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Probing the QCD Phase Diagram Via Holographic Models HELSINKI INSTITUTE OF PHYSICS INTERNAL REPORT SERIES HIP-2020-01 Probing the QCD Phase Diagram via Holographic Models Jere Remes Helsinki Institute of Physics & Department of Physics, Faculty of Science University of Helsinki Finland DOCTORAL DISSERTATION To be presented for public discussion with the permission of the Faculty of Science of the University of Helsinki, in the auditorium D101 at Physicum, Gustaf Hällströmin katu 2, Helsinki, on the 14th of December 2020 at 14 o’clock. Helsinki 2020 ISBN 978-951-51-1291-0 (print) ISBN 978-951-51-1292-7 (pdf) ISSN 1455-0563 http://ethesis.helsinki.fi Unigrafia Helsinki 2020 Die Menschen machen ihre eigene Geschichte, aber sie machen sie nicht aus freien Stücken, nicht unter selbstgewählten, sondern unter unmittelbar vorgefundenen, gegebenen und überlieferten Umständen. Karl Marx Der achtzehnte Brumaire des Louis Bonaparte (1852) J. Remes: Probing the QCD Phase Diagram via Holographic Models, University of Helsinki 2020, 97 pages, Helsinki Institute of Physics, Internal Report Series, HIP-2020-01, ISBN 978-951-51-1291-0, ISSN 1455-0563. Abstract Quantum Chromodynamics (QCD) is the quantum field theory describing strong nuclear interac- tions. Due to the titular strong nature of these interactions, obtaining reliable predictions from the theory has proven challenging in many physically interesting regions of the phase diagram. The most well-established current framework for handling strongly coupled, non-perturbative systems is that of lattice simulations. Even this framework has its weaknesses when applied to QCD, however, such as simulating systems where real-time dynamics are relevant or that have non-zero chemical potential. Such cases are found in e.g. the early-time dynamics of heavy-ion collisions and inside neutron stars, respectively. These nonperturbative systems provide us with an ideal testing ground for new methods such as holography. Holography is an umbrella term for various dualities which connect a quantum field theory with a higher-dimensional theory of quantum gravity. One general property of these dualities is that they map operators in strongly coupled field theories into fields in weakly coupled classical gravity. It therefore seems natural to apply the methods provided by these dualities to the study of strong coupled real-world theories such as QCD. However, there is no known holographic dual for QCD yet, and we must resort to some modeling if we wish to compute predictions via holographic methods. In this thesis, we apply holographic models of QCD – namely Improved Holographic QCD and its extension called V-QCD – in the study of both the thermalization of hot quark-gluon plasma produced in heavy-ion collisions and the structure and astrophysical properties of cold, dense matter in neutron stars. We also provide an introduction to the different facets concerning these applications from the motivation in QCD and the challenges the QCD phase diagram provides to current computational methods, to holography, heavy-ion collision phenomenology and neutron star observations. ii Acknowledgments First and foremost I thank Umut Gürsoy for agreeing to act as my opponent and Aleksi Vuorinen for performing the duties of the kustos. The pre-examiners of this thesis, Nick Evans and Tuomas Lappi, gave astute criticism and comments on this dissertation, and for that they have my gratitude. The work done in this thesis would not have been possible without my supervisors: Kimmo Tuominen, Aleksi Vuorinen and Niko Jokela. I heartily thank you for conversations, guidance, support, challenging my thinking and for always answering my dire e-mails. The research that forms the backbone of this thesis was not, and could not have been done alone. It was thanks to my collaborators, Timo Alho, Matti Järvinen and Govert Nijs that it reached the light of day, and having the privilege of working with them has taught me a lot about physics. I additionally thank Matti for his insightful and detailed comments on the manuscript of this thesis. I also thank my colleagues at the Department of Physics and Helsinki Institute of Physics for discussions. Especially Keijo Kajantie has given me many timely comments and tips on research and academia. Fellow doctoral students of all stripes from various universities have also been of importance to my time at the university, and I wish to thank you all collectively for the comradery without naming names. I would go amiss, if after spending nearly a decade at the campus, I would not thank all the staff and administration at Helsinki Institute of Physics, the Department of Physics, Faculty of Science, Doctoral School in Natural Sciences, Doctoral Programme in Particle Physics and Universe Sciences and especially at Physicum