Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories

[1]  S. Piunikhin Quantum and Floer cohomology have the same ring structure , 1994, hep-th/9401130.

[2]  J. Hurtubise Holomorphic maps of a Riemann surface into a flag manifold , 1996 .

[3]  R. Stora Equivariant cohomology and cohomological field theories , 1995 .

[4]  D. Morrison,et al.  Summing the instantons: Quantum cohomology and mirror symmetry in toric varieties , 1994, hep-th/9412236.

[5]  V. Kazakov,et al.  Large N phase transition in the heat kernel on the U (N) group , 1994, hep-th/9410087.

[6]  A. Matytsin,et al.  Some properties of large-N two-dimensional Yang-Mills theory , 1994, hep-th/9410054.

[7]  W. Taylor,et al.  Large N phases of chiral QCD2 , 1994, hep-th/9408115.

[8]  C. Vafa,et al.  N = 4 topological strings , 1994, hep-th/9407190.

[9]  J. Sonnenschein,et al.  The string theory approach to generalized 2D Yang-Mills theory , 1994, hep-th/9407114.

[10]  S. Wadia,et al.  STRING FIELD THEORY OF TWO-DIMENSIONAL QCD ON A CYLINDER: A REALIZATION OF W∞ CURRENT ALGEBRA , 1994, hep-th/9407026.

[11]  H. Schnitzer,et al.  The String calculation of Wilson loops in two-dimensional Yang-Mills theory , 1994, hep-th/9406100.

[12]  J. Barb'on,et al.  Effective Hamiltonians for 1/N expansion in two-dimensional QCD , 1994, hep-th/9406046.

[13]  M. Kontsevich Enumeration of Rational Curves Via Torus Actions , 1994, hep-th/9405035.

[14]  V. Sadov On equivalence of Floer's and quantum cohomology , 1993, hep-th/9310153.

[15]  S. Rajeev QUANTUM HADRODYNAMICS IN TWO DIMENSIONS , 1994 .

[16]  V. Arnold Plane curves, their invariants, Perestroikas, and classifications , 1994 .

[17]  E. Witten Monopoles and four-manifolds , 1994, hep-th/9411102.

[18]  M. Douglas,et al.  Large N Gauge Theory -- Expansions and Transitions , 1994, hep-th/9409098.

[19]  G. Moore 2D Yang-Mills Theory and Topological Field Theory , 1994, hep-th/9409044.

[20]  E. Witten,et al.  A Strong coupling test of S duality , 1994, hep-th/9408074.

[21]  R. Rudd The String Partition Function for QCD on the Torus , 1994, hep-th/9407176.

[22]  M. Cornalba,et al.  Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves , 1994, alg-geom/9406008.

[23]  C. Becchi,et al.  A FUNCTIONAL AND LAGRANGIAN FORMULATION OF TWO DIMENSIONAL TOPOLOGICAL GRAVITY , 1994, hep-th/9406096.

[24]  W. Taylor Counting Strings and Phase Transitions in 2D QCD , 1994, hep-th/9404175.

[25]  S. Hyun,et al.  N = 2 Topological Yang-Mills Theories and Donaldson's Polynomials , 1994, hep-th/9404009.

[26]  A. Matytsin,et al.  Instanton induced large N phase transitions in two and four dimensional QCD , 1994, hep-th/9404004.

[27]  O. Tirkkonen,et al.  Equivariance, BRST symmetry, and superspace , 1994, hep-th/9403126.

[28]  R. Milgram,et al.  The topology of the space of rational maps into generalized flag manifolds , 1994 .

[29]  M. Kontsevich,et al.  Gromov-Witten classes, quantum cohomology, and enumerative geometry , 1994, hep-th/9402147.

[30]  A. Niemi,et al.  On the Duistermaat-Heckman Integration Formula And Integrable Models , 1994, hep-th/9402041.

[31]  M. Douglas Some Comments on QCD String , 1994, hep-th/9401073.

[32]  J. Baez,et al.  Strings and two-dimensional QCD for finite N☆ , 1994, hep-th/9401041.

[33]  Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes , 1993, hep-th/9309140.

