as my advisor. Your patience, respect and trust are a happy anomaly. My scientific brother, Christian Copetti, has been the best possible teammate. As in a doubles game, one stayed in the net as the other served. I hope I have contributed to your growth as much as you have contributed to mine. I would also like to thank all the rest of my collaborators. Yan Liu and Matthias Kaminski deserve a special mention because they have also been international ref- erees for this thesis. Along with Matthias, I should also thank all the people from Tuscaloosa that made my stay one of the most interesting periods of the PhD. An- gela, Casey, Jana, Markus, Roshan... thank you for your hospitality and considera- tion. All the people that have been members of the IFT in the last years are responsible for creating the right atmosphere for this thesis to be completed. However, I would like to especially thank Thomas Biekötter, Iñaki Lara, Javier Martín, Diego Medrano, Sebastián Montes, Javier Rodríguez-Laguna, Sara Saa and Nadir Samos for your friendship and the long conversations... about everything. Good luck to everyone! I am eternally grateful to Francisco Fernández and Diego Gutiérrez for their friendship during our shared year in Madrid and their capability to make those stressful times fun. I must confess that during the last four years I have missed those lunches at Plaza Mayor. Another close friend that shared some months with me in Madrid, although our friendship started long before, is Fafa. Our mutual support during times of uncer- tainty stays with us forever. With him, I would also like to mention the rest of my non-Physics-related friends. You are too many to be included here, but achieve- ments like this can only be made with a solid network of support. My family has taught me so many things it is impossible to sum them all up here. Your generosity and commitment have always shined a light on my path, and they are an endless source of confidence and happiness. I love you so much! I have saved the last words of gratitude for my partner. Paula, you have been understanding and supporting me for almost nine years now, and I can safely say that your contribution to this thesis is almost as important as mine. Your strength and enthusiasm are my inspiration every day. Russian physicist Lev Landau once said, “It is important to do everything with passion, it embellishes life enormously”. My life is certainly more beautiful with you. Thank you! Danke schön! Grazie mille! ""! ¡Muchas gracias! v Summary Anomalous transport has been a topic of great interest in the last decade. New dissi- pationless contributions to the charge and energy currents arise due to the existence of a chiral anomaly, which is the breaking at the quantum level of the chiral symme- try. Those transport phenomena are studied using holography because they are ex- pected to be important in experimental setups at strong coupling. Moreover, we know that the anomaly has the same value independently of the energy scale, so we can expect to extract the universal behavior of anomalous transport by performing our computations in the nonperturbative regime. Therefore, in this thesis we use the AdS/CFT correspondence to study different features of anomaly induced transport. Let us now summarize the content of each chapter. In Chapter1, anomalous transport is presented in relation to the experimental setups in which it appears and the content of the other chapters is summarized. In Chapter2, all the theoretical background required for this thesis is introduced. In particular, the chapter includes sections for anomalies, relativistic hydrodynamics, linear response theory and holography. Both Chapters1 and2 serve as an introduc- tion. In Chapter3, we explore how symmetries in gravity can be exploited to simplify the computation of anomalous transport coefficients. In holography, the radial coor- dinate of AdS is dual to an energy scale for the field theory. Therefore, holographic renormalization group flows can be better understood through radially conserved charges. It has been shown in previous works that the bulk gauge and diffeomor- phism symmetries can be used to find conserved quantities associated to the charge and heat currents. However, the application to anomalous transport is cumbersome, because Chern-Simons terms in the action break gauge invariance and, moreover, the gravitational Chern-Simons involves a higher number of derivatives. Neverthe- less, we show that conservation laws can still be derived and they allow to obtain the field theory observables in terms of quantities evaluated at the horizon. In Chapter4, we study a case in which it becomes evident that the construction of membrane currents from Chapter3 is necessary to compute the charge and energy currents. Translation symmetry breaking is introduced through the use of spatially linear scalar field backgrounds and a further coupling between the scalars and an electromagnetic field is included to produce disorder on the charged sector. The result we find is that the electric conductivity can vanish for certain values of the translation symmetry breaking couplings, and the chiral magnetic and chiral vor- tical conductivities are not affected by the inclusion of momentum relaxation and charged disorder. This is to be expected from the dissipationless nature of anoma- lous transport. In Chapter5, we study the holographic model of Weyl semimetals that was pro- posed by our research group some months before the beginning of this PhD. Its vi main feature is the appearance of a topological quantum phase transition between a topological phase with nonvanishing anomalous Hall effect and a trivial phase without such effect. Our work has focused on studying the universality of this phase transition as a function of the free parameters of the model and then extending the computation of the anomalous Hall effect in the vector current to the analogous con- tribution in the axial current. As a result, we find that the phase transition appears for a large region of parameter space, and the axial Hall effect can be found to give the expected value once a renormalization of the external axial fields due to their coupling to the scalars is considered. In Chapter6, we extend the study of anomalous transport to out of equilibrium setups. In order to do that, we use generalized Vaidya metrics with momentum relaxation to induce sudden changes in the energy and charge of the system. As a result, we find that the chiral magnetic effect presents a significantly large equilibra- tion time that depends on the length of the Vaidya quench and the momentum re- laxation parameter. We expect this to give some hints on the phenomenology of the quark-gluon plasma produced in heavy ion collisions. In particular, we propose an explanation of why the experimental results from the RHIC collider in Brookhaven seem to be more compatible with anomalous transport than the ones from the LHC in Geneva. In Chapter7, a discussion in English and Spanish of the work done and the results obtained in this thesis is included. Finally, a list of all the references cited in the chapters closes the thesis. vii Resumen El transporte anómalo ha despertado gran interés en la última década. Nuevas con- tribuciones no disipativas aparecen en las corrientes de carga y energía como conse- cuencia de la existencia de una anomalía quiral, que es la rotura a nivel cuántico de la simetría quiral. La holografía permite estudiar estos fenómenos de transporte porque se espera que sean importantes en sistemas experimentales en acoplo fuerte. Además, se sabe que la anomalía tiene el mismo valor independientemente de la escala de energías, así que podemos extraer el comportamiento universal del transporte anómalo a través de cálculos en el régimen no perturbativo. Por tanto, en esta tesis usamos la correspondencia AdS/CFT para estudiar diferentes aspectos del transporte in- ducido por anomalías. A continuación resumiremos el contenido de cada capítulo. En el Capítulo1, presentamos el transporte anómalo en relación a los sistemas experimentales en los que aparece y resumimos el contenido del resto de capítu- los. En el Capítulo2, se introduce todo el aparataje teórico necesario para esta tesis. El capítulo posee secciones sobre anomalías, sobre hidrodinámica anómala, sobre teoría de respuesta lineal y sobre holografía. Ambos Capítulos1y2 sirven de intro- ducción. En el Capítulo3, exploramos cómo las simetrías en gravedad pueden ser usadas para simplificar el cálculo de los coeficientes de transporte anómalo. En holografía, la coordenada radial de AdS es dual a una escala de energía de la teoría de cam- pos. Por tanto, los flujos del grupo de renormalización holográfico se pueden en- tender mejor utilizando cargas conservadas radialmente. En trabajos previos se ha mostrado que las simetrías gauge y de difeomorfismos del bulk permiten encontrar cantidades conservadas asociadas a las corrientes de carga y calor.