Quantum fields and strings: A course for mathematicians

Preface......Page all_9236_to_00062.cpc0007.djvu
Brief Contents......Page all_9236_to_00062.cpc0009.djvu
Cross-Reference Codes......Page all_9236_to_00062.cpc0011.djvu
Contents......Page all_9236_to_00062.cpc0013.djvu
Lectures on Conformal Field Theory (K. Gawedzki)......Page all_9236_to_00062.cpc0025.djvu
1.1. What is quantum field theory?......Page all_9236_to_00062.cpc0027.djvu
1.2. Euclidean free field and Gaussian functional integrals......Page all_9236_to_00062.cpc0029.djvu
1.3. Feynman-Kac formula......Page all_9236_to_00062.cpc0030.djvu
1.4. Massless free field with values in S¹......Page all_9236_to_00062.cpc0033.djvu
1.5. Toroidal compactifications: the partition functions......Page all_9236_to_00062.cpc0036.djvu
1.6. Toroidal compact ificat ions: the correlation functions......Page all_9236_to_00062.cpc0039.djvu
2.1. Conformal field theory data......Page all_9236_to_00062.cpc0047.djvu
2.2. Conformal Ward identities......Page all_9236_to_00062.cpc0048.djvu
2.3. Physical positivity and Hilbert space picture......Page all_9236_to_00062.cpc0053.djvu
2.4. Virasoro algebra and its primary fields......Page all_9236_to_00062.cpc0055.djvu
2.5. Highest weight representations of Vir......Page all_9236_to_00062.cpc0060.djvu
2.6. Segal\'s axioms and vertex operator algebras......Page all_9236_to_00124.cpc.djvu
3.1. 1PI effective action and large deviations......Page all_9236_to_00124.cpc0009.djvu
3.2. Geometric sigma models......Page all_9236_to_00124.cpc0011.djvu
3.3. Regularization and renormalization......Page all_9236_to_00124.cpc0012.djvu
3.4. Renormalization group effective actions......Page all_9236_to_00124.cpc0013.djvu
3.5. Background field effective action......Page all_9236_to_00124.cpc0016.djvu
3.6. Dimensional regularization......Page all_9236_to_00124.cpc0017.djvu
3.7. Renormalization of the sigma models to 1 loop......Page all_9236_to_00124.cpc0020.djvu
3.8. Renormalization group analysis of sigma models......Page all_9236_to_00124.cpc0023.djvu
4.1. WZW model......Page all_9236_to_00124.cpc0027.djvu
4.2. Gauge symmetry Ward identities......Page all_9236_to_00124.cpc0029.djvu
4.3. Scalar product of non-abelian theta functions......Page all_9236_to_00124.cpc0031.djvu
4.4. KZB connection......Page all_9236_to_00124.cpc0034.djvu
4.5. Coset theories......Page all_9236_to_00124.cpc0036.djvu
4.6. WZW factory......Page all_9236_to_00124.cpc0037.djvu
String Theory (E. D\'Hoker)......Page all_9236_to_00124.cpc0043.djvu
1. Point Particles vs Strings......Page all_9236_to_00124.cpc0047.djvu
1.2. Interactions......Page all_9236_to_00124.cpc0048.djvu
1.3. Loop expansion—topology of closed surfaces......Page all_9236_to_00124.cpc0050.djvu
1.4. Transition amplitudes for strings......Page all_9236_to_00124.cpc0052.djvu
1.5. Weyl invariance and vertex operator formulation......Page all_9236_to_00124.cpc0054.djvu
1.7. Transition amplitude for a single point particle......Page all_9236_to_00124.cpc0055.djvu
1.8. Generalized point particle propagation......Page all_9236_to_00124.cpc0056.djvu
2. Spectrum of Free Bosonic Strings......Page all_9236_to_00124.cpc0059.djvu
