String Theory on Calabi-Yau Manifolds

Abstract

These lectures are devoted to introducing some of the basic features of quantum geometry that have been emerging from compactified string theory over the last couple of years. The developments discussed include new geometric features of string theory which occur even at the classical level as well as those which require non-perturbative effects. These lecture notes are based on an evolving set of lectures presented at a number of schools but most closely follow a series of seven lectures given at the TASI-96 summer school on Strings, Fields and Duality.

LaTeX file; 150 pages; please latex 3 times; contains 44 figures in postscript format. Lectures given at TASI96

References in corpus (11)

• Applied Conformal Field Theory
• Some Comments On String Dynamics
• Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties
• Towards Mirror Symmetry as Duality for Two-Dimensional Abelian Gauge Theories
• TASI Lectures on Perturbative String Theories
• The Moduli Space of N = 2 Superconformal Field Theories
• Mirror Symmetry Constructions: A Review
• Spacetime Topology Change: The Physics of Calabi-Yau Moduli Space
• Phases of mirror symmetry
• Notes on N=2 $\sigma$-models$
• Black Hole Condensation and the Web of Calabi-Yau Manifolds

Cited by in corpus (118)

• D-Brane Gauge Theories from Toric Singularities and Toric Duality
• D-brane Instantons in Type II String Theory
• The First Three Seconds: a Review of Possible Expansion Histories of the Early Universe
• Black Holes and Solitons in String Theory
• Les Houches Lectures on Constructing String Vacua
• Phase Structure of D-brane Gauge Theories and Toric Duality
• Dirichlet branes, homological mirror symmetry, and stability
• Chiral Supersymmetric Standard Model Spectra from Orientifolds of Gepner Models
• Localized Tachyons and RG Flows
• Physics of F-theory compactifications without section
• Six-dimensional (1,0) effective action of F-theory via M-theory on Calabi-Yau threefolds
• Instanton sums and five-dimensional gauge theories
• Life at the Interface of Particle Physics and String Theory
• The Fall of Stringy de Sitter
• Projections in string theory and boundary states for Gepner models
• The effective action of type II Calabi-Yau orientifolds
• Lectures on complex geometry, Calabi-Yau manifolds and toric geometry
• A mini-course on topological strings
• Brane Gases on K3 and Calabi-Yau Manifolds
• Phase transitions, double-scaling limit, and topological strings
• D-Brane Topology Changing Transitions
• D-branes at Singular Curves of Calabi-Yau Compactifications
• Calabi-Yau Fourfolds with Flux and Supersymmetry Breaking
• M-theory cosmologies from singular Calabi-Yau compactifications
• Type IIB orientifolds on Gepner points
• The effective action of the heterotic string compactified on manifolds with SU(3) structure
• The effective action of D-branes in Calabi-Yau orientifold compactifications
• Effective Supergravity Actions for Flop Transitions
• Flop Transitions in M-theory Cosmology
• Black Holes and Flop Transitions in M-Theory on Calabi-Yau Threefolds
• Intersecting D-brane Models
• Populating the Whole Landscape
• Generalised discrete torsion and mirror symmetry for G_2 manifolds
• Crosscaps in Gepner Models and Type IIA Orientifolds
• Les Houches Lectures on Fields, Strings and Duality
• Fuzzy Toric Geometries
• The Geometer's Toolkit to String Compactifications
• Non-Kaehler attracting manifolds
• The Pfaffian Calabi-Yau, its Mirror, and their link to the Grassmannian G(2,7)
• Warped Strings: Self-dual Flux and Contemporary Compactifications
• Symmetries of perturbed conformal field theories
• CYJAX: A package for Calabi-Yau metrics with JAX
• Fibre Inflation and Reheating
• On the complete classification of the unitary N=2 minimal superconformal field theories
• Dual Pairs of Gauged Linear Sigma Models and Derived Equivalences of Calabi-Yau threefolds
• Complex/Symplectic Mirrors
• Type IIB Conifold Transitions in Cosmology
• Brane Probes, Toric Geometry, and Closed String Tachyons
• Toric geometry and local Calabi-Yau varieties: An introduction to toric geometry (for physicists)