for their work. I have also had the privilege to be taught by many a wonderful teacher, to whom I owe much. I also wish to extend a special recognition to all the wraiths – past and present – of the notorious A313. They have provided me with a worthwhile looking-glass, to which I can rave and ramble and which meanders in kind in response. “Lasciate ogne speranza, voi ch’intrate”? Considering the circumstances that have greatly helped me in retaining some form of a life, especially through the pandemic, I thank Oranssi – and in particular my neighbors – for maintaining the fragile circle of light. And in a similar vein, I thank my co-orbiters for their flexibility and for distracting me from time to time. I would not be here without the trouble with being born; my family has my gratitude for bringing me up and encouraging me to dive into the subjects I was interested in. Kiitos tuestanne, työstänne ja ennen kaikkea rohkeudestanne, joka on aina toiminut esimerkkinä muutoksen tavoittelussa. The list is long, but I have saved the personally most significant recognition to last, as is the custom: I thank K for their love and over-extending patience with my occasional monomania. The amount of labor is roughly constant, no matter who is spending the time in the attic. Also, thank you Mila, even if you cannot read this. iii Included Publications This thesis is based on the following publications [I–III] I N. Jokela, M. Järvinen, J. Remes: Holographic QCD in the Veneziano limit and neutron stars, JHEP 1903 (2019) 041. arXiv:1809.07770 [hep-ph] II T. Alho, J. Remes, K. Tuominen, A. Vuorinen: Quasinormal modes and thermalization in Improved Holographic QCD, Phys. Rev. D101 (2020) 10, 106025. arXiv:2002.09544 [hep-ph] III N. Jokela, M. Järvinen, G. Nijs, J. Remes: Unified weak/strong coupling framework for nuclear matter and neutron stars arXiv:2006.01141 [hep-ph] The authors are listed alphabetically according to particle physics convention. The author’s contribution In article I, the author co-wrote the numerical codes, produced the band plots and took part in writing the article. In article II, the author co-wrote the numerical codes, produced all the plots and co-wrote the article. In article III, the author wrote the numerical codes to produce the neutron star data, produced the data used in the final plots, produced most of the plots and co-wrote the article. iv Contents 1 Introduction 1 2 Quantum Chromodynamics 5 2.1 Lagrangian and Parameters .............................. 7 2.2 Asymptotic Freedom .................................. 8 2.3 Confinement ....................................... 10 2.4 On the Approximate Symmetries of the Lagrangian ................. 11 2.4.1 Chiral symmetry ................................ 12 2.4.2 Conformal Invariance ............................. 13 2.5 Lattice QCD ...................................... 14 2.6 QCD Phase Diagram .................................. 16 3 Holography 21 3.1 A Primer on Anti-de Sitter Spacetimes ........................ 21 3.2 A Sketch of an Argument for AdS/CFT Duality .................. 23 3.3 Holographic Thermodynamics ............................. 25 3.4 Building Models: Bottom-Up and Top-Down .................... 27 4 Holographic QCD in the Veneziano limit 31 4.1BuildingBlocksoftheModel............................. 32 4.1.1 Improved Holographic QCD .......................... 32 4.1.2 Flavor Action . ............................... 33 4.2 Matching the Model to QCD ............................. 37 4.2.1 Fitting Glue ................................... 38 4.2.2 Fitting Flavor . ............................... 40 4.3 Thermodynamics of the Model ............................ 43 5 Heavy-Ion Collisions and Holography 47 5.1 Time-evolution of Heavy-Ion Collisions ........................ 48 5.2 Holographic Thermalization .............................. 51 5.2.1 Thermalization in IHQCD ........................... 52 v CONTENTS 6 Neutron Stars and Holography 55 6.1 Neutron Stars . .................................... 55 6.1.1 Neutron Star Observations .......................... 56 6.1.2 Equation of State and the Structure of a Neutron Star ........... 58 6.2 Neutron Stars in V-QCD ............................... 61 6.2.1 Hybrid Equations of State ........................... 61 6.2.2 Some Key Results ............................... 64 7 Summary 67 References 69 vi Chapter 1 Introduction In his book The Structure of Scientific Revolutions, philosopher Thomas Kuhn argued that science does not progress solely in a linear manner – by accumulating more and more new knowledge – but also by undergoing revolutionary periods, during which the prevailing theory of the field in question is overthrown and replaced by a new one [1]. After this paradigm shift, one enters again the stage of conceptual continuity, of
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