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These pedagogical lectures given at the Corfu Summer Institute 2018 review two generalised notions of T-duality, non-Abelian T-duality and Poisson-Lie duality, and their applications.
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A. Catal-Ozer, Non-Abelian T-duality as a Transformation in Double Field Theory
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C. Montonen and D. I. Olive, Magnetic Monopoles as Gauge Particles?
1977
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M. E. Peskin, Mandelstam ’t Hooft Duality in Abelian Lattice Models
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V. E. Zakharov and A. V. Mikhailov, Relativistically Invariant Two-Dimensional Models in Field Theory Integrable by the Inverse Problem Technique. (In Russian)
1978
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A. B. Zamolodchikov and A. B. Zamolodchikov, Factorized s Matrices in Two-Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Models
1978
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H. Osborn, Topological Charges for N=4 Supersymmetric Gauge Theories and Monopoles of Spin 1
1979
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R. Savit, Duality in Field Theory and Statistical Systems
1980
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Y. Y. Goldschmidt and E. Witten, Conservation Laws in Some Two-dimensional Models
1980
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C. R. Nappi, Some Properties of an Analog of the Nonlinear σ \sigma Model
1980
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C. Dasgupta and B. I. Halperin, Phase Transition in a Lattice Model of Superconductivity
1981
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E. Abdalla, M. C. B. Abdalla, and M. Gomes, Anomaly in the Nonlocal Quantum Charge of the CP (n-1)
1981
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I. V. Cherednik, Relativistically Invariant Quasiclassical Limits of Integrable Two-dimensional Quantum Models
1981
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E. Witten, Nonabelian Bosonization in Two-Dimensions
1983
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K. Kikkawa and M. Yamasaki, Casimir Effects in Superstring Theories
1984
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L. D. Faddeev and N. Yu. Reshetikhin, Integrability of the Principal Chiral Field Model in (1+1)-dimension
1986
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J. M. Maillet, New Integrable Canonical Structures in Two-dimensional Models
1986
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T. H. Buscher, A Symmetry of the String Background Field Equations
1987
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N. Sakai and I. Senda, Vacuum Energies of String Compactified on Torus
1987
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T. H. Buscher, Path Integral Derivation of Quantum Duality in Nonlinear Sigma Models
1988
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V. G. Drinfeld, A New realization of Yangians and quantized affine algebras
1988
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K. Bardakci, E. Rabinovici, and B. Saering, String Models with c < 1 Components
1988
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K. Gawedzki and A. Kupiainen, G/h Conformal Field Theory from Gauged WZW Model
1988
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K. Uhlenbeck, Harmonic maps into Lie groups: classical solutions of the chiral model
1989
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C. M. Hull and B. J. Spence, The Gauged Nonlinear σ \sigma Model With Wess-Zumino Term
1989
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C. Destri and H. J. de Vega, Light Cone Lattices and the Exact Solution of Chiral Fermion and σ \sigma Models
1989
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P. Hasenfratz, M. Maggiore, and F. Niedermayer, The Exact mass gap of the O(3) and O(4) nonlinear sigma models in d = 2
1990
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M. J. Duff, Duality Rotations in String Theory
1990
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A. A. Tseytlin, Duality Symmetric Formulation of String World Sheet Dynamics
1990
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A. A. Tseytlin, Duality symmetric closed string theory and interacting chiral scalars
1991
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M. Rocek and E. P. Verlinde, Duality, quotients, and currents
1992
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J. Balog, S. Naik, F. Niedermayer, and P. Weisz, Exact mass gap of the chiral SU(n) x SU(n) model
1992
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E. Witten, On Holomorphic factorization of WZW and coset models
1992
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X. C. de la Ossa and F. Quevedo, Duality symmetries from nonAbelian isometries in string theory
1993
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M. Gasperini, R. Ricci, and G. Veneziano, A Problem with nonAbelian duality?
