Lecture Notes for Felix Klein Lectures

These are lecture notes for a series of talks at the Hausdorff Mathematical Institute, Bonn, Oct. 1-11, 2012 December 5, 2012

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[34]  Cluster χ-varieties, amalgamation, and Poisson—Lie groups , 2005, math/0508408.

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[37]  J. Maldacena,et al.  Bubbling AdS space and 1/2 BPS geometries , 2004, hep-th/0409174.

[38]  B. Pioline.  Four ways across the wall , 2011, 1103.0261.

[39]  M 5-brane and superconformal (0,2) tensor multiplet in six dimensions , 1997, hep-th/9711161.

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[43]  Self-dual strings and N = 2 supersymmetric field theory , 1996, hep-th/9604034.

[44]  Daniel S. Freed.  Dirac Charge Quantization and Generalized Differential Cohomology , 2000 .

[45]  K-Theory in Quantum Field Theory , 2002, math-ph/0206031.

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[47]  Yan Soibelman,et al.  Stability structures, motivic Donaldson-Thomas invariants and cluster transformations , 2008, 0811.2435.

[48]  E. Ó Colgáin,et al.  On the generality of the LLM geometries in M-theory , 2010, 1010.5982.

[49]  T. Banks.  Modern quantum field theory : a concise introduction , 2008 .

[50]  Shlomo S. Razamat,et al.  The 4d Superconformal Index from q-deformed 2d Yang-Mills , 2011, 1104.3850.

[51]  G. Moore,et al.  On 2d TQFTs whose values are holomorphic symplectic varieties , 2011, 1106.5698.

[52]  Yinan Song,et al.  A theory of generalized Donaldson–Thomas invariants , 2008, 0810.5645.

[53]  J. Distler,et al.  Tinkertoys for the DN series , 2011, 1106.5410.

[54]  G. Moore,et al.  On 6d N = (2, 0) theory compactified on a Riemann surface with finite area , 2011, Progress of Theoretical and Experimental Physics.

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[58]  S. Lukyanov,et al.  Quantum sine(h)-Gordon model and classical integrable equations , 2010, 1003.5333.

[59]  G. Festuccia,et al.  Rigid supersymmetric theories in curved superspace , 2011, 1105.0689.

[60]  M. Kontsevich,et al.  Motivic Donaldson-Thomas invariants: Summary of results , 2009, 0910.4315.

[61]  L. Alday,et al.  Liouville Correlation Functions from Four-Dimensional Gauge Theories , 2009, 0906.3219.

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[63]  A. Kapustin,et al.  Topological boundary conditions in abelian Chern-Simons theory , 2010, 1008.0654.

[64]  BPS Structure of Argyres-Douglas Superconformal Theories , 1999, hep-th/9910182.

[65]  A. Kapustin,et al.  Three-dimensional topological field theory and symplectic algebraic geometry I , 2008, 0909.3643.

[66]  F. Passerini,et al.  (de)Tails of Toda CFT , 2010, 1012.1352.

[67]  M. Yamazaki,et al.  $ {\text{SL}}\left( {2,\mathbb{R}} \right) $ Chern-Simons, Liouville, and gauge theory on duality walls , 2011, 1103.5748.

[68]  I. M. Singer,et al.  Quadratic functions in geometry, topology, and M-theory , 2002, math/0211216.

[69]  N. Drukker,et al.  Loop operators and S-duality from curves on Riemann surfaces , 2009, 0907.2593.

[70]  On S-duality for Non-Simply-Laced Gauge Groups , 2006, hep-th/0603048.

[71]  J. Maldacena,et al.  The gravity duals of N=2 superconformal field theories , 2009, 0904.4466.

[72]  Sergei Gukov,et al.  3-Manifolds and 3d Indices , 2011, 1112.5179.

[73]  Yuji Tachikawa,et al.  Mirrors of 3d Sicilian theories , 2010, 1007.0992.

[74]  Duality relations among topological effects in string theory , 1999, hep-th/9912086.

[75]  T. Banks,et al.  Symmetries and Strings in Field Theory and Gravity , 2010, 1011.5120.

[76]  N. Seiberg,et al.  S-duality in N=2 supersymmetric gauge theories , 2007, 0711.0054.

[77]  J. Manschot,et al.  Wall crossing from Boltzmann black hole halos , 2010, 1011.1258.

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[79]  A brief review of `little string theories' , 1999, hep-th/9911147.

[80]  G. Moore,et al.  Framed BPS states , 2010, 1006.0146.

[81]  D. Freed,et al.  Topological Quantum Field Theories from Compact Lie Groups , 2009, 0905.0731.

[82]  Yuji Tachikawa.  S-duality via outer-automorphism twists , 2010, 1009.0339.

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[84]  Shlomo S. Razamat,et al.  Gauge Theories and Macdonald Polynomials , 2011, 1110.3740.

[85]  L. Alday,et al.  Liouville/Toda central charges from M5-branes , 2009, 1106.1172.

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[88]  B. Pioline,et al.  Wall-crossing, Rogers dilogarithm, and the QK/HK correspondence , 2011, 1110.0466.

[89]  Holographic Uniformization , 2011, 1109.3724.

[90]  Moduli spaces of local systems and higher Teichmüller theory , 2003, math/0311149.

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[92]  Some Comments On String Dynamics , 1995, hep-th/9507121.

