Condensed Matter Applications of AdS/CFT: Focusing on Strange Metals (Springer Theses)

The book deals with applications of the AdS/CFT correspondence to strongly coupled condensed matter systems. In particular, it concerns with the study of thermo-electric transport properties of holographic models exhibiting momentum dissipation and their possible applications to the transport properties of strange metals. The present volume constitutes one of the few examples in the literature in which the topic is carefully reviewed both from the experimental and theoretical point of view, including not only holographic results but also standard condensed matter achievements developed in the past decades. This work might be extremely useful both for scientific and pedagogical purposes. Supervisors’ Foreword 7 Abstract 9 Acknowledgements 10 Contents 11 Introduction 14 References1. Martin Ammon and Johanna Erdmenger, Gauge/Gravity Duality (Cambridge University Press, Cambridge, UK, 2015)2. Sean A. Hartnoll, Lectures on Holographic Methods for Condensed Matter Physics. Class. Quant. Grav. 26, 224002 (2009)3. Sean A. Hartnoll, Andrew Lucas, Subir Sachdev, Holographic Quantum Matter, Dec 21, (2016), pp. 178. arXiv:1612.07324 [hep-th]4. Juan Martin Maldacena, The large N limit of superconformal field theories and supergravity. Int. J. Theor. Phys. 38, 1113–1133 (1999). [Adv. Theor. Math. Phys. 2,231(1998)]5. Makoto Natsuume, AdS/CFT Duality User Guide. Lect. Notes Phys. 903, 1–294 (2015)6. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, 2001)7. Jan Zaanen, Ya-Wen Sun, Yan Liu, Koenraad Schalm, Holographic Duality in Condensed Matter Physics (Cambridge University Press, 2015)8. A. Zaffaroni, Introduction to the AdS–CFT correspondence. Class. Quant. Grav. 17, 3571–3597 (2000)9. A. Amoretti and A. Braggio and N Maggiore, N Magnoli. Thermo-electric transport in gauge/gravity models. In: Adv. Phys. X 2.2 (2017), pp. 409–42710. A. Amoretti, N. Magnoli, On Conformal Perturbation Theory, May 9, (2017), pp. 20. arXiv:1705.03502 [hep-th]11. A. Amoretti, D. Arean, R. Argurio, D. Musso, Z. Pando, A. Leopoldo. A holographic perspective on phonons and pseudo-phonons. In: JHEP 1705 (2017) 051. arXiv:1611.09344 [hep-th]12. A. Amoretti, M. Baggioli, N. Magnoli, D. Musso. Chasing the cuprates with dilatonic dyons. In: JHEP 06 (2016), p. 113. arXiv:1603.03029 [hep-th]13. A. Amoretti, D. Musso. Magneto-transport from momentum dissipating holography. In: JHEP 09 (2015), p. 094. arXiv:1502.02631 [hep-th]14. A. Amoretti, A. Braggio, N. Magnoli, D. Musso. Bounds on charge and heat diffusivities in momentum dissipating holography. In: JHEP 07 (2015), p. 102. arXiv:1411.6631 [hep-th]15. A. Amoretti, A. Braggio, G. Caruso, N. Maggiore, N. Magnoli. Introduction of a boundary in topological field theories. In: Phys. Rev. D90.12 (2014), p. 125006. arXiv:1410.2728 [hep-th]16. A. Amoretti, A. Braggio, N. Maggiore, N. Magnoli, D. Musso. Analytic dc thermoelectric conductivities in holography with massive gravitons. In: Phys. Rev. D91.2 (2015), p. 025002. arXiv:1407.0306 [hep-th]17. A. Amoretti, A. Braggio, N. Maggiore, N. Magnoli, D. Musso. Thermo-electric transport in gauge/gravity models with momentum dissipation. In: JHEP 09 (2014), p. 160. arXiv:1406.4134 [hep-th]18. A. Amoretti, A. Braggio, G. Caruso, N. Maggiore, N. Magnoli. Holography in flat spacetime: 4D theories and electromagnetic duality on the border. In: JHEP 04 (2014), p. 142. arXiv:1401.7101 [hep-th]19. A. Amoretti, A. Braggio, N. Maggiore, N. Magnoli, D. Musso. Coexistence of two vector order parameters: a holographic model for ferromagnetic superconductivity. In: JHEP 01 (2014), p. 054. arXiv:1309.5093 [hep-th]20. A. Amoretti, A. Braggio, G. Caruso, N. Maggiore, N. Magnoli. 3+1D Massless Weyl spinors from bosonic scalar-tensor duality. In: Adv. High Energy Phys. (2014), p. 635286. arXiv:1308.6674 [hep-th]21. A. Amoretti, A. Blasi, G. Caruso, N. Maggiore, N. Magnoli. Duality and Dimensional Reduction of 5D BF Theory. In: Eur. Phys. J. C73.6 (2013), p. 2461. arXiv:1301.3688 [hep-th]22. A. Amoretti, A. Blasi, N. Maggiore, N. Magnoli. Three-dimensional dynamics of four-dimensional topological BF theory with boundary. In: New J.Phys. 14 (2012), p. 113014. 