[34]  J. Minahan,et al.  Interacting fermion systems from two-dimensional QCD , 1993, hep-th/9309044.

[35]  I. Antoniadis,et al.  Topological amplitudes in string theory , 1994 .

[36]  Jae-Suk Park Holomorphic Yang-Mills theory on compact Kähler manifolds , 1993, hep-th/9305095.

[37]  E. Getzler Two-dimensional topological gravity and equivariant cohomology , 1993, hep-th/9305013.

[38]  Jae-Suk Park N=2 topological Yang-Mills theory on compact Kähler surfaces , 1993, hep-th/9304060.

[39]  D. Salamon,et al.  J-Holomorphic Curves and Quantum Cohomology , 1994 .

[40]  C. Taubes THE SEIBERG-WITTEN INVARIANTS AND SYMPLECTIC FORMS , 1994 .

[41]  Y. Ruan,et al.  A mathematical theory of quantum cohomology , 1994 .

[42]  P. Kronheimer,et al.  The Genus of Embedded Surfaces in the Projective Plane , 1994 .

[43]  I. Bars QCD and Strings in 2D , 1993, hep-th/9312018.

[44]  Petr Hořava Topological Strings and QCD in Two Dimensions , 1993, hep-th/9311156.

[45]  M. Douglas,et al.  Conformal Field Theory Techniques in Large N Yang-Mills Theory , 1993, hep-th/9311130.

[46]  D. Gross,et al.  Two-dimensional QCD and strings , 1993, hep-th/9311072.

[47]  A. Nersessian Equivariant localization: BV geometry and supersymmetric dynamics , 1993 .

[48]  M. Blau,et al.  Lectures on 2d Gauge Theories: Topological Aspects and Path Integral Techniques , 1993, hep-th/9310144.

[49]  J. Minahan,et al.  Classical solutions for two-dimensional QCD on the sphere , 1993, hep-th/9309119.

[50]  J. Baez Strings, Loops, Knots and Gauge Fields , 1993, hep-th/9309067.

[51]  J. Kalkman BRST model applied to symplectic geometry , 1993, hep-th/9308132.

[52]  S. Ramgoolam Comment on two-dimensional O(N) and Sp(N) Yang-Mills theories as string theories , 1993, hep-th/9307085.

[53]  F. Kirwan,et al.  Localization for nonabelian group actions , 1993, alg-geom/9307001.

[54]  D. Birmingham,et al.  The algebraic structure of cohomological field theory , 1993 .

[55]  G. Moore Finite in All Directions , 1993, hep-th/9305139.

[56]  H. Schnitzer,et al.  TWO-DIMENSIONAL YANG-MILLS THEORIES ARE STRING THEORIES , 1993, hep-th/9305097.

[57]  M. Douglas,et al.  Large N phase transition in continuum QCD2 , 1993, hep-th/9305047.

[58]  Jaap Kalkman,et al.  BRST model for equivariant cohomology and representatives for the equivariant thom class , 1993 .

[59]  A. Losev Descendants constructed from matter field in Landau-Ginzburg theories coupled to topological gravity , 1993 .

[60]  A. Polyakov A Few Projects in String Theory , 1993, hep-th/9304146.

[61]  D. Morrison Compactifications of moduli spaces inspired by mirror symmetry , 1993, alg-geom/9304007.

[62]  M. Douglas,et al.  Conformal Field Theory Techniques for Large N Group Theory , 1993, hep-th/9303159.

[63]  J. Minahan,et al.  Equivalence of two-dimensional QCD and the C = 1 matrix model , 1993, hep-th/9303153.

[64]  D. Gross,et al.  Twists and Wilson Loops in the String Theory of Two Dimensional QCD , 1993, hep-th/9303046.

[65]  T. Eguchi,et al.  Topological Strings, Flat Coordinates and Gravitational Descendants , 1993, hep-th/9302048.

[66]  E. Witten Phases of N = 2 theories in two dimensions , 1993, hep-th/9301042.

[67]  Minahan Summing over inequivalent maps in the string theory interpretation of two-dimensional QCD. , 1993, Physical review. D, Particles and fields.

[68]  D. Gross Two-dimensional QCD is a string theory , 1992, hep-th/9212149.