[93]  A. Kapustin,et al.  Three-dimensional topological field theory and symplectic algebraic geometry II , 2010 .

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[96]  Curves of marginal stability, and weak- and strong-coupling BPS spectra in N = 2 supersymmetric QCD , 1996, hep-th/9605101.

[97]  A. A. Tseytfin.  Harmonic superpositions of M-branes , 1996 .

[98]  Shlomo S. Razamat,et al.  Bootstrapping the superconformal index with surface defects , 2012, 1207.3577.

[99]  Shlomo S. Razamat,et al.  S-duality and 2d topological QFT , 2009, 0910.2225.

[100]  E. Witten.  Five-brane effective action in M theory , 1996, hep-th/9610234.

[101]  E. Witten.  Fivebranes and Knots , 2011, 1101.3216.

[102]  Andreas Gustavsson.  Algebraic structures on parallel M2-branes , 2007, 0709.1260.

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[104]  Shlomo S. Razamat,et al.  The superconformal index of the E6 SCFT , 2010, 1003.4244.

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[107]  D. Gaiotto,et al.  Gauge Theories Labelled by Three-Manifolds , 2011, 1108.4389.

[108]  2d Wall-Crossing, R-twisting, and a Supersymmetric Index , 2010, 1002.3638.

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[113]  D. Gaiotto.  Surface operators in $ \mathcal{N} $ = 2 4d gauge theories , 2009, 0911.1316.

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[115]  G. Moore,et al.  Split states, entropy enigmas, holes and halos , 2007, hep-th/0702146.

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[120]  L. Alday,et al.  Affine SL(2) Conformal Blocks from 4d Gauge Theories , 2010, Letters in Mathematical Physics.

[121]  C. Vafa,et al.  $\mathcal{N} = 2$ quantum field theories and their BPS quivers , 2011, 1112.3984.

[122]  Cluster ensembles, quantization and the dilogarithm , 2003, math/0311245.

[123]  F. Denef.  Supergravity Flows and D-brane Stability , 2000, hep-th/0005049.

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[126]  L. Alday,et al.  Central charges of Liouville and Toda theories from M5-branes. , 2010, Physical review letters.

[127]  A. Kapustin.  Topological Field Theory, Higher Categories, and Their Applications , 2010, 1004.2307.

[128]  Notes on theories with 16 supercharges , 1997, hep-th/9705117.

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

[130]  C. Vafa,et al.  Classification of Complete N = 2 Supersymmetric Theories in 4 Dimensions , 2011, 1103.5832.

[131]  C. Papageorgakis,et al.  Nonabelian (2,0) tensor multiplets and 3-algebras , 2010, 1007.2982.

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[133]  A Derivation of K theory from M theory , 2000, hep-th/0005090.

[134]  L. Alday,et al.  Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry , 2009, 0909.0945.

[135]  S. Raju,et al.  Indices for superconformal field theories in 3, 5 and 6 dimensions , 2008, Journal of High Energy Physics.

[136]  G. Moore,et al.  Spectral Networks and Snakes , 2012, 1209.0866.

[137]  Cluster Ensembles, Quantization and the Dilogarithm II: The Intertwiner , 2007, math/0702398.

[138]  M. Rozali.  Matrix Theory and U-Duality in Seven Dimensions , 1997, hep-th/9702136.

[139]  G. Moore,et al.  Wall-crossing in coupled 2d-4d systems , 2011, 1103.2598.

[140]  C. Vafa,et al.  R-Twisting and 4d/2d Correspondences , 2010, 1006.3435.

[141]  Jacob Lurie,et al.  On the Classification of Topological Field Theories , 2009, 0905.0465.

[142]  C. Vafa,et al.  BPS Wall Crossing and Topological Strings , 2009, 0910.2615.

[143]  Shlomo S. Razamat,et al.  Exceptional indices , 2012, 1203.5517.

[144]  P. Ho,et al.  A non-abelian self-dual gauge theory in 5 + 1 dimensions , 2011, 1104.4040.

[145]  G. Moore,et al.  Wall-crossing from supersymmetric galaxies , 2010, 1008.0030.

[146]  Yuji Tachikawa.  On W-algebras and the symmetries of defects of 6d $ \mathcal{N} = \left( {2,0} \right) $ theory , 2011, 1102.0076.

[147]  N. Drukker,et al.  The virtue of defects in 4D gauge theories and 2D CFTs , 2010, 1003.1112.

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

[149]  W. Taylor,et al.  Charge lattices and consistency of 6D supergravity , 2011, 1103.0019.

[150]  Dual Teichmuller and lamination spaces , 2005, math/0510312.

[151]  G. Segal,et al.  D-branes and K-theory in 2D topological field theory , 2006, hep-th/0609042.

[152]  W. Nahm,et al.  Classification of all simple graded Lie algebras whose Lie algebra is reductive. II. Construction of the exceptional algebras , 1976 .

[153]  Self-Dual Strings in Six Dimensions: Anomalies, the ADE-Classification, and the World-Sheet WZW-Model , 2004, hep-th/0405056.

[154]  C. Papageorgakis,et al.  M5-Branes, D4-Branes and quantum 5D super-Yang-Mills , 2010, 1012.2882.

[155]  N. Seiberg,et al.  Matrix description of M-theory on T4 and T5 , 1997, hep-th/9704089.

[156]  Open p-branes , 1995, hep-th/9512059.