16 Part I Condensed Matter Background 18 1 Preamble: Transport Coefficients Definition 19 2 Standard Metals and the Fermi Liquid 21 References 25 3 The Fermi Liquid Breakdown: High-Tc Superconductivity 26 3.1 Cuprates: Crystalline Structure and Electronic Properties 27 3.2 Cuprates: Phase Diagram 30 3.3 Cuprates: In-Plane Transport Properties in the Non-superconducting Phase 31 3.3.1 Resistivity and Hall Angle 33 3.3.2 Magneto-Resistance and the Koheler's Rule 36 3.3.3 Thermal Transport 38 References 39 4 Theoretical Attempts 43 4.1 Anderson's Model 43 4.2 Phenomenological Marginal Fermi Liquid 44 4.3 Quantum Criticality 47 References 49 Part II Introduction to Holography 50 5 The Gauge Gravity Duality 51 5.1 Review: Conformal Field Theory 51 5.1.1 The Conformal Group 51 5.1.2 Field Theory and Conformal Invariance 54 5.1.3 Unitarity Bounds 60 5.2 Review: Anti-de Sitter Spaces 60 5.2.1 AdS as a Maximally Symmetric Solution of Einstein's Equations 60 5.2.2 Hyper-Surface Embedding and Geometric Properties 62 5.2.3 Geodesic Motion in AdSd+1 63 5.2.4 Carter-Penrose Diagram and Conformal Boundary 65 5.3 Motivating the Duality 67 5.4 The GKPW Rule and Its Consequences 70 5.4.1 Holographic Renormalization and the Prescription for the Correlators 73 5.5 An Example: Scalar Field in AdSd+1 75 5.6 Thermal AdS/CFT 84 5.6.1 Introducing Temperature in Holography 87 5.6.2 Holography at Finite Charge Density 90 5.7 Summa: The Holographic Dictionary 93 References 94 Part III Thermo-electric Transport in AdS/CFT 95 6 Preamble: Linear Response Theory 96 Reference 98 7 The Simple Raissner-Nordström Case 99 7.1 Bulk Solution 99 7.2 Fluctuations 102 7.2.1 Renormalization of the Fluctuation Action 103 7.3 Correlators and Transport Coefficients 104 7.4 Physical Properties of Transport Coefficients 106 References 108 8 Momentum Dissipation in Holography 109 8.1 Adding a Mass to the Graviton to Break Momentum Conservation 109 8.1.1 The Massive Gravity Model 109 8.1.2 Background and Thermodynamic 110 8.1.3 Massive Gravity and Momentum Dissipation 112 8.1.4 Fluctuations and Transport in the Massive Case 113 8.1.5 Counter-Terms and Transport Coefficients Definition 116 8.2 Spectral Properties of Transport Coefficients 117 8.3 DC Transport Coefficients 118 8.3.1 The Electric Conductivity and the Seebeck Coefficient 118 8.3.2 Thermal Conductivity and Onsager Reciprocity 122 8.3.3 DC Properties of the Transport Coefficients 124 8.4 Adding the Dilaton 126 8.4.1 Properties of DC Transport Coefficients 128 8.5 Holographic Magneto-Transport 129 8.5.1 Thermodynamics 130 8.5.2 Transport Coefficients 132 8.5.3 Structure of the Thermoelectric Transport Coefficients 138 8.5.4 Bulk Electromagnetic Duality and Its Consequences from the Boundary Perspective 140 References 141 9 Physical Implications 143 9.1 Criticality and Diffusion Bounds 144 9.1.1 The Shear Viscosity Bound and the Concept of Planckian Dissipation 144 9.1.2 The Diffusivity Bounds Conjecture in Cuprates 147 9.1.3 On the Existence of Diffusivity Bounds in Holography 150 9.2 Holographic Inspired Phenomenology 155 References 159 Appendix A Basics of Fermi Liquid Theory 161 A.1 Quasi-particles and Interactions 161 A.2 Thermodynamic Properties 164 A.3 Quasi-particle Life-Time: The Fermi Liquid Stability 165 A.3.1 The Renormalization Group Approach 165 A.3.2 The Quasi-particle Life-Time 167 A.4 Thermo-Electric Transport 169 A.4.1 The Kinetic Equation 170 A.4.2 Electric Conductivity in a Galilean Invariant Fermi Liquid 171 A.4.3 Scattering Mechanism in a Metal 172 A.4.3.1 Elastic Scattering: Impurities and the Wiedemann-Franz Law 173 A.4.3.2 Electron-Phonon Scattering 177 References 183 Appendix B Asymptotically AdS Space-Time: AdS Black Holes 184 B.1 AdS-Schwarzshild Black Hole 185 B.1.1 Black Hole Interpretation 186 B.1.2 Thermodynamical Quantities 187 References 191 Appendix C Radial Quantization and Unitarity Bounds 192 C.1 The Radial Quantization 192 C.1.1 State-Operator Correspondence 193 C.1.2 Two Point Functions in Radial Quantization 194 C.2 Unitarity Bounds 195 Reference 196 Appendix D Effect of Linear Source in Time on DC Transport 197 Appendix E Technical Aspects of Holographic Magneto-Transport 199 E.1 Fluctuations Equations with Electric Ansatz 199 E.2 Fluctuations Equations with Thermal Ansatz 200 E.3 Stress-Energy Tensor with Thermal Gradient 201 Reference 201 Appendix F Einstein Relations for Charge and Heat Diffusion Constants 202 Appendix Curriculum Vitae 204 Personal Information 204 Working Experience 204 Education 204 Honors and Awards 205 Scientific Publications 205 Front Matter....Pages i-xx Front Matter....Pages 1-1 Preamble: Transport Coefficients Definition....Pages 3-4 Standard Metals and the Fermi Liquid....Pages 5-9 The Fermi Liquid Breakdown: High- \(T_c\) Superconductivity....Pages 11-27 Theoretical Attempts....Pages 29-35 Front Matter....Pages 37-37 The Gauge Gravity Duality....Pages 39-82 Front Matter....Pages 83-83 Preamble: Linear Response Theory....Pages 85-87 The Simple Raissner-Nordström Case....Pages 89-98 Momentum Dissipation in Holography ....Pages 99-132 Physical Implications ....Pages 133-150 Back Matter....Pages 151-199