[69]  Bong H. Lian,et al.  New perspectives on the BRST-algebraic structure of string theory , 1992, hep-th/9211072.

[70]  M. Blau,et al.  N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant , 1991, hep-th/9112012.

[71]  P. Aspinwall,et al.  Topological field theory and rational curves , 1991, hep-th/9110048.

[72]  R. Forman Small volume limits of 2-d Yang-Mills , 1993 .

[73]  E. Witten Algebraic Geometry Associated with Matrix Models of Two Dimensional Gravity , 1993 .

[74]  D. Gross Some new/old approaches to QCD , 1992, hep-th/9212148.

[75]  A.Lossev Descendants constructed from matter fields in topological Landau-Ginzburg theories coupled to topological gravity , 1992, hep-th/9211090.

[76]  J. Polchinski Strings and QCD , 1992, hep-th/9210045.

[77]  A. Sengupta The Yang-Mills measure for S2 , 1992 .

[78]  M. Blau,et al.  Quantum Yang-Mills theory on arbitrary surfaces , 1992 .

[79]  Maxim Kontsevich,et al.  Intersection theory on the moduli space of curves and the matrix airy function , 1992 .

[80]  E. Witten Two-dimensional gauge theories revisited , 1992, hep-th/9204083.

[81]  Michèle Vergne,et al.  Heat Kernels and Dirac Operators: Grundlehren 298 , 1992 .

[82]  M. Blau The Mathai-Quillen formalism and topological field theory , 1992, hep-th/9203026.

[83]  E. Witten The N matrix model and gauged WZW models , 1992 .

[84]  Y. Fukuda,et al.  2-D Quantum Gravity , 1992 .

[85]  Petr Hořava Two-dimensional string theory and the topological torus , 1992, hep-th/9202008.

[86]  石井 勝 Introduction to Topological Yang-Mills Theory , 1992 .

[87]  S. Yau Essays on mirror manifolds , 1992 .

[88]  V. Ginzburg,et al.  Infinitesimal structure on moduli space of G-bundles , 1992 .

[89]  E. Witten Mirror Manifolds And Topological Field Theory , 1991, hep-th/9112056.

[90]  M. Blau,et al.  Topological field theory , 1991 .

[91]  E. Witten On quantum gauge theories in two dimensions , 1991 .

[92]  G. Moore,et al.  From loops to states in two-dimensional quantum gravity , 1991 .

[93]  Hirosi Ooguri,et al.  Geometry of N=2 strings , 1991 .

[94]  D. Fine Quantum Yang-Mills on a Riemann surface , 1991 .

[95]  J.A.Harvey,et al.  String Theory and the Donaldson Polynomial , 1991, hep-th/9108020.

[96]  P. Braam Floer homology groups for homology three-spheres , 1991 .

[97]  Xenia de la Ossa,et al.  A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory , 1991 .

[98]  E. Witten Introduction to cohomological field theories , 1991 .

[99]  H. Verlinde,et al.  Topological strings in d < 1 , 1991 .

[100]  H. Verlinde,et al.  A Solution of Two-dimensional Topological Quantum Gravity , 1991 .

[101]  H. Verlinde,et al.  Loop equations and Virasoro con - straints in nonperturbative two - dimensional quantum gravity , 1991 .

[102]  I. Singer,et al.  Conformally invariant gauge fixed actions for 2-D topological gravity , 1991 .

[103]  W. Massey A basic course in algebraic topology , 1991 .

[104]  S. Shenker The Strength of Nonperturbative Effects in String Theory , 1991 .

[105]  I. Morrison,et al.  Slopes of effective divisors on the moduli space of stable curves , 1990 .

[106]  H. Verlinde,et al.  Notes on topological string theory and 2-D quantum gravity , 1990 .

[107]  D. Fine Quantum Yang-Mills on the two-sphere , 1990 .

[108]  E. Witten,et al.  Mean field theory, topological field theory, and multi-matrix models , 1990 .

[109]  J. Distler 2D quantum gravity, topological field theory and the multicritical matrix models , 1990 .

[110]  E. Witten On the Structure of the Topological Phase of Two-dimensional Gravity , 1990 .

