Naturalness, String Landscape and Multiverse: A Modern Introduction with Exercises

Description

This book presents a string-theoretic approach to new ideas in particle physics, also known as Physics Beyond the Standard Model, and to cosmology. The concept of Naturalness and its apparent violation by the low electroweak scale and the small cosmological constant is emphasized. It is shown that string theory, through its multitude of solutions, known as the landscape, offers a partial resolution to these naturalness problems as well as suggesting more speculative possibilities like that of a multiverse. The book is based on a one-semester course, as such, it has a pedagogical approach, is self-contained and includes many exercises with solutions. Notably, the basics of string theory are introduced as part of the lectures. These notes are aimed at graduate students with a solid background in quantum field theory, as well as at young researchers from theoretical particle physics to mathematical physics. This text also benefits students who are in the process of studying string theory at a deeper level. In this case, the volume serves as additional reading beyond a formal string theory course. Preface Acknowledgements Contents About the Author 1 The Standard Model and Its Hierarchy Problem(s) 1.1 Standard Model—The Basic Structure 1.2 Standard Model—Parameter Count 1.3 Effective Field Theories—Cutoff Perspective 1.4 Effective Field Theories—QFTUV vs. QFTIR 1.5 The Standard Model as an Effective Field Theory 1.6 The Electroweak Hierarchy Problem 1.7 Fine-tuning 1.8 Gravity and the Cosmological Constant Problem 1.9 Problems 1.9.1 Electroweak Symmetry Breaking 1.9.2 The Standard Model Is Anomaly Free 1.9.3 The Standard Model and SU(5) 1.9.4 Weyl Spinors 1.9.5 Covariant Expression for the 1-Loop Vacuum Energy 2 Supersymmetry and Supergravity 2.1 SUSY Algebra and Superspace 2.2 Superfields 2.3 Chiral Superfields 2.4 SUSY-Invariant Lagrangians 2.5 Wess-Zumino-Type Models 2.6 Real Superfields 2.7 SUSY Breaking 2.8 Supersymmetrising the Standard Model 2.9 Supersymmetric and SUSY Breaking Masses and Non-renormalisation 2.10 The Minimal Supersymmetric Standard Model (MSSM) 2.11 Supergravity: Superspace Approach 2.12 Supergravity: Component Approach 2.13 Problems 2.13.1 Simple Manipulations Within the Superspace Approach 2.13.2 Deriving Component Actions 2.13.3 Fierz Identities for Weyl Spinors 2.13.4 SUSY in Components 2.13.5 Gauge Coupling Unification 2.13.6 Graviton Spin (Helicity) 3 String Theory: Bosonic String 3.1 Strings: Basic Ideas 3.2 Symmetries, Equations of Motion, Gauge Choice 3.3 Open String 3.4 Quantisation 3.5 Explicit Construction of Physical States: Open String 3.6 Explicit Construction of Physical States: Closed String 3.7 The 26d Action 3.8 Problems 3.8.1 Point Particle Action 3.8.2 Commutation Relations of Oscillator Modes 3.8.3 Trace of the Energy-Momentum Tensor 3.8.4 Virasoro Algebra 3.8.5 Normal Ordering Constant as Casimir Energy 3.8.6 Kalb-Ramond Field from the Worldsheet Perspective 4 String Theory: Interactions and Superstring 4.1 State-Operator Correspondence 4.2 Scattering Amplitudes 4.3 Worldsheet Supersymmetry 4.4 Worldsheet Supergravity 4.5 Quantisation of the Superstring 4.6 GSO or Gliozzi-Scherk-Olive Projection 4.7 Consistent Type II Superstring Theories 4.8 Other 10d Theories 4.9 Problems 4.9.1 Explicit State-Operator Mapping in the Free Case 4.9.2 Euler Number and Genus of Riemann Surfaces 4.9.3 Dilaton vs. String Coupling 4.9.4 Elementary Exercises with 2d Spinors 4.9.5 SUSY Algebra in 2d 5 10d Actions and Compactification 5.1 10d Supergravities and Type IIB as an Example 5.2 Kaluza–Klein Compactification 5.3 Towards Calabi–Yau Manifolds 5.4 Homology and Cohomology 5.5 Calabi–Yau Moduli Spaces 5.6 Explicit Parameterisation of Calabi–Yau Moduli Spaces 5.7 An Aside on String Model Building: From Heterotic Compactifications to Orientifold Models with Branes and F-Theory 5.8 Problems 5.8.1 Dimensional Reduction 5.8.2 SO(2n) vs. U(n) 5.8.3 Complex Projective Spaces 6 The Flux Landscape 6.1 Compact Geometries with p-Form Fluxes 6.2 Bousso–Polchinski Model 6.3 The Type IIB Flux Landscape (GKP) 6.4 Kahler Modulus Stabilisation and SUSY Breaking (KKLT) 6.5 The Anti-D3-Brane Uplift of KKLT 6.6 The Large Volume Scenario 6.7 Vacuum Statistics and the Tuning of the Cosmological Constant 6.8 Higgs Mass and Other Landscape-Related Issues 6.9 Problems 6.9.1 No-Scale Kahler Potentials and KKLT 6.9.2 The LVS Scalar Potential and Stabilisation Mechanism 7 Eternal Inflation and the Measure Problem 7.1 From Slow-Roll Inflation to the Eternal Regime 7.2 Eternal Inflation in the Landscape 7.3 Tunnelling Transitions in Quantum Mechanics 7.4 Tunnelling Transitions in Field Theory 7.5 Tunnelling in Gravitational Theories 7.6 Our Universe in the Eternally Inflating Landscape 7.7 Making Statistical Predictions and the Measure Problem 7.8 Proposed Measures 7.9 Predictions from First Principles? 7.10 Problems 7.10.1 Coleman–De Luccia Tunnelling 8 Concluding Remarks and Some Alternative Perspectives 8.1 Low-Scale SUSY Versus Technicolor 8.2 From the `Little Higgs' to Large or Warped Extra Dimensions 8.3 Cosmological Selection and the Relaxion 8.4 The Swampland Program 8.5 The Swampland and de Sitter 8.6 More Direct Approaches to Quantum Gravity 8.7 Asymptotic Safety and the Hierarchy Problem 9 Summary References Index