2.1. Basics of conformal field theory......Page all_9236_to_00124.cpc0060.djvu
2.2. The free closed bosonic string conformal field theory......Page all_9236_to_00186.cpc0002.djvu
2.3. The free open bosonic string conformal field theory......Page all_9236_to_00186.cpc0004.djvu
2.4. Fock space, negative norm states......Page all_9236_to_00186.cpc0005.djvu
2.5. Integration over Met(Σ)-Virasoro constraints......Page all_9236_to_00186.cpc0006.djvu
2.6. Physical spectrum, no-ghost theorem......Page all_9236_to_00186.cpc0007.djvu
2.7. Spectrum of the critical bosonic string with D = 26, a = 1......Page all_9236_to_00186.cpc0010.djvu
2.8. Lightcone gauge, density of states......Page all_9236_to_00186.cpc0011.djvu
2.9. Primary fields and vertex operators for physical states......Page all_9236_to_00186.cpc0012.djvu
2.10. Identifying the graviton: vertex operators from background fields......Page all_9236_to_00186.cpc0014.djvu
2.11. Internal degrees of freedom of open strings: Chan-Paton rules......Page all_9236_to_00186.cpc0015.djvu
3. String Amplitudes and Moduli Space of Curves......Page all_9236_to_00186.cpc0021.djvu
3.1. Finite-dimensional case......Page all_9236_to_00186.cpc0022.djvu
3.2. Basic notation: tensors, derivatives......Page all_9236_to_00186.cpc0023.djvu
3.3. Space of metrics - moduli space of Riemann surfaces......Page all_9236_to_00186.cpc0024.djvu
3.4. Factorizing the integration measure......Page all_9236_to_00186.cpc0027.djvu
3.5. Weyl rescalings of functional determinants......Page all_9236_to_00186.cpc0029.djvu
3.6. Critical central charge - critical dimension......Page all_9236_to_00186.cpc0032.djvu
3.7. Flat space-time manifold M......Page all_9236_to_00186.cpc0033.djvu
3.8. Non-critical strings......Page all_9236_to_00186.cpc0035.djvu
3.9. Tree level amplitudes......Page all_9236_to_00186.cpc0036.djvu
3.10. One loop amplitudes......Page all_9236_to_00186.cpc0042.djvu
4.1. Determinants and b-c systems......Page all_9236_to_00186.cpc0045.djvu
4.2. Ghost representation of the Faddeev-Popov determinant......Page all_9236_to_00186.cpc0047.djvu
4.3. Conformal field theory of the b-c system......Page all_9236_to_00186.cpc0048.djvu
4.4. Bosonization of the b-c system......Page all_9236_to_00186.cpc0049.djvu
4.5. The b-c Fock space......Page all_9236_to_00186.cpc0050.djvu
4.6. BRST quantization......Page all_9236_to_00186.cpc0052.djvu
5.1. Worldsheets with constant curvature metric (h≥2)......Page all_9236_to_00186.cpc0057.djvu
5.2. Holomorphicity in moduli......Page all_9236_to_00186.cpc0058.djvu
5.3. The chiral splitting theorem......Page all_9236_to_00186.cpc0060.djvu
5.4. Holomorphic and meromorphic differentials (a brief review of basics)......Page all_9236_to_00186.cpc0061.djvu
5.5. Green functions, determinants and chiral splitting......Page all_9236_to_00248.cpc0003.djvu
6. Strings on General Manifolds......Page all_9236_to_00248.cpc0005.djvu
6.1. Perturbation theory around general field configurations......Page all_9236_to_00248.cpc0006.djvu
6.2. Renormalization of generalized non-linear sigma models......Page all_9236_to_00248.cpc0007.djvu
6.3. General structure of Weyl dependence......Page all_9236_to_00248.cpc0011.djvu