[111]  H. Ooguri,et al.  SELF-DUALITY AND N=2 STRING MAGIC , 1990 .

[112]  A. Jevicki Topological field theories , 1990 .

[113]  B. Rusakov Loop averages and partition functions in U(N) gauge theory on two-dimensional manifolds , 1990 .

[114]  Topological gravity and moduli space , 1990 .

[115]  D. Salamon Morse theory, the Conley index and Floer homology , 1990 .

[116]  M. Atiyah,et al.  Topological Lagrangians and cohomology , 1990 .

[117]  Edward Witten,et al.  Two-dimensional gravity and intersection theory on moduli space , 1990 .

[118]  S. Donaldson Polynomial invariants for smooth four-manifolds , 1990 .

[119]  N. Hitchin The geometry and topology of moduli spaces , 1990 .

[120]  M. Hammermesh,et al.  Group theory and its applications to physical problems , 1989 .

[121]  A. Floer Symplectic fixed points and holomorphic spheres , 1989 .

[122]  E. Witten The search for higher symmetry in string theory , 1989, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[123]  Nicholas P. Warner,et al.  Chiral rings in N = 2 superconformal theories , 1989 .

[124]  M. Henneaux,et al.  Existence, uniqueness and cohomology of the classical BRST charge with ghosts of ghosts , 1989 .

[125]  H. Kanno Weil algebra structure and geometrical meaning of BRST transformation in topological quantum field theory , 1989 .

[126]  Edward Witten,et al.  Quantum field theory and the Jones polynomial , 1989 .

[127]  L. Gross,et al.  Two dimensional Yang-Mills theory via stochastic differential equations , 1989 .

[128]  G. Moore,et al.  Classical and quantum conformal field theory , 1989 .

[129]  I. Singer,et al.  The topological sigma model , 1989 .

[130]  D. Kutasov Geometry on the space of conformal field theories and contact terms , 1989 .

[131]  S. Ouvry,et al.  On the Algebraic Characterization of Witten's Topological Yang-Mills Theory , 1989 .

[132]  Jin-quan Chen Group Representation Theory For Physicists , 1989 .

[133]  C. Isham,et al.  Modern Differential Geometry For Physicists , 1989 .

[134]  A. Floer WITTEN'S COMPLEX AND INFINITE DIMENSIONAL MORSE THEORY , 1989 .

[135]  Edward Witten,et al.  Topological gravity in two dimensions , 1988 .

[136]  I. M. Singer,et al.  Topological Yang-Mills symmetry , 1988 .

[137]  G. Moore,et al.  Polynomial equations for rational conformal field theories , 1988 .

[138]  A. Floer,et al.  The unregularized gradient flow of the symplectic action , 1988 .

[139]  A. Floer,et al.  An instanton-invariant for 3-manifolds , 1988 .

[140]  E. Verlinde,et al.  Fusion Rules and Modular Transformations in 2D Conformal Field Theory , 1988 .

[141]  Edward Witten,et al.  Topological quantum field theory , 1988 .

[142]  Edward Witten,et al.  Topological sigma models , 1988 .

[143]  G. Segal The Definition of Conformal Field Theory , 1988 .

[144]  Michael Atiyah,et al.  Topological quantum field theories , 1988 .

[145]  Robert C. Penner,et al.  Perturbative series and the moduli space of Riemann surfaces , 1988 .

[146]  David,et al.  Topological Strings* , 1988 .

[147]  E. Witten,et al.  Nonperturbative Effects on the String World Sheet , 1987 .

[148]  D. Espriu,et al.  On the fine structure of strings , 1987 .

[149]  S. Donaldson Geometry of four-manifolds , 1990 .

[150]  J. Bismut Localization formulas, superconnections, and the index theorem for families , 1986 .

[151]  D. Quillen,et al.  Superconnections, thom classes, and equivariant differential forms , 1986 .

[152]  Edward Y. Miller,et al.  THE HOMOLOGY OF THE MAPPING CLASS GROUP , 1986 .

[153]  Frances Kirwan,et al.  On spaces of maps from Riemann surfaces to Grassmannians and applications to the cohomology of moduli of vector bundles , 1985 .

