An Introduction to T-Duality in String Theory

Abstract

In these lectures a general introduction to T-duality is given. In the abelian case the approaches of Buscher, and Roucek and Verlinde are reviewed. Buscher's prescription for the dilaton transformation is recovered from a careful definition of the gauge integration measure. It is also shown how duality can be understood as a quite simple canonical transformation. Some aspects of non-abelian duality are also discussed, in particular what is known on relation to canonical transformations. Some implications of the existence of duality on the cosmological constant and the definition of distance in String Theory are also suggested.

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• Plane Gravitational Waves in String Theory
• Using Functional Methods to Compute Quantum Effects in the Liouville Model
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Cited by in corpus (185)

• Duality in the Type--II Superstring Effective Action
• Superstring Cosmology
• U-duality and M-Theory
• Double Field Theory: A Pedagogical Review
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• T-Duality: Topology Change from H-flux
• Multiple Dp-branes in Weak Background Fields
• AdS_5 x S^5 Untwisted
• Type IIB Supergravity Solutions with AdS${}_5$ From Abelian and Non-Abelian T Dualities
• T-Duality in the Green-Schwarz Formalism, and the Massless/Massive IIA Duality Map
• Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality
• Heterotic $\alpha$'-corrections in Double Field Theory
• T-duality and world-sheet supersymmetry
• The effective action of type II Calabi-Yau orientifolds
• Generalized N=(2,2) Supersymmetric Non-Linear Sigma Models
• Effective action of type II superstring theories at order ${\alpha }^{\prime 3}$: NS-NS couplings
• Renormalization and asymptotic safety in truncated quantum Einstein gravity
• Quantum Poisson-Lie T-duality and WZNW model
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• Remark About Non-Relativistic String in Newton-Cartan Background and Null Reduction
• Conformal Twists, Yang-Baxter $\sigma$-models & Holographic Noncommutativity
• Frequency-Independent Response of Self-Complementary Checkerboard Screens
• Effective action of bosonic string theory at order ${\alpha }^{\prime 2}$
• Quantum Gravity: A Brief History of Ideas and Some Prospects
• Integrability in dipole-deformed N=4 super Yang-Mills
• One loop renormalizability of the Poisson-Lie sigma models
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Duality constraints on effective actions
• Four-derivative couplings via T-duality constraint
• T-duality in Ramond-Ramond backgrounds
• Strings, Branes and Extra Dimensions
• Dualising the Baryonic Branch: Dynamic SU(2) and confining backgrounds in IIA
• T duality and Wald entropy formula in the Heterotic Superstring effective action at first order in ${\alpha }^{\prime }$
• On Conformal Properties of the Dualized Sigma-Models
• String duality transformations in $f(R)$ gravity from Noether symmetry approach
• T-Dual Cosmological Solutions of Double Field Theory II
• T-duality of the Riemann curvature corrections to supergravity
• Ricci curvature corrections to type II supergravity
• Are the String and Einstein Frames Equivalent
• Worldsheet Formalism for Decoupling Limits in String Theory
• Timelike Hopf Duality and Type IIA^* String Solutions
• On NS-NS couplings at order ${\alpha }^{\prime 3}$
• Para-Hermitian Geometries for Poisson-Lie Symmetric $\sigma$-models
• Note About T-duality of Non-Relativistic String
• BTZ black hole from Poisson-Lie T-dualizable sigma models with spectators
• S-matrix elements from T-duality
• T-duality in Massive Integrable Field Theories: The Homogeneous and Complex sine-Gordon Models
• Hodge Duality and Cosmological Constant
• T-duality in the weakly curved background
• The minimum mass of a charged spherically symmetric object in $D$ dimensions, its implications for fundamental particles, and holography
• On type II superstrings in bosonic backgrounds: the role of fermions and T-duality
