Superstring Theory

About this course:

Exercise 1:

Keywords: –

Exercise 2:

Keywords: Polyakov Action, Global Symmetries, Poincaré Transformations, Poincaré Invariance, Conserved Currents, Noether’s Theorem, Noether Procedure, Infinitesimal Transformation, Fields, Metric, Local Symmetries, Worldsheet Reparametrization, Weyl Transformations, Energy-momentum Tensor, Two-dimensions, Einstein’s Equations, Einstein Field Equations, Riemann Tensor, Riemann curvature Tensor, Worldsheet Coordinates, Gauge-fixed Metric, Action, Equations of Motion, Boundary Term, Dirichlet Boundary Condition, Neumann Boundary Condition, Closed Strings

Exercise 3:

Keywords: Classical closed String, Mode Expansion, Gauge-fixed Action, Canonical conjugated Momentum, Poisson Brackets, Angular Momentum, Conserved Current, Conformal Gauge, Poincaré Algebra, Worldsheet, Open String, Equations of Motion, Neumann Boundary Conditions, Dirichlet Boundary Conditions, Energy-momentum Tensor, Two-dimensions, Light-cone Coordinates, Fourier Expansion, Virasoro Algebra, Worldsheet Metric, Diffeomorphism Symmetry, Action, Invariance, Conserved Current, Conserved Charge

Exercise 4:

Keywords: Worldsheet Coordinates, Wick Rotation, Metric, Euclidean Metric, Worldsheet Fields, Commutators, Operators, Normal Ordering, Virasoro Generators, Quantum Operators, Commutation Relations, Quantum Virasoro Algebra, Central Extension, Classical Virasoro Algebra, Lie Algebra, Jacobi identity, Vacuum State, Conserved Currents, Conserved Charge, Representations of the Lorentz Group

Exercise 5:

Keywords: Mass-shell Condition, Normal-ordered Operator, Physical States, Spurious States, Null States, First excited State, Open String Theory, Vacuum, Polarization Vector, Number Operator, Virasoro Algebra, Spacetime Dimensions, Riemann Zeta Function, Zeta Function Regularization, Meromorphic Function, Light-cone gauge Quantization, Normal Ordering, Critical Bosonic String Theory, Open Bosonic String Theory, NN Boundary Conditions, Closed Bosonic String Theory, SO(24) Representations, Young Tableau, SO(25) Representations, Little Groups, Little Group Representations, Level-matching Condition

Exercise 6:

Keywords: Euclidean d-dimensional Spacetime, Metric, Conformal Transformation, Angle preserving, Conformal Group, Poincaré Group, Infinitesimal Coordinate Transformation, Infinitesimal Translation, Infinitesimal Rotations, Infinitesimal Scale Transformation, Special Conformal Transformation, Finite Conformal Transformations, Generators, Conformal Algebra, SO(d+1,d) Algebra, Minkowski Spacetime, SO(d,2) Algebra, Primary Field, Conformal Dimension, Global Conformal Transformations, Quasi-primary Field, Secondary Field, Holomorphic Part, Chiral Part, Infinitesimal Conformal Transformations, Two-point Correlation Function, Conformal Invariance, Infinitesimal Global Conformal Transformations, Three-point Functions

Exercise 7:

Keywords: 2D Conformal invariant Theory, Energy-momentum Tensor, Chiral Part, Anti-chiral Part, Conserved Currents, Conserved Charges, Infinitesimal Conformal Transformations, Fields, Mode Expansion, Generic Operators, Radial Ordering, Operator Product Expansion, OPE, Primary Field, Laurent Expansion, Virasoro Generators, Virasoro Algebra, Free Boson, Euclidean Action, Propagator, Normal ordered Operators, Conformal Weights, Free Majorana Fermion, Dirac Matrices, Dirac Algebra, Two-component Spinor, Equations of Motion, Correlator, Kinetic Term, Differential Equation, Green’s Function, Ghost System, Anti-commuting Fields, Wick’s Theorem, Conformal Dimensions, Central Charge

Exercise 8:

Keywords: Vertex Operator, Free Bosonic Field, Operator Product Expansion, OPE, Two-point Function, Schwarzian Derivative, Primary Field, Conformal Weight, Energy-momentum Tensor, Quasi-primary Field, Conformal Dimension, Worldsheet, Free closed String, Cylinder, Wick Rotation, Casimir Energy, 2D Conformal Field Theory, 2D CFT, 2D Manifold, Metric, Curvature, Central Charge, Quantum Breaking, Scale Invariance, Trace Anomaly

Exercise 9:

Keywords: Virasoro Algebra, Unitary Representation, Negative-norm States, Unitarity, Singular Vectors, Kac Determinant, Verma Module, Gram Matrix, Determinant, Descendant Field, String of Primary Fields, Conformal Dimension, Correlators, Differential Equation, Three-point Function

Exercise 10:

Keywords: Superstring Theory, Action, Supersymmetry Extension, Polyakov Action, Scalar Multiplet, Supergravity Multiplet, Local Supersymmetry Transformations, Worldsheet Symmetries, Gauge, Worldsheet Metric, Worldsheet Gravitino, Superconformal Gauge, Energy-momentum Tensor, Worldsheet Supercurrents, Operator Product Expansion, OPE, Primary Fields, Conformal Weights, Superconformal Transformations, Generators, Anti-commuting infinitesimal parameter, Commutator, Conformal Transformation, Superconformal Algebra, Anti-holomorphic Copy, Superconformal Field Theory, SCFT, Supercurrent, Cylindrical Coordinate, Closed String, Periodicity Conditions, Ramond, Neveu-Schwarz, Conformal Plane, Laurent Expansion, Fermionic Fields, Infinite-dimensional Super Lie-Algebra, OSP(1|2), SL(2,C)/Z₂