6.4. General structure of Weyl anomaly in low energy expansion......Page all_9236_to_00248.cpc0013.djvu
6.5. Background field quantization method......Page all_9236_to_00248.cpc0015.djvu
6.6. Covariant expansion methods......Page all_9236_to_00248.cpc0016.djvu
6.7. Reformulation as an SO(1,D-1) gauge theory......Page all_9236_to_00248.cpc0018.djvu
6.8. Weyl variation of the effective action......Page all_9236_to_00248.cpc0020.djvu
6.9. Low energy string field equations and string effective action......Page all_9236_to_00248.cpc0022.djvu
6.10. A first look at compactification......Page all_9236_to_00248.cpc0023.djvu
Appendix A......Page all_9236_to_00248.cpc0024.djvu
7. Free Superstrings......Page all_9236_to_00248.cpc0027.djvu
7.1. Degrees of freedom of the RNS string......Page all_9236_to_00248.cpc0028.djvu
7.2. Ramond and Neveu-Schwarz Fock spaces......Page all_9236_to_00248.cpc0031.djvu
7.3. Local supersymmetry on the worldsheet......Page all_9236_to_00248.cpc0032.djvu
7.4. Functional integral representation of transition amplitudes......Page all_9236_to_00248.cpc0033.djvu
7.5. Super-Virasoro algebra and physical spectrum......Page all_9236_to_00248.cpc0035.djvu
7.6. The spectrum of physical states at low mass......Page all_9236_to_00248.cpc0037.djvu
7.7. The GSO projection, space-time supersymmetry......Page all_9236_to_00248.cpc0039.djvu
7.8. Type II A, B superstrings and their spectra......Page all_9236_to_00248.cpc0044.djvu
7.9. Type I superstring......Page all_9236_to_00248.cpc0047.djvu
8. Heterotic Strings......Page all_9236_to_00248.cpc0053.djvu
8.1. Free fermion realization of internal degrees of freedom......Page all_9236_to_00248.cpc0054.djvu
8.2. Free fermion realization of the Spin(32)/Z₂ heterotic string......Page all_9236_to_00248.cpc0057.djvu
8.3. Free fermion realization of the E₈ ⨯ E₈ heterotic string......Page all_9236_to_00248.cpc0059.djvu
8.4. Bosonic realizations of the Spin(32)/Z₂ and E₈ ⨯ E₈ strings......Page all_9236_to_00248.cpc0062.djvu
9.1. N = 1 supergeometry (also called N = 1, D = 2 supergravity)......Page all_9236_to_00310.cpc0005.djvu
9.2. Functional integral representation of transition amplitudes......Page all_9236_to_00310.cpc0008.djvu
9.3. Superconformal field theory (some basics)......Page all_9236_to_00310.cpc0010.djvu
9.4. BRST quantization......Page all_9236_to_00310.cpc0011.djvu
9.5. Vertex operators for physical states......Page all_9236_to_00310.cpc0012.djvu
9.6. The chiral splitting theorem......Page all_9236_to_00310.cpc0016.djvu
9.7. Tree-level amplitudes for NS-NS states......Page all_9236_to_00310.cpc0018.djvu
9.8. One loop amplitudes for NS-NS states in Type II A, B......Page all_9236_to_00310.cpc0021.djvu
9.9. One-loop amplitudes in the heterotic string......Page all_9236_to_00310.cpc0025.djvu
9.10. The NS-NS 4 point function......Page all_9236_to_00310.cpc0026.djvu
10.1. Global space-time supersymmetry in the RNS formulation......Page all_9236_to_00310.cpc0031.djvu
10.2. The Green-Schwarz formulation......Page all_9236_to_00310.cpc0033.djvu
10.3. Lightcone gauge quantization of the GS formulation......Page all_9236_to_00310.cpc0036.djvu
10.4. Flat superspace GS formulation......Page all_9236_to_00310.cpc0037.djvu