1993
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W. Siegel, Superspace duality in low-energy superstrings
1993
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W. Siegel, Two vierbein formalism for string inspired axionic gravity
1993
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C. M. Hull and P. K. Townsend, Unity of superstring dualities
1994
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N. Seiberg and E. Witten, Electric - magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
1994
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E. H. Fradkin and F. A. Schaposnik, The Fermion - boson mapping in three-dimensional quantum field theory
1994
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C. P. Burgess and F. Quevedo, Bosonization as duality
1994
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C. P. Burgess and F. Quevedo, NonAbelian bosonization as duality
1994
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A. Giveon and M. Rocek, On nonAbelian duality
1994
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T. Curtright and C. K. Zachos, Currents, charges, and canonical structure of pseudodual chiral models
1994
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E. Alvarez, L. Alvarez-Gaume, and Y. Lozano, On nonAbelian duality
1994
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E. Witten, String theory dynamics in various dimensions
1995
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N. Seiberg, Electric - magnetic duality in supersymmetric nonAbelian gauge theories
1995
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C. Klimčík and P. Ševera, Dual nonAbelian duality and the Drinfeld double
1995
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Y. Lozano, NonAbelian duality and canonical transformations
1995
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S. Elitzur, A. Giveon, E. Rabinovici, A. Schwimmer, and G. Veneziano, Remarks on nonAbelian duality
1995
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C. Klimčík and P. Ševera, Poisson-Lie T duality and loop groups of Drinfeld doubles
1996
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K. Sfetsos, NonAbelian duality, parafermions and supersymmetry
1996
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C. Klimčík and P. Ševera, NonAbelian momentum winding exchange
1996
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hep-th/9605187
L. D. Faddeev, How algebraic Bethe ansatz works for integrable model · 1996
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K. Sfetsos, Poisson-Lie T duality and supersymmetry
1997
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N. Kaloper and K. A. Meissner, Duality beyond the first loop
1997
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C. Klimcik and P. Severa, Open strings and D-branes in WZNW model
1997
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P. Pasti, D. P. Sorokin, and M. Tonin, On Lorentz invariant actions for chiral p forms
1997
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K. Sfetsos, Canonical equivalence of nonisometric sigma models and Poisson-Lie T duality
1998
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J. M. Maldacena, The Large N limit of superconformal field theories and supergravity
1998
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R. R. Metsaev and A. A. Tseytlin, Type IIB superstring action in AdS(5) x S**5 background
1998
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J. M. Evans, M. Hassan, N. J. MacKay, and A. J. Mountain, Local conserved charges in principal chiral models
1999
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K. Hori, D-branes, T duality, and index theory
1999
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M. Rocek and A. A. Tseytlin, Partial breaking of global D = 4 supersymmetry, constrained superfields, and three-brane actions
1999
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N. Seiberg and E. Witten, String theory and noncommutative geometry
1999
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A. Yu. Alekseev and V. Schomerus, D-branes in the WZW model
1999
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2015
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2015
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2015
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2015
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T. R. Araujo and H. Nastase, Non-Abelian T-duality for nonrelativistic holographic duals
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K. Sfetsos, Duality invariant class of two-dimensional field theories
1999
Cited alongside, same era.
S. F. Hassan, T duality, space-time spinors and RR fields in curved backgrounds
2000
Cited alongside, same era.
