Geometric Approaches to Quantum Fields and Strings at Strong Couplings

Abstract

Geometric structures and dualities arise naturally in quantum field theories and string theory. In fact, these tools become very useful when studying strong coupling effects, where standard perturbative techniques can no longer be used. In this thesis we look at several conformal field theories in various dimensions. We first discuss the structure of the nilpotent networks stemming from T-brane deformations in 4D $\mathcal{N}=1$ theories and then go to the stringy origins of 6D superconformal field theories to realize deformations associated with T-branes in terms of simple combinatorial data. We then analyze non-perturbative generalizations of orientifold 3-planes (i.e. S-folds) in order to produce different 4D $\mathcal{N}=2$ theories. Afterwards, we turn our attention towards a few dualities found at strong coupling. For instance, abelian T-duality is known to be a full duality in string theory between type IIA and type IIB. Its nonabelian generalization, Poisson-Lie T-duality, has only been conjectured to be so. We show that Poisson-Lie symmetric $\sigma$-models are at least two-loop renormalizable and their $\beta$-functions are invariant under Poisson-Lie T-duality. Finally, we review recent progress leading to phenomenologically relevant dualities between M-theory on local $G_2$ spaces and F-theory on locally elliptically fibered Calabi-Yau fourfolds. In particular, we find that the 3D $\mathcal{N}=1$ effective field theory defined by M-theory on a local $Spin(7)$ space unifies the Higgs bundle data associated with 4D $\mathcal{N}=1$ M-theory and F-theory vacua. We finish with some comments on 3D interfaces at strong coupling.

