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In this note we summarize a few of the many recent developments in two-dimensional quantum field theories.
Alexander A. Migdal, Recursion Equations in Gauge Theories , Sov.Phys.JETP 42
1975
Earlier work this paper cites.
Edward Witten and Jonathan Bagger, Quantization of Newton’s constant in certain supergravity theories , Phys. Lett. B 115
1982
Earlier work this paper cites.
Andrew Strominger, Yukawa Couplings in Superstring Compactification , Phys.Rev.Lett. 55
1985
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M. Dine, N. Seiberg, X.-G. Wen, and E. Witten, Nonperturbative effects on the string world sheet , Nuclear Phys. B 278
1986
Earlier work this paper cites.
by same author, Superstrings with torsion , Nuclear Phys. B 274
1986
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by same author, Nonperturbative effects on the string world sheet. II , Nuclear Phys. B 289
1987
Earlier work this paper cites.
Doron Gepner, Exactly solvable string compactifications on manifolds of SU ( N ) {\rm SU}(N) holonomy , Phys. Lett. B 199
1987
Earlier work this paper cites.
Wolfgang Lerche, Cumrun Vafa, and Nicholas P. Warner, Chiral rings in N = 2 N=2 superconformal theories , Nuclear Phys. B 324
1989
Earlier work this paper cites.
B. R. Greene and M. R. Plesser, Duality in Calabi-Yau moduli space , Nuclear Phys. B 338
1990
Earlier work this paper cites.
Vipul Periwal and Andrew Strominger, Kähler geometry of the space of N = 2 N=2 superconformal field theories , Phys. Lett. B 235
1990
Earlier work this paper cites.
B. Ye. Rusakov, Loop averages and partition functions in U ( N ) {\rm U}(N) gauge theory on two-dimensional manifolds , Modern Phys. Lett. A 5
1990
Earlier work this paper cites.
Philip Candelas, Xenia C. de la Ossa, Paul S. Green, and Linda Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory , Nuclear Phys. B 359
1991
Earlier work this paper cites.
Jacques Distler, Notes on N=2 sigma models , (1992)
1992
Earlier work this paper cites.
Edward Witten, Mirror manifolds and topological field theory , Essays on mirror manifolds, Int. Press, Hong Kong, 1992, pp. 120–158. MR 1191422 (94c:81194)
1992
Earlier work this paper cites.
David J. Gross and Washington Taylor, IV, Two-dimensional QCD is a string theory , Nuclear Phys. B 400
1993
Earlier work this paper cites.
Victor V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties , J. Algebraic Geom. 3
1994
Earlier work this paper cites.
David R. Morrison and M. Ronen Plesser, Summing the instantons: quantum cohomology and mirror symmetry in toric varieties , Nuclear Phys. B 440
1995
Earlier work this paper cites.
N. Seiberg, Electric-magnetic duality in supersymmetric non-abelian gauge theories , Nuclear Phys. B 435
1995
Earlier work this paper cites.
by same author, Towards mirror symmetry as duality for two-dimensional abelian gauge theories , Strings ’95 (Los Angeles, CA, 1995), World Sci. Publ., River Edge, NJ, 1996, pp. 374–387. MR 1660724 (99m:81224)
1996
Earlier work this paper cites.
Victor V. Batyrev and Lev A. Borisov, Dual cones and mirror symmetry for generalized Calabi-Yau manifolds , Mirror symmetry, II, AMS/IP Stud. Adv. Math., vol. 1, Amer. Math. Soc., Providence, RI, 1997, pp. 71–86. MR 1416334 (98b:14033)
1997
Earlier work this paper cites.
Ralph Blumenhagen, Rolf Schimmrigk, and Andreas Wißkirchen, ( 0 , 2 ) (0,2) mirror symmetry , Nuclear Phys. B 486
1997
Earlier work this paper cites.
Ralph Blumenhagen and Savdeep Sethi, On orbifolds of ( 0 , 2 ) (0,2) models , Nuclear Phys. B 491
1997
Earlier work this paper cites.
Eric Sharpe, D-branes, derived categories, and Grothendieck groups , Nuclear Phys. B 561
1999
Earlier work this paper cites.
Kentaro Hori and Cumrun Vafa, Mirror symmetry , (2000)
2000
Earlier work this paper cites.
Allan Adams, Anirban Basu, and Savdeep Sethi, ( 0 , 2 ) (0,2) duality , Adv. Theor. Math. Phys. 7
2003
Earlier work this paper cites.
Anirban Basu and Savdeep Sethi, World-sheet stability of ( 0 , 2 ) (0,2) linear sigma models , Phys. Rev. D (3) 68
2003
Earlier work this paper cites.
Chris Beasley and Edward Witten, Residues and world-sheet instantons , J. High Energy Phys. (2003), no. 10, 065, 39 pp. (electronic). MR 2030598 (2005f:81223)
2003
Earlier work this paper cites.
Ilarion V. Melnikov and M. Ronen Plesser, The Coulomb branch in gauged linear sigma models , J. High Energy Phys. (2005), no. 6, 013, 33. MR 2158560 (2007a:81135)
2005
Earlier work this paper cites.
