Analytic Studies of Fermions in the Conformal Bootstrap

Abstract

In this thesis, we analyze unitary conformal field theories in three dimensional spaces by applying analytic conformal bootstrap techniques to correlation functions of non-scalar operators, in particular Majorana fermions. Via the analysis of these correlation functions, we access several sectors in the spectrum of conformal field theories that have been previously unexplored with analytic methods, and we provide new data for several operator families. In the first part of the thesis, we achieve this by the large spin expansions that have been traditionally used in the conformal bootstrap program for scalar correlators, whereas in the second part we carry out the computations by combining several analytic tools that have been recently developed such as weight shifting operators, harmonic analysis for the Euclidean conformal group, and the Lorentzian inversion formula. We compare these methods and demonstrate the superiority of the latter by computing nonperturbative correction terms that are inaccessible in the former. A better analytic grasp of the spectrum of fermionic conformal field theories can help in many directions including making new precise analytic predictions for supersymmetric models, computing the binding energies of fermions in curved space, and describing quantum phase transitions in condensed matter systems with emergent Lorentz symmetry.

arXiv commentPhD Thesis, 156 pages, 11 figures, 4 tables. arXiv admin note: text overlap with arXiv:2006.07374, arXiv:1904.00032

References in corpus (111)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Solving the 3D Ising Model with the Conformal Bootstrap
• Conformal Four Point Functions and the Operator Product Expansion
• Conformal Partial Waves and the Operator Product Expansion
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Precision Islands in the Ising and $O(N)$ Models
• The Analytic Bootstrap and AdS Superhorizon Locality
• Projectors, Shadows, and Conformal Blocks
• The Bootstrap Program for Boundary CFT_d
• Bootstrapping the O(N) Vector Models
• Spinning Conformal Blocks
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• OPE Convergence in Conformal Field Theory
• Bounds on 4D Conformal and Superconformal Field Theories
• The critical exponents of the superfluid transition in He4
• Bootstrapping Conformal Field Theories with the Extremal Functional Method
• Superconformal Symmetry, Correlation Functions and the Operator Product Expansion
• Radial Coordinates for Conformal Blocks
• Walking, Weak first-order transitions, and Complex CFTs
• Large Spin Perturbation Theory
• The $(2,0)$ superconformal bootstrap
• Six-dimensional Methods for Four-dimensional Conformal Field Theories
• Universal Constraints on Conformal Operator Dimensions
• Bootstrapping the 3d Ising twist defect
• Towards Feynman rules for Mellin amplitudes in AdS/CFT
• A Mellin space approach to the conformal bootstrap
• Conformal Partial Waves: Further Mathematical Results
• Bounds in 4D Conformal Field Theories with Global Symmetry
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• A Proof of the Conformal Collider Bounds
• Conformal Field Theories in Fractional Dimensions
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• $d$-dimensional SYK, AdS Loops, and $6j$ Symbols
• Central Charge Bounds in 4D Conformal Field Theory
• Rigorous Limits on the Interaction Strength in Quantum Field Theory
• Constraints on 2d CFT partition functions
• Computation of Critical Exponent ηat O(1/N^3) in the Four Fermi Model in Arbitrary Dimensions
• Bootstrapping $\mathcal{N}=2$ chiral correlators
• Universal anomalous dimensions at large spin and large twist
• Conformal Bootstrap, Universality and Gravitational Scattering
• Bootstrapping phase transitions in QCD and frustrated spin systems
• Bootstrapping the Three-Dimensional Supersymmetric Ising Model
• Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap
• Diagonal Limit for Conformal Blocks in d Dimensions
• Bootstrapping SCFTs with Four Supercharges
• Critical Behaviour of the 3d Gross-Neveu and Higgs-Yukawa Models
• On the Advancements of Conformal Transformations and their Associated Symmetries in Geometry and Theoretical Physics
• A tauberian theorem for the conformal bootstrap
• Multipoint Conformal Blocks in the Comb Channel
• Solving CFTs with Weakly Broken Higher Spin Symmetry
• Conformal Blocks for Arbitrary Spins in Two Dimensions
• The 3d Stress-Tensor Bootstrap
• Universal Bounds on Charged States in 2d CFT and 3d Gravity
• Bootstrapping $O(N)$ Vector Models in $4<d<6$
• Bounds on $\mathcal{N}=1$ Superconformal Theories with Global Symmetries
• On duality of color and kinematics in (A)dS momentum space
• Spinning Witten Diagrams
• Crossing Symmetry in Alpha Space
• Approaching conformal window of $O(n)\times O(m)$ symmetric Landau-Ginzburg models from conformal bootstrap
• Projectors and seed conformal blocks for traceless mixed-symmetry tensors
• Fractal dimensions of self-avoiding walks and Ising high-temperature graphs in 3D conformal bootstrap
• Conformal Collider Physics from the Lightcone Bootstrap
• A universal feature of CFT Renyi entropy
• Conformal Bootstrap in the Regge Limit
• Eikonalization of Conformal Blocks
• Radial expansion for spinning conformal blocks
• Solving M-theory with the Conformal Bootstrap
• Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions)
• $\mathcal{N}=1$ Superconformal Blocks for General Scalar Operators
• Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications
• Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N) Models
• Dimensional Reduction for Conformal Blocks
• Current OPEs in Superconformal Theories
• Casimir recursion relations for general conformal blocks
• Constraints on Flavored 2d CFT Partition Functions
• Remarks on the Convergence Properties of the Conformal Block Expansion
• Generalized bootstrap equations for N=4 SCFT
• An étude of momentum space scalar amplitudes in AdS
• Holographic dual of the five-point conformal block
• Non-Abelian Binding Energies from the Lightcone Bootstrap
• (2,2) Superconformal Bootstrap in Two Dimensions
• On critical exponents without Feynman diagrams
• Modular Constraints on Conformal Field Theories with Currents
• TASI Lectures on the Higher Spin - CFT duality
• Bootstrapping Mixed Correlators in 4D $\mathcal{N}=1$ SCFTs
• On loop celestial amplitudes for gauge theory and gravity
• Superembedding methods for 4d N=1 SCFTs
• Anomalous dimensions at finite conformal spin from OPE inversion
• 3D CFT Archipelago from Single Correlator Bootstrap
• On spinning loop amplitudes in Anti-de Sitter space
• Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions
• Crossing Kernels for Boundary and Crosscap CFTs
• In search of conformal theories
• Superembedding Methods for Current Superfields
• Bootstrap bound for conformal multi-flavor QCD on lattice
• Landscape of Simple Superconformal Field Theories in 4d
• Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach
• Inverse Bootstrapping Conformal Field Theories
• On Calculation of 1/n Expansions of Critical Exponents in the Gross-Neveu Model with the Conformal Technique
• Interplay of universality classes in a three-dimensional Yukawa model
• A search for minimal 4d N=1 SCFT
• The unitary subsector of generalized minimal models
• Lower bound on the entropy of boundaries and junctions in 1+1d quantum critical systems
• Closed-form expression for cross-channel conformal blocks near the lightcone
• Unitarity violation in non-integer dimensional Gross-Neveu-Yukawa model
• Universal Bounds on Operator Dimensions in General 2D Conformal Field Theories
• (No) Bootstrap for the Fractal Ising Model
• Bootstrapping Pure Quantum Gravity in AdS3
• Further Results on a Function Relevant for Conformal Blocks
• Clifford Algebras in Physics