arXiv commentPhD thesis

References in corpus (158)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators in Three Dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological invariants of time-reversal-invariant band structures
• Generalized Global Symmetries
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• N=2 dualities
• Solutions Of Four-Dimensional Field Theories Via M Theory
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Seeing the magnetic monopole through the mirror of topological surface states
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• Symmetries and Strings in Field Theory and Gravity
• Topological phases of fermions in one dimension
• Double Field Theory
• Classifying quantum phases using Matrix Product States and PEPS
• Generalized metric formulation of double field theory
• Baryons And Branes In Anti de Sitter Space
• Superspace Duality in Low-Energy Superstrings
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• M-Theory on Eight-Manifolds
• Reading between the lines of four-dimensional gauge theories
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• New N=2 Superconformal Field Theories in Four Dimensions
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Fermion Path Integrals And Topological Phases
• Some Comments On String Dynamics
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Duality Symmetries from Non--Abelian Isometries in String Theories
• Exploring 2-Group Global Symmetries
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• Signature of magnetic monopole and Dirac string dynamics in spin ice
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Analytic Continuation Of Chern-Simons Theory
• An N=2 Superconformal Fixed Point with E_6 Global Symmetry
• Interacting fermionic topological insulators/superconductors in three dimensions
• Some Global Aspects of Duality is String Theory
• Superconformal Fixed Points with E_n Global Symmetry
• Toroidal Compactification Without Vector Structure
• Classification of interacting electronic topological insulators in three dimensions
• Branes and Six Dimensional Supersymmetric Theories
• F-Theory at Constant Coupling
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• Non-trivial Fixed Points of The Renormalization Group in Six Dimensions
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Exploring Double Field Theory
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Branes at Orbifolds versus Hanany Witten in Six Dimensions
• T-Branes and Monodromy
• Anomaly polynomial of general 6d SCFTs
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• On the Defect Group of a 6D SCFT
• Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
• Classifying bases for 6D F-theory models
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• N=1 Deformations and RG Flows of N=2 SCFTs
• A Proof of the Conformal Collider Bounds
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index
• N=3 four dimensional field theories
• Cohomogeneity One Manifolds of Spin(7) and G(2) Holonomy
• Central Charges and $U(1{)}_R$ Symmetries in $\mathcal{N}=1$ Super Yang-Mills
• New Complete Non-compact Spin(7) Manifolds
• T-duality and ${\alpha }^{\prime }$-corrections
• De Sitter from T-branes
• Witten effect in a crystalline topological insulator
• S-folds and 4d N=3 superconformal field theories
• String Junctions for Arbitrary Lie Algebra Representations
• Born Reciprocity in String Theory and the Nature of Spacetime
• Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory
• Branes and Six Dimensional Fixed Points
• Supersymmetric gauge theories with decoupled operators and chiral ring stability
• Poisson-Lie T-Duality in Double Field Theory
• Doubled aspects of generalised dualities and integrable deformations
• The BPS Spectra and Superconformal Points in Massive N=2 Supersymmetric QCD
• The all-loop non-Abelian Thirring model and its RG flow
• 750 GeV Diphotons from a D3-brane
• Anomaly polynomial of E-string theories
• The Odd story of ${\alpha }^{\prime }$-corrections
• New N=1 Dualities
• Why are fractional charges of orientifolds compatible with Dirac quantization?
• 6D RG Flows and Nilpotent Hierarchies
• RG Fixed Points and Flows in SQCD with Adjoints
• VOAs labelled by complex reflection groups and 4d SCFTs
• D-type Conformal Matter and SU/USp Quivers
• Quiver Tails and N=1 SCFTs from M5-branes
• The Global Gauge Group Structure of F-theory Compactification with U(1)s
• Composite Dirac liquids: parent states for symmetric surface topological order
• A Note on Compactifications on Spin(7)-Holonomy Manifolds
• Anomalies of Duality Groups and Extended Conformal Manifolds
• On time-reversal anomaly of 2+1d topological phases
• F-theory and Dark Energy
• F-theory on singular spaces
• Matter From Geometry Without Resolution
• Holographic duals of 3d S-fold CFTs
• Conformal perturbation theory beyond the leading order
• Pixelated Dark Energy
• M5 brane and four dimensional N=1 theories I
• Renormalization of Lorentz non-invariant actions and manifest T-duality
• A Unique Connection for Born Geometry
• 6D Fractional Quantum Hall Effect
• Conformal chiral boson models on twisted doubled tori and non-geometric string vacua
• 4d $\mathcal{N}=2$ S-folds
• Integrable flows between exact CFTs
• 27/32
• Integrable 2d sigma models: quantum corrections to geometry from RG flow
• Revisiting the classifications of 6d SCFTs and LSTs
• An Exceptional Sector for F-theory GUTs
• 4D Gauge Theories with Conformal Matter
• Charting Class ${\mathcal{S}}_k$ Territory
• Quantum correction to generalized T-dualities
• UV Completions for Non-Critical Strings
• T-Branes at the Limits of Geometry
• Hitchin's Equations and M-Theory Phenomenology
• $\lambda$-deformations of left-right asymmetric CFTs
• Anomaly matching on the Higgs branch
• Studying superconformal symmetry enhancement through indices
• Quantum equivalence in Poisson-Lie T-duality
• New N=1 Dualities from M5-branes and Outer-automorphism Twists
• Electroweak Symmetry Breaking in the DSSM
• Conifold Transitions and Five-Brane Condensation in M-Theory on Spin(7) Manifolds
• All-loop correlators of integrable $\lambda$-deformed $\sigma$-models
• Parity anomaly in four dimensions
• From 6D SCFTs to Dynamic GLSMs
• Exceptional $\mathcal{N}=3$ theories
• Duality group actions on fermions
• Anomalies involving the space of couplings and the Zamolodchikov metric
• There and back again: A T-brane's tale
• 4d $\mathcal{N}=3$ indices via discrete gauging
• Towards Exotic Matter and Discrete Non-Abelian Symmetries in F-theory
• SUSY enhancement from T-branes
• A search for minimal 4d N=1 SCFT
• Para-Hermitian Geometries for Poisson-Lie Symmetric $\sigma$-models
• T-Branes and $G_2$ Backgrounds
• Theories of Class F and Anomalies
• The moduli spaces of S-fold CFTs
• Sigma models with local couplings: a new integrability -- RG flow connection
• Quantum Dirac fermions in half space and their interaction with electromagnetic field
• Compact T-branes
• The Higgs as a Probe of Supersymmetric Extra Sectors
• Variations on S-fold CFTs
• Kinetic Mixing at Strong Coupling
• BPS Partition Functions for S-folds
• How many surface modes does one see on the boundary of a Dirac material?
• S and T for SCFTs
• A sheaf-theoretic SL(2,C) Floer homology for knots
• A note on 4d N = 3 from little string theory