Tony Pantev and Eric Sharpe, Notes on gauging noneffective group actions , (2005)
2005
Earlier work this paper cites.
Allan Adams, Jacques Distler, and Morten Ernebjerg, Topological heterotic rings , Adv. Theor. Math. Phys. 10
2006
Earlier work this paper cites.
Sheldon Katz and Eric Sharpe, Notes on certain ( 0 , 2 ) (0,2) correlation functions , Comm. Math. Phys. 262
2006
Earlier work this paper cites.
by same author, A A -model correlators from the Coulomb branch , J. High Energy Phys. (2006), no. 2, 044, 21. MR 2219460 (2007d:81209)
2006
Earlier work this paper cites.
by same author, GLSMs for gerbes (and other toric stacks) , Adv. Theor. Math. Phys. 10
2006
Earlier work this paper cites.
by same author, String compactifications on Calabi-Yau stacks , Nuclear Phys. B 733
2006
Earlier work this paper cites.
by same author, Notes on correlation functions in ( 0 , 2 ) (0,2) theories , Snowbird lectures on string geometry, Contemp. Math., vol. 401, Amer. Math. Soc., Providence, RI, 2006, pp. 93–104. MR 2222532 (2007e:81100)
2006
Earlier work this paper cites.
Meng-Chwan Tan, Two-dimensional twisted sigma models and the theory of chiral differential operators , Adv. Theor. Math. Phys. 10
2006
Earlier work this paper cites.
Volker Braun, Maximilian Kreuzer, Burt A. Ovrut, and Emanuel Scheidegger, Worldsheet instantons, torsion curves and non-perturbative superpotentials , Phys. Lett. B 649
2007
Cited alongside, same era.
Volker Braun, Burt A. Ovrut, Maximilian Kreuzer, and Emanuel Scheidegger, Worldsheet instantons and torsion curves. A. Direct computation , J. High Energy Phys. (2007), no. 10, 022, 58. MR 2357956 (2009i:14080)
2007
Cited alongside, same era.
by same author, Worldsheet instantons and torsion curves. B. Mirror symmetry , J. High Energy Phys. (2007), no. 10, 023, 53. MR 2357955 (2009i:14079)
2007
Cited alongside, same era.
Simeon Hellerman, André Henriques, Tony Pantev, Eric Sharpe, and Matt Ando, Cluster decomposition, T T -duality, and gerby CFTs , Adv. Theor. Math. Phys. 11
2007
Cited alongside, same era.
by same author, Notes on orbifold Gromov-Witten theory , Fifth International Congress of Chinese Mathematicians. Part 1, 2, AMS/IP Stud. Adv. Math., 51, pt. 1, vol. 2, Amer. Math. Soc., Providence, RI, 2012, pp. 327–340. MR 2908078
2012
Later among the works it cites.
Ofer Aharony, Nathan Seiberg, and Yuji Tachikawa, Reading between the lines of four-dimensional gauge theories , J. High Energy Phys. (2013), no. 8, 115, front matter+41. MR 3106323
2013
Later among the works it cites.
Lara B. Anderson, Bei Jia, Ryan Manion, Burt Ovrut, and Eric Sharpe, General aspects of heterotic string compactifications on stacks and gerbes , (2013)
2013
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Matthew Ballard, Dragos Deliu, David Favero, M. Umut Isik, and Ludmil Katzarkov, Homological Projective Duality via Variation of Geometric Invariant Theory Quotients , (2013)
2013
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Kentaro Hori and David Tong, Aspects of non-abelian gauge dynamics in two-dimensional N = ( 2 , 2 ) N=(2,2) theories , J. High Energy Phys. (2007), no. 5, 079, 41 pp. (electronic). MR 2318130 (2009d:81351)
2007
Cited alongside, same era.
by same author, Homological projective duality , Publ. Math. Inst. Hautes Études Sci. (2007), no. 105, 157–220. MR 2354207 (2008k:14043)
2007
Cited alongside, same era.
by same author, Two-dimensional twisted sigma models, the mirror chiral de Rham complex, and twisted generalised mirror symmetry , J. High Energy Phys. (2007), no. 7, 013, 80 pp. (electronic). MR 2326774 (2009g:81184)
2007
Cited alongside, same era.
Elena Andreini, Yunfeng Jiang, and Hsian-Hua Tseng, On Gromov-Witten theory of root gerbes , (2008)
2008
Cited alongside, same era.
by same author, Worldsheet instantons and torsion curves , Advances in string theory, AMS/IP Stud. Adv. Math., vol. 44, Amer. Math. Soc., Providence, RI, 2008, pp. 231–240. MR 2494190 (2010e:14008)
2008
Cited alongside, same era.
Ron Donagi and Eric Sharpe, GLSMs for partial flag manifolds , J. Geom. Phys. 58
2008
Cited alongside, same era.
by same author, Derived categories of quadric fibrations and intersections of quadrics , Adv. Math. 218
2008
Cited alongside, same era.