G. Felder, J. Frohlich, J. Fuchs, and C. Schweigert, The Geometry of WZW branes
2000
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S. Stanciu, D-branes in group manifolds
2000
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C. Klimčík, Yang-Baxter sigma models and dS/AdS T duality
2002
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L. Snobl and L. Hlavaty, Classification of six-dimensional real Drinfeld doubles
2002
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2015
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R. Blumenhagen, F. Hassler, and D. Lust, Double Field Theory on Group Manifolds
2015
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P. Ševera, Poisson?Lie T-Duality and Courant Algebroids
2015
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T. Matsumoto and K. Yoshida, Yang–Baxter sigma models based on the CYBE
2015
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F. Delduc, M. Magro, and B. Vicedo, Integrable double deformation of the principal chiral model
2015
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G. Arutyunov, R. Borsato, and S. Frolov, Puzzles of η \eta -deformed AdS 5 × {}_{5}\times S 5
2015
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2015
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C. Appadu and T. J. Hollowood, Beta function of k deformed AdS 5 × {}_{5}\times S 5
2015
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K. Sfetsos and K. Siampos, The anisotropic λ \lambda -deformed SU(2) model is integrable
2015
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2015
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A. Karch and D. Tong, Particle-Vortex Duality from 3d Bosonization
2016
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2016
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2016
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2016
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S. Demulder, D. Dorigoni, and D. C. Thompson, Resurgence in η \eta -deformed Principal Chiral Models
2016
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2016
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2016
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2016
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L. A. Pando Zayas, V. G. J. Rodgers, and C. A. Whiting, Supergravity solutions with AdS 4
2016
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S. Driezen, A. Sevrin, and D. C. Thompson, Aspects of the Doubled Worldsheet
2016
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2016
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R. Borsato and L. Wulff, Integrable Deformations of T T -Dual σ \sigma Models
2016
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C. Klimčík, Poisson-Lie T-duals of the bi-Yang-Baxter models
2016
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2016
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R. Borsato and L. Wulff, Target space supergeometry of η \eta and λ \lambda -deformed strings
2016
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Y. Chervonyi and O. Lunin, Generalized λ \lambda -deformations of AdS p × {}_{p}\times S p
2016
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2016
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2016
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R. Borsato and L. Wulff, On non-abelian T-duality and deformations of supercoset string sigma-models
2017
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G. Itsios, Y. Lozano, J. Montero, and C. Nunez, The AdS 5
2017
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2017
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Y. Lozano, C. Nunez, and S. Zacarias, BMN Vacua, Superstars and Non-Abelian T-duality
2017
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J. van Gorsel and S. Zacarías, A Type IIB Matrix Model via non-Abelian T-dualities
2017
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2017
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D. Osten and S. J. van Tongeren, Abelian Yang–Baxter deformations and TsT transformations
2017
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B. Hoare and D. C. Thompson, Marginal and non-commutative deformations via non-abelian T-duality
2017
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C. Klimcik, Yang-Baxter σ \sigma -model with WZNW term as ℰ {\mathcal{E}} -model
2017
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2017
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2017
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S. J. van Tongeren, Almost abelian twists and AdS/CFT
2017
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2017
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G. Georgiou and K. Sfetsos, A new class of integrable deformations of CFTs
2017
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2017
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F. A. Smirnov and A. B. Zamolodchikov, On space of integrable quantum field theories
2017
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M. Hong, Y. Kim, and E. O. Colgáin, On non-Abelian T-duality for non-semisimple groups
2018
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2018
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2018
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2018
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2018
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2018
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R. Borsato and L. Wulff, Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
2018
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2018
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L. Wulff, Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly
2018
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2018
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T. Araujo, E. O. Colgáin, and H. Yavartanoo, Embedding the modified CYBE in Supergravity
2018
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2018
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2018
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E. Sagkrioti, K. Sfetsos, and K. Siampos, RG flows for λ \lambda -deformed CFTs
2018
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S. Driezen, A. Sevrin, and D. C. Thompson, D-branes in λ \lambda -deformations
2018
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M. Guica, An integrable Lorentz-breaking deformation of two-dimensional CFTs
2018
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D. M. Schmidtt, Lambda Models From Chern-Simons Theories
2018
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Y. Lozano, N. T. Macpherson, and J. Montero, AdS 6
2019
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C. Klimcik, Affine Poisson and affine quasi-Poisson T-duality
2019
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2019
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2019
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