• Noether symmetries and duality transformations in cosmology
• S-duality of S-matrix
• Fermionic T-duality: A snapshot review
• Discrete Symmetries of Functional Determinants
• Confinement, brane symmetry and the Julia-Toulouse approach for condensation of defects
• Non-Abelian Duality for Open Strings
• Solution of the Size and Horizon Problems from Classical String Geometry
• Ramond-Ramond corrections to type II supergravity at order ${\alpha }^{\prime 3}$
• The Embedding of Superstring Backgrounds in Einstein Gravity
• On S-duality of D${}_3$-brane S-matrix
• Doubling, T-Duality and Generalized Geometry: a Simple Model
• T-Duality of Green-Schwarz Superstrings on AdS(d) x S(d) x M(10-2d)
• Abelian duality in WZW models
• A Note on T-duality in Heterotic String Theory
• Duality and Central Charges in Supersymmetric Quantum Mechanics
• Non-Abelian T-duality for nonrelativistic holographic duals
• Surface terms in the effective actions via duality constraints
• $O(d,d)$ transformations preserve classical integrability
• Real fermionic symmetry in type II supergravity
• On S-duality in (2+1)-Chern-Simons Supergravity
• $O(9,9)$ symmetry of NS-NS couplings at order ${\alpha }^{\prime 3}$
• Exact Type IIB Superstring Backgrounds
• T-dualization in a curved background in absence of a global symmetry
• T-duality diagram for a weakly curved background
• Ramond-Ramond S-matrix elements from T-dual Ward identity
• T-duality of D-brane action at order ${\alpha }^{\prime }$ in bosonic string theory
• Geometric Transitions on non-Kaehler Manifolds
• Goursat's Problem and the Holographic Principle
• Duality family of scalar field
• Newtonian M(atrix) Cosmology
• T-duality and Effective D-Brane Actions
• Non-Abelian Axial-Vector Duality: a Geometric Description
• Electrically Charged Topological Solitons
• More on $(4,4)$ supermultiplets in $SU(2)\times SU(2)$ harmonic superspace
• Duality transformation and conformal equivalent scalar-tensor theories
• Note About Integrability and Gauge Fixing for Bosonic String on AdS(5)xS(5)
• Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation
• Symmetries for generating string cosmologies
• Non-abelian fermionic T-duality in supergravity
• String Primer
• Higher-derivative field redefinitions in the presence of boundary
• Jacobi-Lie symmetry and Jacobi-Lie T-dual sigma models on group manifolds
• Holomorphic Couplings In Non-Perturbative String Compactifications
• T-duality of axial and vector dyonic integrable models
• Fermionic T-Duality of $Ad{S}_n\times S^n(\times S^n)\times T^m$ using IIA Supergravity
• Gauged Supergravities from Spherical Reductions
• $O(25,25)$ symmetry of bosonic string theory at order ${\alpha }^{\prime 2}$
• K-Models and Type IIB Superstring Backgrounds
• ${\alpha }^{\prime }$-corrections to DBI action via T-duality constraint
• S-duality constraint on higher-derivative couplings
• Codimension Two Holography
• Bosonization and Duality in Condensed Matter Systems
• S-duality of color-ordered amplitudes
• The dual string sigma-model of the SU_q(3) sector
• Torsion formulation of gravity
• T-duality and Generalized Complex Geometry
• SL(2, Z) Multiplets of Type II Superstrings in $D<10$
• Dualised sigma-models at the two-loop order
• T-Duality in 2-D Integrable Models
• Surface terms in effective action of O-plane at order ${\alpha }^{\prime 2}$
• Quantum structure of T-dualized models with symmetry breaking
• Central Charges and Extra Dimensions in Supersymmetric Quantum Mechanics
• T-duality constraint on R-R couplings
• Principal Chiral Model without and with WZ term: Symmetries and Poisson-Lie T-Duality
• T-Dualities and Doubled Geometry of the Principal Chiral Model
• Courant bracket as T-dual invariant extension of Lie bracket
• Fermionic T-duality in fermionic double space
• Courant bracket twisted both by a 2-form $B$ and by a bi-vector $\theta$
• Courant bracket found out to be T-dual to Roytenberg bracket
• Fractonic self-duality and covariant magnetic fractons