Jock McOrist and Ilarion V. Melnikov, Half-twisted correlators from the Coulomb branch , J. High Energy Phys. (2008), no. 4, 071, 19. MR 2425232 (2009h:81272)
2008
Cited alongside, same era.
Francesco Benini, Richard Eager, Kentaro Hori, and Yuji Tachikawa, Elliptic genera of 2d N=2 gauge theories , (2013)
2013
Later among the works it cites.
Ron Donagi, Josh Guffin, Sheldon Katz, and Eric Sharpe, Physical aspects of quantum sheaf cohomology for deformations of tangent bundles of toric varieties , Adv. Theor. Math. Phys. 17
2013
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Nima Doroud, Jaume Gomis, Bruno Le Floch, and Sungjay Lee, Exact results in D = 2 D=2 supersymmetric gauge theories , J. High Energy Phys. (2013), no. 5, 093, front matter+69. MR 3080568
2013
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Davide Gaiotto, Gregory W. Moore, and Andrew Neitzke, Framed BPS states , Adv. Theor. Math. Phys. 17
2013
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Richard S. Garavuso and Eric Sharpe, Analogues of Mathai-Quillen forms in sheaf cohomology and applications to topological field theory , (2013)
2013
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Amin Gholampour and Hsian-Hua Tseng, On Donaldson-Thomas invariants of threefold stacks and gerbes , Proc. Amer. Math. Soc. 141
2013
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Daniel Halpern-Leistner and Ian Shipman, Autoequivalences of derived categories via geometric invariant theory , (2013)
2013
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James Halverson, Vijay Kumar, and David R. Morrison, New methods for characterizing phases of 2D supersymmetric gauge theories , J. High Energy Phys. (2013), no. 9, 143, front matter+31. MR 3107702
2013
Later among the works it cites.
Kentaro Hori, Duality in two-dimensional ( 2 , 2 ) (2,2) supersymmetric non-Abelian gauge theories , J. High Energy Phys. (2013), no. 10, 2013:121, front matter+74. MR 3118316
2013
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Kentaro Hori and Johanna Knapp, Linear sigma models with strongly coupled phases - one parameter models , JHEP 1311
2013
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by same author, A few Ricci-flat stacks as phases of exotic GLSM’s , Phys.Lett. B726
2013
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by same author, Predictions for Gromov-Witten invariants of noncommutative resolutions , J. Geom. Phys. 74
2013
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Nicolas M. Addington, Edward P. Segal, and Eric Sharpe, D-brane probes, branched double covers, and noncommutative resolutions , Adv. Theor. Math. Phys. 18
2014
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Lara B. Anderson, James Gray, and Eric Sharpe, Algebroids, Heterotic Moduli Spaces and the Strominger System , JHEP 1407
2014
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Paul S. Aspinwall and Benjamin Gaines, Rational Curves and (0,2)-Deformations , (2014)
2014
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by same author, Elliptic genera of two-dimensional N = 2 {N}=2 gauge theories with rank-one gauge groups , Lett. Math. Phys. 104
2014
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Jin Chen, Xiaoyi Cui, Mikhail Shifman, and Arkady Vainshtein, N=(0,2) deformation of (2, 2) sigma models: Geometric structure, holomorphic anomaly, and exact β \beta functions , Phys.Rev. D90
2014
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Xenia de la Ossa and Eirik E. Svanes, Holomorphic Bundles and the Moduli Space of N=1 Supersymmetric Heterotic Compactifications , JHEP 1410
2014
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by same author, A mathematical theory of quantum sheaf cohomology , Asian J. Math. 18
2014
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Abhijit Gadde and Sergei Gukov, 2d index and surface operators , J. High Energy Phys. (2014), no. 3, 080, front matter+40. MR 3190966
2014
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Abhijit Gadde, Sergei Gukov, and Pavel Putrov, (0, 2) trialities , JHEP 1403
2014
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by same author, Exact Solutions of 2d Supersymmetric Gauge Theories , (2014)
2014
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Bei Jia, Eric Sharpe, and R. Wu, Notes on nonabelian (0,2) theories and dualities , JHEP 1408
2014
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by same author, Two-sphere partition functions and Gromov-Witten invariants , Comm. Math. Phys. 325
2014
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David Kutasov and Jennifer Lin, (0,2) ADE Models From Four Dimensions , (2014)
2014
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by same author, (0,2) Dynamics From Four Dimensions , Phys.Rev. D89
2014
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Hai Lin, Baosen Wu, and Shing-Tung Yau, Heterotic String Compactification and New Vector Bundles , (2014)
2014
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by same author, Decomposition in diverse dimensions , Phys.Rev. D90
2014
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Yuji Tachikawa, On the 6d origin of discrete additional data of 4d gauge theories , JHEP 1405
2014
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Xiang Tang and Hsian-Hua Tseng, Duality theorems for étale gerbes on orbifolds , Adv. Math. 250
2014
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J. Guo, B. Jia, and E. Sharpe, Chiral operators in two-dimensional (0,2) theories and a test of triality , (2015)
2015
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