10.5. Supergravity and low energy superstrings......Page all_9236_to_00310.cpc0039.djvu
10.6. Type II A, D = 10, N = 2 and D = 11, N = 1 supergravities......Page all_9236_to_00310.cpc0040.djvu
10.8. Type I - Heterotic, D = 10, N = 1 supergravities......Page all_9236_to_00310.cpc0043.djvu
10.9. Superspace formulation of supergravities in D = 11 and D = 10......Page all_9236_to_00310.cpc0045.djvu
10.10. Local supersymmetric coupling of superstrings to supergravity......Page all_9236_to_00310.cpc0048.djvu
Exercises......Page all_9236_to_00310.cpc0051.djvu
1. General remarks......Page all_9236_to_00372.cpc.djvu
2. Example: D = 2, N = 1 in the notations of §9.1 of D\'Hoker\'s lectures......Page all_9236_to_00372.cpc0002.djvu
0.1. Contents of these notes......Page all_9236_to_00372.cpc0005.djvu
0.2. Some background on D-modules......Page all_9236_to_00372.cpc0008.djvu
1.1. Definition of chiral algebras......Page all_9236_to_00372.cpc0013.djvu
1.2. Lie-* algebras and construction of chiral algebras......Page all_9236_to_00372.cpc0015.djvu
1.3. Conformal blocks, correlation functions......Page all_9236_to_00372.cpc0019.djvu
2.1. Local O-modules on X......Page all_9236_to_00372.cpc0023.djvu
2.2. A formulation of CFT (central charge 0)......Page all_9236_to_00372.cpc0027.djvu
2.3. Introducing the central charge......Page all_9236_to_00372.cpc0031.djvu
3.1. Heisenberg and Kac-Moody algebras......Page all_9236_to_00372.cpc0037.djvu
3.2. The linear dilaton......Page all_9236_to_00372.cpc0040.djvu
3.3. The bc-system......Page all_9236_to_00372.cpc0043.djvu
4.1. The BRST complex......Page all_9236_to_00372.cpc0049.djvu
4.2. String amplitudes......Page all_9236_to_00372.cpc0052.djvu
5.1. Chiral algebras via the Ran space......Page all_9236_to_00372.cpc0055.djvu
5.2. Geometry of the affine Grassmannian......Page all_9236_to_00372.cpc0059.djvu
5.3. Chiral algebra attached to the affine Grassmannian......Page all_9236_to_00372.cpc0062.djvu
6.1. The canonical line bundle......Page all_9236_to_00434.cpc0005.djvu
6.2. Construction of the bosonic chiral algebra......Page all_9236_to_00434.cpc0008.djvu
Bibliography......Page all_9236_to_00434.cpc0015.djvu
Kaluza-Klein Compactiflcations, Supersymmetry, and Calabi-Yau Spaces (A. Strominger)......Page all_9236_to_00434.cpc0017.djvu
1.1. Kaluza-Klein Model......Page all_9236_to_00434.cpc0021.djvu
1.2. Compactifying Einstein\'s Equation from dimension ten to dimension four......Page all_9236_to_00434.cpc0024.djvu
1.3. Adding Matter to the Mix......Page all_9236_to_00434.cpc0025.djvu
1.4. The Effective action from ten-dimensional heterotic string theory......Page all_9236_to_00434.cpc0027.djvu
2.1. Review of material from the first lecture......Page all_9236_to_00434.cpc0031.djvu
2.2. Partially breaking the Supersymmetry by compactifying down to dimension four......Page all_9236_to_00434.cpc0032.djvu
2.3. Geometric consequence of the unbroken supersymmetry......Page all_9236_to_00434.cpc0034.djvu
2.4. Massless fields in the low energy effective Lagrangian......Page all_9236_to_00434.cpc0038.djvu
2.5. Relation to Grand Unification Theory......Page all_9236_to_00434.cpc0040.djvu
Dynamics of Quantum Field Theory (E. Witten)......Page all_9236_to_00434.cpc0045.djvu