• Stability of the non-perturbative $O(D,D)$ de-Sitter spacetime. The isotropic case
• $O(D,D)$-constraint on $D$-dimensional effective actions
• T-duality of Non-Relativistic String in Torsional Newton-Cartan Background
• A correspondence between the free and interacting field theories
• Twisted C-brackets
• Gravitational higher-form symmetries and the origin of hidden symmetries in Kaluza-Klein compactifications
• Fractional exclusion and braid statistics in one dimension: a study via dimensional reduction of Chern-Simons theory
• Solitons with Isospin
• Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field
• Dirichlet boundary conditions in type IIB superstring theory and fermionic T-duality
• $Ad{S}_3\times S^3$ Background from Poisson-Lie T-Duality
• Duality between amplitude and derivative coupled particle detectors in the limit of large energy gaps
• Weighing the Vacuum Energy
• Dualization between supersymmetric self-dual and topologically massive models coupled to matter in four-dimensional superspace
• Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field -- the general case
• Non-Abelian T-duality and Modular Invariance
• The $\mathrm{SL}(2,\mathbb{R})$ Wess-Zumino-Novikov-Witten spin-chain $\sigma$-model
• Theoretical Equivalence in Physics
• A Novel Symmetry in Sigma Models
• Note About Canonical Description of T-duality Along Light-Like Isometry
• Comments on Dualities on Group Manifolds and Supersymmetry
• Loops versus strings
• T-duality of D-brane versus O-plane actions
• Combined fermionic and bosonic T-duality of type II superstring theory with coordinate dependent RR field
• Geometric Quantization: Particles, Fields and Strings
• Towards quantum Mechanics on the curved cotangent bundle
• Jacobi-Lie symmetry in WZW model on the Heisenberg Lie group $H_4$
• Open string T-duality in a weakly curved background
• Topological T-duality, Automorphisms and Classifying Spaces
• Topological T-duality and Kaluza-Klein Monopoles
• Compactification of IIB Theory with Fluxes and Axion-Dilaton String Cosmology
• The SL(2,R)WZWN string model as a deformed oscillator and its classical-quantum string regimes
• First Order Actions and Duality
• Quantum Gravity
• A Vector Non-abelian Chern-Simons Duality
• Dual Instantons
• On T-duality in dilatonic gravity
• Transformation of Black-Hole Hair under Duality and Supersymmetry
• S-Duality and Exact Type IIB Superstring Backgrounds
• Modeling M-Theory Vacua via Gauged S-Duality
• T-duality to Scattering Amplitude and Wilson Loop in Non-commutative Super Yang-Mills Theory
• Searching for new homogeneous sine-Gordon theories using T-duality symmetries
• Hidden Symmetries of M Theory
• The physics of intersecting thick to thin branes
• Killings, Duality and Characteristic Polynomials
• Critical Non-Abelian Vortex String and 2D N=2 Black Hole
• S-duality and Canonical Transformations in String Theory
• Proceedings to the 'Euroconference on Symmetries Beyond the Standard Model', 12. - 17. July 2003, Portoroz, Slovenia (Part 1 of 2)
• Canonical Description of T-duality with NSNS Background
• A Two-loop Test of Buscher's T-duality I
• Kaluza-Klein and H-Dyons in String Theory
• Supersymmetric Quantum Corrections and Poisson-Lie T-Duality
• T-Duality in Lattice Regularized Sigma Models
• Exotic Aspects of Extended Field Theories
• Non-Abelian target space duals of Thurston geometries
• Hearing the shape of a Dirac drum: Dual quantum Hall states on curved surfaces
• (Pseudo-)Synthetic BRST quantisation of the bosonic string and the higher quantum origin of dualities
• Nonrelativistic strings and the limits of $\mathcal{N}=2$ dualities
• Canonical Description of T-duality for Fundamental String and D1-Brane and Double Wick Rotation
• Time and a Temporally Statistical Quantum Geometrodynamics
• Complexified sigma model and duality
• T-duality for open strings in the presence of backgrounds and noncommutativity
• Explicitly connecting T and Buscher dualities in String Theory
• Renormalisability of non-homogeneous T-dualised sigma-models