[154]  P. Olesen Strings and {QCD} , 1985 .

[155]  M. Gromov Pseudo holomorphic curves in symplectic manifolds , 1985 .

[156]  P. Ginsparg,et al.  The Structure of Gauge and Gravitational Anomalies , 1985 .

[157]  L. Alvarez-Gaumé Supersymmetry and Index Theory , 1985 .

[158]  J. Zuber,et al.  Strong Coupling Expansion of Large $N$ {QCD} and Surfaces , 1985 .

[159]  S. Morita Characteristic classes of surface bundles , 1984 .

[160]  J. Thierry-Mieg,et al.  Algebraic Structure of Quantum Gravity and the Classification of the Gravitational Anomalies , 1984 .

[161]  F. Kirwan Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31 , 1984 .

[162]  I. Kostov Multicolor QCD in terms of random surfaces , 1984 .

[163]  M. Atiyah,et al.  Dirac operators coupled to vector potentials. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[164]  Allan L. Edmonds,et al.  On the classification of generic branched coverings of surfaces , 1984 .

[165]  M. Guest Topology of the Space of Absolute Minima of the Energy Functional , 1984 .

[166]  Michael Atiyah,et al.  The moment map and equivariant cohomology , 1984 .

[167]  A. Migdal Loop equations and 1N expansion , 1983 .

[168]  J. Drouffe,et al.  Strong coupling and mean field methods in lattice gauge theories , 1983 .

[169]  F. Knudsen The projectivity of the moduli space of stable curves, II: The stacks $M_{g,n}$ , 1983 .

[170]  V. Kazakov U(∞) lattice gauge theory as a free lattice string theory , 1983 .

[171]  L. Alvarez-Gaumé Supersymmetry and the Atiyah-Singer index theorem , 1983 .

[172]  M. Waldrop Supersymmetry and supergravity. , 1983, Science.

[173]  Orlando Alvarez,et al.  Theory of Strings with Boundaries: Fluctuations, Topology, and Quantum Geometry , 1983 .

[174]  S. Donaldson An application of gauge theory to four-dimensional topology , 1983 .

[175]  M. Artin,et al.  Arithmetic and Geometry , 1983 .

[176]  Raoul Bott,et al.  The Yang-Mills equations over Riemann surfaces , 1983, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[177]  David Mumford,et al.  Towards an Enumerative Geometry of the Moduli Space of Curves , 1983 .

[178]  Edward Witten,et al.  Constraints on Supersymmetry Breaking , 1982 .

[179]  J. Duistermaat,et al.  On the variation in the cohomology of the symplectic form of the reduced phase space , 1982 .

[180]  Loring W. Tu,et al.  Differential forms in algebraic topology , 1982, Graduate texts in mathematics.

[181]  D. Mumford,et al.  On the Kodaira dimension of the moduli space of curves , 1982 .

[182]  E. Witten Supersymmetry and Morse theory , 1982 .

[183]  V. Kazakov,et al.  COMPUTATION OF THE WILSON LOOP FUNCTIONAL IN TWO-DIMENSIONAL U(°°) LATTICE GAUGE THEORY , 1981 .

[184]  L. Bers Finite dimensional Teichmüller spaces and generalizations , 1981 .

[185]  A. Polyakov Quantum Geometry of Bosonic Strings , 1981 .

[186]  A. Strominger Loop space solution of two-dimensional QCD , 1981 .

[187]  V. Kazakov WILSON LOOP AVERAGE FOR AN ARBITRARY CONTOUR IN TWO-DIMENSIONAL U(N) GAUGE THEORY , 1981 .

[188]  N. Bralić Exact computation of loop averages in two-dimensional Yang-Mills theory , 1980 .

[189]  V. Kazakov,et al.  Non-linear strings in two-dimensional U(∞) gauge theory , 1980 .

[190]  Andrew J. Hanson,et al.  Gravitation, Gauge Theories and Differential Geometry , 1980 .

[191]  D. Gross,et al.  Possible Third Order Phase Transition in the Large N Lattice Gauge Theory , 1980 .

[192]  A. Polyakov Gauge fields as rings of glue , 1980 .