1.0. Theories and realizations......Page all_9236_to_00434.cpc0047.djvu
1.1. What is symmetry breaking, and why it does not happen in quantum mechanics......Page all_9236_to_00434.cpc0051.djvu
1.2. Still no symmetry breaking in quantum field theory in finite volume......Page all_9236_to_00434.cpc0054.djvu
1.3. Symmetry breaking in quantum field theory in infinite volume......Page all_9236_to_00434.cpc0056.djvu
1.4. Infinite volume asymptotics of correlation functions......Page all_9236_to_00434.cpc0057.djvu
1.5. Continuous symmetry breaking......Page all_9236_to_00434.cpc0059.djvu
1.6. Goldstone\'s theorem......Page all_9236_to_00434.cpc0062.djvu
1.7. Infrared behavior of purely non-renormalizable field theories......Page all_9236_to_00496.cpc0005.djvu
1.8. Effective action for Goldstone bosons......Page all_9236_to_00496.cpc0006.djvu
2.2. Breaking of gauge symmetry and charges at infinity......Page all_9236_to_00496.cpc0011.djvu
2.4. No massless particles of higher spin......Page all_9236_to_00496.cpc0016.djvu
2.5. Infrared limits......Page all_9236_to_00496.cpc0019.djvu
3.1. The general setup......Page all_9236_to_00496.cpc0023.djvu
3.2. The BRST differential......Page all_9236_to_00496.cpc0024.djvu
3.3. The properties of the BRST derivation......Page all_9236_to_00496.cpc0025.djvu
3.5. Renormalization and BRST differential......Page all_9236_to_00496.cpc0026.djvu
3.6. The Hamiltonian approach......Page all_9236_to_00496.cpc0027.djvu
3.7. Anomalies......Page all_9236_to_00496.cpc0030.djvu
4.1. Infrared behavior of certain two-dimensional sigma models......Page all_9236_to_00496.cpc0035.djvu
4.2. Computation of the infrared behavior in the N --> ∞ limit......Page all_9236_to_00496.cpc0036.djvu
4.3. Computation of the S-matrix......Page all_9236_to_00496.cpc0039.djvu
5.1. The questions......Page all_9236_to_00496.cpc0047.djvu
5.2. An equivalent formulation......Page all_9236_to_00496.cpc0048.djvu
5.3. The large N effective theory......Page all_9236_to_00496.cpc0050.djvu
5.4. Real Grassmannians......Page all_9236_to_00496.cpc0054.djvu
5.5. Pure gauge theory......Page all_9236_to_00496.cpc0055.djvu
5.6. Classical electromagnetism in two dimensions......Page all_9236_to_00496.cpc0057.djvu
5.7. Quantum theory with matter......Page all_9236_to_00496.cpc0058.djvu
6.1. 2-dimensional gauge theories with fermions......Page all_9236_to_00558.cpc.djvu
6.2. Chiral symmetry......Page all_9236_to_00558.cpc0002.djvu
6.5. Bose-Fermi correspondence......Page all_9236_to_00558.cpc0004.djvu
6.6. Bose-Fermi correspondence for nonlinear theories......Page all_9236_to_00558.cpc0007.djvu
7.1. Infrared behavior of U(1) gauge theories with bosons in 2-dimensions......Page all_9236_to_00558.cpc0011.djvu
7.3. Instantons......Page all_9236_to_00558.cpc0012.djvu
7.4. Instanton gas......Page all_9236_to_00558.cpc0013.djvu
7.5. Summing over instantons......Page all_9236_to_00558.cpc0014.djvu
7.6. The Wilson line operator......Page all_9236_to_00558.cpc0017.djvu
7.7. The path integral representation of the Wilson line operator......Page all_9236_to_00558.cpc0020.djvu
7.8. The Higgs and the confinement regimes......Page all_9236_to_00558.cpc0022.djvu