• Lectures on Mirror Symmetry and Topological String Theory
• Spin(7)-manifolds in compactifications to four dimensions
• The singularity problem in string theory
• Conifolds From D-branes
• Graph Theory and Qubit Information Systems of Extremal Black Branes
• Fourier Mukai Transforms and Applications to String Theory
• Parameter spaces of massive IIA solutions
• M2-brane Flows and the Chern-Simons Level
• Closed string tachyons, flips and conifolds
• Special Geometry and Mirror Symmetry for Open String Backgrounds with N=1 Supersymmetry
• Gaugino Condensation with a Doubly Suppressed Gravitino Mass
• Non-compact Gepner Models, Landau-Ginzburg Orbifolds and Mirror Symmetry
• TASI lectures: special holonomy in string theory and M-theory
• New Heterotic Non-Kahler Geometries
• D-Branes in Topological String Theory
• On Algebraic Singularities, Finite Graphs and D-Brane Gauge Theories: A String Theoretic Perspective
• Mirror Maps in Chern-Simons Gauge Theory
• Hunting for the New Symmetries in Calabi-Yau Jungles
• Holomorphic Couplings In Non-Perturbative String Compactifications
• On nonsupersymmetric $\BC^4/\BZ_N$, tachyons, terminal singularities and flips
• Toric Geometry and String Theory
• Seeking de-Sitter Vacua in the String Landscape
• Hodge-elliptic genera and how they govern K3 theories
• Localized Tachyons and the g_cl conjecture
• Landau-Ginzburg Description of Boundary Critical Phenomena in Two Dimensions
• Transformation of algebraic Gromov-Witten invariants of three-folds under flops and small extremal transitions, with an appendix from the stringy and the symplectic viewpoint
• Prepotentials, Bi-linear Forms on Periods and Enhanced Gauge Symmetries in Type-II Strings
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Lectures on 4d N=1 dynamics and related topics
• A Collection of Exercises in Two-Dimensional Physics, Part 1
• The Spectra of Supersymmetric States in String Theory
• Universal Calabi-Yau Algebra: Towards an Unification of Complex Geometry
• On Black Objects in Type IIA Superstring Theory on Calabi-Yau Manifolds
• Matrix factorisations for rational boundary conditions by defect fusion
• Phases of unstable conifolds
• Finding the Mirror of the Beauville Manifold
• Frobenius Modules and Hodge Asymptotics
• Off-shell nilpotent (anti-)BRST symmetries for a free particle system on a toric geometry: superfield formalism
• Moduli Stabilization in Type IIB Flux Compactifications
• SW(3/2,2) subsymmetry in G${}_2$, Spin(7) and N=2 CFTs
• Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces
• Sasakian quiver gauge theory on the Aloff-Wallach space $X_{1,1}$
• Singular manifolds, topology change and the dynamics of compactification
• The evolution of conifolds
• On A-twisted moduli stack for curves from Witten's gauged linear sigma models
• Kahler Potentials on Toric Varieties
• Asymptotically flat black holes and gravitational waves in three-dimensional massive gravity
• Free-field Representations and Geometry of some Gepner models
• Moduli Stabilisation on the Worldsheet
• On algebraic geometric and computer algebra aspects of mirror symmetry
• Unification, the Big Bang, and the Cosmological Constant
• Lectures on Warped Compactifications and Stringy Brane Constructions
• The Implications of N = 2 Supergravity Cosmology On the Topology of the Calabi-Yau Manifold
• Algebro-geometrical orientifolds and IR dualities
• Turing's Landscape: decidability, computability and complexity in string theory
• Supersymmetric Gauge Theories from String Theory
• Introduction to String Theory
• Strongly Homotopy Lie Algebras from Multisymplectic Geometry
• The gravitational dynamics of warped throats
• Combinatorics in N = 1 Heterotic Vacua
• Superstrings beyond one loop
• Geometric prequantization on the path space of a prequantized manifold
• Qubits and STU Black Holes with Eight Electric and Magnetic Charges
• Backreaction I: The Torus
• Out of Nowhere: The 'emergence' of spacetime in string theory
• D-branes, Supersymmetry Breaking, and Neutrinos
• Topics in Supergravity Phenomenology
• Correlation Functions in N=3 Superconformal Theory
• Towards Homological Mirror Symmetry