[193]  M. Daniel,et al.  The Geometrical Setting of Gauge Theories of the {Yang-Mills} Type , 1980 .

[194]  P. West,et al.  Supersymmetric Yang-Mills Theories , 1980 .

[195]  Raymond O. Wells,et al.  Differential analysis on complex manifolds , 1980 .

[196]  Graeme Segal,et al.  The topology of spaces of rational functions , 1979 .

[197]  O. Babelon,et al.  The geometrical interpretation of the Faddeev-Popov determinant , 1979 .

[198]  A. Edmonds Deformation of Maps to Branched Coverings in Dimension Two , 1979 .

[199]  宮嶋 公夫 On the existence of Kuranishi family for deformations of holomorphic maps , 1979 .

[200]  難波 誠 Families of meromorphic functions on compact Riemann surfaces , 1979 .

[201]  M. Atiyah,et al.  Self-duality in four-dimensional Riemannian geometry , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[202]  C. Ezell Branch point structure of covering maps onto nonorientable surfaces , 1978 .

[203]  I. Singer Some remarks on the Gribov ambiguity , 1978 .

[204]  A. Schwarz The partition function of degenerate quadratic functional and Ray-Singer invariants , 1978 .

[205]  Joe W. Harris,et al.  Principles of Algebraic Geometry , 1978 .

[206]  C. DeWitt-Morette,et al.  Analysis, manifolds, and physics , 1977 .

[207]  S. Okubo Casimir invariants and vector operators in simple and classical Lie algebras , 1977 .

[208]  E. Horikawa On deformations of holomorphic maps. III , 1976 .

[209]  I. Bars A quantum string theory of hadrons and its relation to quantum chromodynamics in two dimensions , 1976 .

[210]  A. Hanson,et al.  Quarks at the ends of the string , 1976 .

[211]  F. Knudsen,et al.  Projectivity of the moduli space of stable curves , 1976 .

[212]  R. Stora,et al.  Renormalization of the abelian Higgs-Kibble model , 1975 .

[213]  J. Birman Braids, Links, and Mapping Class Groups. , 1975 .

[214]  A. Migdal Recursion Equations in Gauge Theories , 1975 .

[215]  G. Hooft A Planar Diagram Theory for Strong Interactions , 1974 .

[216]  R. Bott On the Chern-Weil homomorphism and the continuous cohomology of Lie-groups , 1973 .

[217]  A. Partensky On the Generalized Exchange Operators for SU(n) , 1972 .

[218]  堀川 穎ニ On Deformations of Holomorphic Maps (代数幾何学の最近の発展) , 1972 .

[219]  E. Horikawa On Deformations of Holomorphic Maps (代数幾何学の最近の発展) , 1972 .

[220]  M. Atiyah,et al.  The Index of Elliptic Operators: IV , 1971 .

[221]  William Fulton,et al.  Hurwitz Schemes and Irreducibility of Moduli of Algebraic Curves , 1969 .

[222]  D. Quillen,et al.  Rational homotopy theory , 1969 .

[223]  M. Atiyah,et al.  The Index of Elliptic Operators: II , 1968 .

[224]  M. Atiyah,et al.  The Index of elliptic operators. 1 , 1968 .

[225]  M. Atiyah,et al.  The Index of elliptic operators. 3. , 1968 .

[226]  G. Veneziano Construction of a crossing-simmetric, Regge-behaved amplitude for linearly rising trajectories , 1968 .

[227]  K. Nomizu,et al.  Foundations of Differential Geometry , 1963 .

[228]  A. Mullin,et al.  Group Theory and its Applications to Physical Problems , 1962 .

[229]  M. Hamermesh Group theory and its application to physical problems , 1962 .

[230]  N. N. Bogoliubov,et al.  Introduction to the theory of quantized fields , 1960 .

[231]  J. Conway,et al.  Functions of a Complex Variable , 1964 .

[232]  R. E. Ingram Some characters of the symmetric group , 1950 .

[233]  D. Fnedan,et al.  Supersymmetric Derivation of the Atiyah-singer Index and the Chiral Anomaly , 2022 .

[234]  R. Ho Algebraic Topology , 2022 .