7.9. The confinement conjecture......Page all_9236_to_00558.cpc0024.djvu
8.1. Introduction......Page all_9236_to_00558.cpc0027.djvu
8.2. Duality in two dimensions......Page all_9236_to_00558.cpc0028.djvu
8.3. Duality in three dimensions......Page all_9236_to_00558.cpc0032.djvu
8.4. Application to the Polyakov model......Page all_9236_to_00558.cpc0034.djvu
8.5. Duality in four dimensions and SL(2,ℤ)......Page all_9236_to_00558.cpc0042.djvu
8.6. The Hamiltonian formalism......Page all_9236_to_00558.cpc0045.djvu
9.2. Solitons and components of the space of classical solutions......Page all_9236_to_00558.cpc0049.djvu
9.3. Solitons and quantization......Page all_9236_to_00558.cpc0050.djvu
9.4. Solitons in theories with fermions......Page all_9236_to_00558.cpc0051.djvu
9.5. Solitons in 2+1 and 3+1 dimensions......Page all_9236_to_00558.cpc0052.djvu
9.6. The 3+1-dimensional theory with the θ-angle......Page all_9236_to_00558.cpc0054.djvu
10.1. \'t Hooft loop operator......Page all_9236_to_00558.cpc0057.djvu
10.2. Hilbert space interpretation of the \'t Hooft loop operator......Page all_9236_to_00558.cpc0059.djvu
10.3. The picture of confinement......Page all_9236_to_00558.cpc0060.djvu
11.1. The partition function in two dimensional Yang-Mills theory......Page all_9236_to_00620.cpc0003.djvu
11.2. A finite dimensional analogue: the Cartan model......Page all_9236_to_00620.cpc0004.djvu
11.3. Infinite dimensional Cartan: the descent equations......Page all_9236_to_00620.cpc0005.djvu
11.4. Equivariant integration and localization......Page all_9236_to_00620.cpc0007.djvu
11.5. Equivariant integration: the infinite dimensional case......Page all_9236_to_00620.cpc0009.djvu
11.6. The partition function of Yang-Mills theory......Page all_9236_to_00620.cpc0010.djvu
12.2. Supersymmetric solitons (BPS states)......Page all_9236_to_00620.cpc0021.djvu
12.3. The role of BPS states in quantum theory......Page all_9236_to_00620.cpc0023.djvu
12.4. N = 2 supersymmetry in 2 dimensions......Page all_9236_to_00620.cpc0024.djvu
12.5. N = 2 BPS states......Page all_9236_to_00620.cpc0025.djvu
12.6. N = 1 Supersymmetry in 4 dimensions......Page all_9236_to_00620.cpc0027.djvu
12.7. N = 2 Supersymmetry in 4 dimensions......Page all_9236_to_00620.cpc0028.djvu
13.1. Introduction......Page all_9236_to_00620.cpc0031.djvu
13.2. Generalities on N = 2 SUSY theories in dimension two......Page all_9236_to_00620.cpc0032.djvu
13.3. The U(1) Theories......Page all_9236_to_00620.cpc0036.djvu
13.4. One Example......Page all_9236_to_00620.cpc0038.djvu
13.5. Another example: flops......Page all_9236_to_00620.cpc0044.djvu
13.6. Cases in which c₁ ≠ 0......Page all_9236_to_00620.cpc0046.djvu
14. N = 2 SUSY Theories in Dimension Two, Part II: Chiral Rings and Twisted Theories......Page all_9236_to_00620.cpc0053.djvu
14.1. R-symmetry revisited......Page all_9236_to_00620.cpc0054.djvu
14.2. Q-cohomology of operators......Page all_9236_to_00620.cpc0056.djvu
14.3. Twisting the theory to give it global meaning......Page all_9236_to_00620.cpc0057.djvu
14.4. A Gauge Theory Example......Page all_9236_to_00620.cpc0060.djvu
14.5. A σ-model example......Page all_9236_to_00682.cpc0002.djvu
15.1. Landau-Ginzburg models......Page all_9236_to_00682.cpc0005.djvu
