The gauge theory - From Sigma Models to Four-dimensional QFT

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The Coulomb branchof the moduli spaceof vacua of thed=4 N=2 supersymmetricgauge theoryis the baseof a complex (algebraic)integrable system
The Coulomb branchof the same theory,compactified on a circle downto three dimensionsis the phasespace ofthe same integrable system
Page 1 and 2: Classical GeometryofQuantum Integra
Page 3 and 4: Earlier workG.Moore, NN, S.Shatashv
Page 5: The supersymmetricgauge theorieswit
Page 8: OperatorsThe « twisted chiral ring
Page 11 and 12: The effective twistedsuperpotential
Page 13 and 14: The effective twistedsuperpotential
Page 15 and 16: The miracle of Bethe ansatz:The spe
Page 17 and 18: The elliptic Calogero-MosersystemN
Page 19 and 20: It is clear that one shouldget anin
Page 21 and 22: The gauge theoryThe N=2 d=2 theory,
Page 23 and 24: The two dimensional theoryHas aneff
Page 25 and 26: The effective twisted superpotentia
Page 27 and 28: In particular, for the N=2 * theory
Page 29 and 30: Bethe equationsFactorized S-matrixT
Page 31 and 32: Bethe equationsFactorized S-matrixH
Page 33 and 34: Dictionary
Page 35 and 36: DictionaryclassicalEllipticCM4d N=2
Page 37 and 38: DictionaryThe(complexified)systemTh
Page 39 and 40: DictionaryThe correspondenceExtends
Page 41 and 42: Two ways of gettingtwo dimensional
Page 43 and 44: In the mid-nineties of the 20centur
Page 47: Special coordinateson the moduli sp
Page 51 and 52: The moduli spaceofvacua ofd=3 N=4 t
Page 53 and 54: The resulting effective susygauge t
Page 55 and 56: The Hitchin moduli spaceis the Higg
Page 57 and 58: One can allow the Riemann surfacewi
Page 59 and 60: For example,the N=2* SU(2) theoryCo
Page 61 and 62: Hitchin systemGauge theory on a Rie
Page 63 and 64: Hitchin systemModulo gauge transfor
Page 65 and 66: Hyperkahler structure of M HThree K
Page 67 and 68: Hyperkahler structureThe linear com
Page 69 and 70: The integrable structureThese funct
Page 71 and 72: The integrable structureThe action-
Page 73 and 74: Thinking about the Ω - deformation
Page 75 and 76: M H as themoduli space of G C flatc
Page 81 and 82: Opers on a sphereFor example, on a
Page 83 and 84: Opers on a sphereAll in all we get
Page 85 and 86: The variety of opers isLagrangian w
Page 87 and 88: α i , β i
Page 89 and 90: The moduli space is going to be cov
Page 91 and 92: The maximal complex structure degen
Page 93 and 94: The α i coordinates are nothing bu
Page 95 and 96: The local data involving the cycle
Page 97 and 98: The local picture:four holes, two i
Page 99 and 100:
The coordinates α i ,β i can beth
Page 101 and 102:
The construction of the hyperbolic
Page 103 and 104:
Our polygons sit in the group manif
Page 105 and 106:
The local data involving the cycle
Page 107 and 108:
The s-t channel flop:the generating
Page 109 and 110:
The s-u flop =composition ofthe 1-2
Page 111 and 112:
The theoryWhy did the twisted super
Page 113 and 114:
The theoryWhy did these hyperbolic
Page 115 and 116:
In the genus zero case it should im
Page 117 and 118:
The prediction of the theoryThe con
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The gauge theory - From Sigma Models to Four-dimensional QFT

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