On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities

Abstract

One of the main topics in the modern String Theory are the AdS/CFT dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality. We review the fundamental concepts and properties of integrability in two-dimensional sigma-models and in the AdS/CFT context. The first part is focused on the AdS_5/CFT_4 duality, especially the classical and quantum integrability of the type IIB superstring on AdS_5 x S^5 are discussed in both pure spinor and Green-Schwarz formulations. The second part is dedicated to the AdS_4/CFT_3 duality with particular attention to the type IIA superstring on AdS_4 x CP^3 and its integrability. This review is based on a shortened and revised version of the author's PhD thesis, discussed at Uppsala University in September 2009.

116 pages, 11 figures, to be published in Advances in High Energy Physics, Special Issue on ''Gauge/String Duality''

References in corpus (38)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Giant Magnons
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Quantum corrections to the string Bethe ansatz
• The all loop AdS4/CFT3 Bethe ansatz
• Spinning strings and AdS/CFT duality
• ICTP Lectures on Covariant Quantization of the Superstring
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
• On AdS_5 x S^5 String S-matrix
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Wrapping at four loops in N=4 SYM
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Wrapping interactions at strong coupling -- the giant magnon
• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• Spinning strings at one-loop in AdS_4 x P^3
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• Two loop integrability for Chern-Simons theories with N=6 supersymmetry
• Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3
• Complete 1-loop test of AdS/CFT
• A Universality Test of the Quantum String Bethe Ansatz
• Exact expressions for quantum corrections to spinning strings
• The Four-Loop Dressing Phase of N=4 SYM
• Two-loop commuting charges and the string/gauge duality
• World-sheet scattering in AdS_5 x S^5 at two loops
• Constructing the AdS/CFT dressing factor
• Simplified TBA equations of the AdS_5 x S^5 mirror model
• Current Algebra of the Pure Spinor Superstring in AdS(5) x S(5)
• Factorized world-sheet scattering in near-flat AdS_5 x S^5
• Two-loop test of the N=6 Chern-Simons theory S-matrix
• Operator Product Expansion for Pure Spinor Superstring on AdS(5)*S(5)
• Aspects of Integrability in AdS/CFT Duality

Cited by in corpus (10)

• Review of AdS/CFT Integrability: An Overview
• Holographic three-point functions of semiclassical states
• Towards integrability for AdS3/CFT2
• Integrability of the AdS_5 x S^5 superstring and its deformations
• Yangians, S-matrices and AdS/CFT
• Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing
• Integrability of D1-brane on Group Manifold with Mixed Three Form Flux
• Integrability of D1-brane on Group Manifold
• Quantum corrections to $Ad{S}_5\times S^5$ left-invariant superstring current algebra
• Pure spinor superstring in AdS_4 x CP^3 with unconstrained ghosts