15.2. The elliptic genus......Page all_9236_to_00682.cpc0008.djvu
15.4. The space of zero-energy states......Page all_9236_to_00682.cpc0012.djvu
15.5. Generalities on the chiral ring......Page all_9236_to_00682.cpc0013.djvu
15.6. More Details on the Ring Structure......Page all_9236_to_00682.cpc0015.djvu
15.7. Calculations for CPⁿ⁻¹......Page all_9236_to_00682.cpc0016.djvu
15.8. Calculations for Fano Hypersurfaces......Page all_9236_to_00682.cpc0017.djvu
16.1. Gauge theory without supersymmetry......Page all_9236_to_00682.cpc0019.djvu
16.2. N = 1 supersymmetric pure gauge theory......Page all_9236_to_00682.cpc0023.djvu
16.3. N = 1 theories with chiral superfields......Page all_9236_to_00682.cpc0026.djvu
17.1. Introduction......Page all_9236_to_00682.cpc0029.djvu
17.2. Low Energy U(1) N = 2 super Yang-Mills Theories......Page all_9236_to_00682.cpc0030.djvu
18.1. Review of material from the last lecture......Page all_9236_to_00682.cpc0043.djvu
18.2. First results about the moduli space M of quantum vacua......Page all_9236_to_00682.cpc0044.djvu
18.3. The nature of infinity in M......Page all_9236_to_00682.cpc0046.djvu
18.4. BPS states and singularities in M......Page all_9236_to_00682.cpc0048.djvu
18.5. The number of singularities in M......Page all_9236_to_00682.cpc0051.djvu
18.6. The new massless particles......Page all_9236_to_00682.cpc0052.djvu
18.7. Explicit nature of the family of elliptic curves......Page all_9236_to_00682.cpc0054.djvu
18.8. Description of the BPS spectrum......Page all_9236_to_00682.cpc0055.djvu
19.1. A survey of N = 2 super-symmetric gauge theories in dimension four......Page all_9236_to_00682.cpc0057.djvu
19.2. From Minkowski space to a compact Riemannian four-manifold......Page all_9236_to_00682.cpc0059.djvu
19.3. The general form of the high energy computations......Page all_9236_to_00744.cpc0003.djvu
19.4. Low Energy Computations for Donaldson theory......Page all_9236_to_00744.cpc0009.djvu
Exercises......Page all_9236_to_00744.cpc0019.djvu
Solutions to Selected Exercises (by Daniel Freed)......Page all_9236_to_00744.cpc0027.djvu
Dynamics of N=1 Supersymmetric Field Theories in Four Dimensions (N. Seiberg)......Page all_9236_to_00744.cpc0041.djvu
1.1. Wess-Zumino model......Page all_9236_to_00744.cpc0043.djvu
1.2. Pure supersymmetric gauge theory......Page all_9236_to_00744.cpc0048.djvu
1.3. Supersymmetric QCD......Page all_9236_to_00744.cpc0050.djvu
2.1. N_f = N_c - 1......Page all_9236_to_00744.cpc0055.djvu
2.2. N_f < N_c - 1......Page all_9236_to_00744.cpc0057.djvu
2.3. N_f = N_c......Page all_9236_to_00744.cpc0060.djvu
2.4. N_f = N_c + 1......Page all_9236_to_00744.cpc0062.djvu
2.5. \'t Hooft anomaly matching condition......Page all_9236_to_00799.cpc.djvu
3.1. 3N_c/2 < N_f < 3N_c: non-trivial infrared fixed points......Page all_9236_to_00799.cpc0005.djvu
3.2. Nc + 2 < N_f < 3N_c/2: infrared free magnetic theory......Page all_9236_to_00799.cpc0008.djvu
3.3. Further tests of duality......Page all_9236_to_00799.cpc0010.djvu
Exercises......Page all_9236_to_00799.cpc0015.djvu
Solutions to Exercises (by Siye Wu)......Page all_9236_to_00799.cpc0017.djvu
Index......Page all_9236_to_00799.cpc0051.djvu