Lectures on the Plane-Wave String/Gauge Theory Duality

Abstract

These lectures give an introduction to the novel duality relating type IIB string theory in a maximally supersymmetric plane-wave background to N=4, d=4, U(N) Super Yang-Mills theory in a particular large N and large R-charge limit due to Berenstein, Maldacena and Nastase. In the first part of these lectures the duality is derived from the AdS/CFT correspondence by taking a Penrose limit of the AdS_5 x S^5 geometry and studying the corresponding double-scaling limit on the gauge theory side. The resulting free plane-wave superstring is then quantized in light-cone gauge. On the gauge theory side of the correspondence the composite Super Yang-Mills operators dual to string excitations are identified, and it is shown how the string spectrum can be mapped to the planar scaling dimensions of these operators. In the second part of these lectures we study the correspondence at the interacting respectively non-planar level. On the gauge theory side it is demonstrated that the large N large R-charge limit in question preserves contributions from Feynman graphs of all genera through the emergence of a new genus counting parameter - in agreement with the string genus expansion for non-zero g_s. Effective quantum mechanical tools to compute higher genus contributions to the scaling dimensions of composite operators are developed and explicitly applied in a genus one computation. We then turn to the interacting string theory side and give an elementary introduction into light-cone superstring field theory in a plane-wave background and point out how the genus one prediction from gauge theory can be reproduced. Finally, we summarize the present status of the plane-wave string/gauge theory duality.

46 pages, Lectures given at the RTN Winter School on Strings, Supergravity and Gauge Theory, Turin 7-11 January 2003; v2: references and comments in section 6.3 added; v3: references added

References in corpus (18)

• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• Quantizing String Theory in AdS_5 X S^5: Beyond the pp-Wave
• On lightcone string field theory from Super Yang-Mills and holography
• Plane-wave Matrix Theory from N=4 Super Yang-Mills on RxS^3
• Shape and holography: studies of dual operators to giant gravitons
• The 3-string vertex and the AdS/CFT duality in the PP-wave limit
• Strings in plane wave backgrounds
• SYM Description of PP-wave String Interactions: Singlet Sector and Arbitrary Impurities
• An alternative formulation of light-cone string field theory on the plane wave
• Derivation of String Field Theory from the Large N BMN Limit
• Note on Plane Wave Quantum Mechanics
• Open+Closed String Field Theory From Gauge Fields
• Worldvolume supersymmetries for branes in plane waves
• D-branes in PP-wave light cone string field theory
• String bits without doubling
• AdS Holography in the Penrose Limit
• Fermion Doubling and Berenstein--Maldacena--Nastase Correspondence

Cited by in corpus (71)

• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Planar N=4 gauge theory and the Inozemtsev long range spin chain
• Spinning strings and AdS/CFT duality
• Spinning strings and integrable spin chains in the AdS/CFT correspondence
• Algebraic Curve for the SO(6) sector of AdS/CFT
• Tiny Graviton Matrix Theory: DLCQ of IIB Plane-Wave String Theory, A Conjecture
• Wrapping interactions and the genus expansion of the 2-point function of composite operators
• Introduction to AdS-CFT
• Gravitational field of a spinning radiation beam-pulse in higher dimensions
• Classification of All 1/2 BPS Solutions of the Tiny Graviton Matrix Theory
• TASI 2003 Lectures on AdS/CFT
• Resolving the Holography in the Plane-Wave Limit of AdS/CFT Correspondence
• Open Spin Chain and Open Spinning String
• Integrable Open Spin Chain in Super Yang-Mills and the Plane-wave/SYM duality
• Magnetic Catalysis of Chiral Symmetry Breaking. A Holographic Prospective
• Splitting spinning strings in AdS/CFT
• Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
• Spin bit models from non-planar N=4 SYM
• On the plane-wave cubic vertex
• D-branes and BCFT in Hpp-wave backgrounds
• N=2 Super Yang-Mills and the XXZ spin chain
• Dual Spikes; New Spiky String Solutions
• A note on dual giant gravitons in $Ad{S}_4\times {\mathbb{CP}}^3$
• The Effect of Gravitational Tidal Forces on Renormalized Quantum Fields
• Holographic cubic vertex in the pp-wave
• String amplitudes in the Hpp-wave limit of AdS3xS3
• Light-Cone String Field Theory in a Plane Wave Background
• Squashed Giants: Bound States of Giant Gravitons
• Non-perturbative contributions to the plane-wave string mass matrix
• Type II pp-wave Matrix Models from Point-like Gravitons
• AdS/CFT v.s. String Loops
• Euler Top Dynamics of Nambu-Goto P-Branes
• Integrable Spin Chains on the Conformal Moose
• Large N limit of SYM theories with 16 supercharges from superstrings on Dp-brane backgrounds
• New aspects of the BMN correspondence beyond the planar limit
• Superstring in the plane-wave background with RR flux as a conformal field theory
• On semiclassical calculation of three-point functions in AdS_5 \times T^(1,1)
• On the Uniqueness of Plane-wave String Field Theory
• Semi-classical Probe Strings on Giant Gravitons Backgrounds
• Decay widths of three-impurity states in the BMN correspondence
• PP-Wave Light-Cone Free String Field Theory at Finite Temperature
• Chaining spins from (super)Yang--Mills
• Near Flat Space limit of strings on AdS_4 x CP^3
• Strings on the deformed T^{1,1}: giant magnon and single spike solutions
• Comments on Supersymmetry Algebra and Contact Term in Matrix String Theory
• Fast spinning strings on $\eta$ deformed $Ad{S}_5\times S^5$
• Oscillator Construction of Spectra of PP-Wave Superalgebras in Eleven Dimensions
• Non-perturbative effects in the BMN limit of N=4 supersymmetric Yang-Mills
• Type IIB tensionless superstrings in a pp-wave background
• Can string bits be supersymmetric?
• Boundary fermions and the plane wave
• New BPS Configurations of BMN Matrix Theory
• The Three-String Vertex for a Plane-Wave Background
• Non-BPS D-Branes in Light-Cone Green-Schwarz Formalism
• On pp wave limit for $\eta$ deformed superstrings
• A note on the universality of the Hagedorn behavior of pp-wave strings
• Strings on Plane Waves and AdS x S
• BMN operators with a scalar fermion pair and operator mixing in N=4 Super Yang-Mills Theory
• Aspects of the Holographic Study of Flavor Dynamics
• Branes in the plane wave background with gauge field condensates
• Loop Equation in D=4, N=4 SYM and String Field Equation on AdS_5 \times S^5
• A note on the Near Flat Limit for strings in the Maldacena-Nunez background
• More on supersymmetric D-branes in type IIB plane wave background
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Tensionless Strings and Supersymmetric Sigma Models: Aspects of the Target Space Geometry
• The AdS/CFT Correspondence: Classical, Quantum, and Thermodynamical Aspects
• Black Hole Production from High Energy Scattering in AdS/CFT
• Turbulent aspects of BMN membrane dynamics
• Strings as sigma models and in the tensionless limit
• Superstring in the pp-wave background with RR flux as a conformal field theory