Matrix Models, Complex Geometry and Integrable Systems. II

Abstract

We consider certain examples of applications of the general methods, based on geometry and integrability of matrix models, described in hep-th/0601212. In particular, the nonlinear differential equations, satisfied by quasiclassical tau-functions are investigated. We also discuss a similar quasiclassical geometric picture, arising in the context of multidimensional supersymmetric gauge theories and the AdS/CFT correspondence.

44 pages, 10 figures, based on several lecture courses and the talks at "Complex geometry and string theory" and the Polivanov memorial seminar; misprints corrected, references added

References in corpus (59)

• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• The Bethe-Ansatz for N=4 Super Yang-Mills
• A semi-classical limit of the gauge/string correspondence
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background
• Bethe Ansatz for Quantum Strings
• TASI Lectures on D-Branes
• Topological Strings and Integrable Hierarchies
• Classical/quantum integrability in AdS/CFT
• A Perturbative Window into Non-Perturbative Physics
• Anti De Sitter Space And Holography
• Spin chains and string theory
• A Large N Duality via a Geometric Transition
• Spinning strings in AdS_5 x S^5 and integrable systems
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Integrable Structure of Interface Dynamics
• Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains
• Matching Higher Conserved Charges for Strings and Spins
• Higher genus correlators for the hermitian matrix model with multiple cuts
• Spinning strings and AdS/CFT duality
• Towards unified theory of $2d$ gravity
• On Quantum Corrections to Spinning Strings and Bethe Equations
• WDVV-like equations in N=2 SUSY Yang-Mills Theory
• Algebraic Curve for the SO(6) sector of AdS/CFT
• Non-Perturbative Effects in Matrix Models and Vacua of Two Dimensional Gravity
• Parity Invariance For Strings In Twistor Space
• Matching quantum strings to quantum spins: one-loop vs. finite-size corrections
• Integrable Structure of the Dirichlet Boundary Problem in Two Dimensions
• The Algebraic Curve of 1-loop Planar N=4 SYM
• Normal random matrix ensemble as a growth problem
• Unification of All String Models with $c<1$
• Quantum corrections to spinning strings in AdS(5)xS(5) and Bethe ansatz: a comparative study
• Quasiclassical QCD Pomeron
• Stringy sums and corrections to the quantum string Bethe ansatz
• Conformal Field Theory Techniques in Random Matrix models
• Complex Curve of the Two Matrix Model and its Tau-function
• On the Three-point Function in Minimal Liouville Gravity
• TASI 2003 Lectures on AdS/CFT
• DV and WDVV
• Unified description of correlators in non-Gaussian phases of Hermitean matrix model
• Integrable Structure of the Dirichlet Boundary Problem in Multiply-Connected Domains
• On Associativity Equations in Dispersionless Integrable Hierarchies
• Semiclassical strings and AdS/CFT
• 1/J corrections to semiclassical AdS/CFT states from quantum Landau-Lifshitz model
• Genus one contribution to free energy in hermitian two-matrix model
• Solitons in high-energy QCD
• Holomorphic matrix integrals
• Unstable fingering patterns of Hele-Shaw flows as a dispersionless limit of the KdV hierarchy
• Matrix models and growth processes: from viscous flows to the quantum Hall effect
• Exact solutions to quantum field theories and integrable equations
• String Theory or Field Theory?
• Polyakov's String: Twenty Five Years After
• Matrix Models, Complex Geometry and Integrable Systems. I
• Determinant Formulas for Matrix Model Free Energy
• Quasiclassical Geometry and Integrability of AdS/CFT Correspondence
• Associativity Equations in Effective SUSY Quantum Field Theories
• Topological versus Non--Topological Theories and $p-q$ Duality in $c\le 1$ 2d Gravity Models
• GL(1) Charged States in Twistor String Theory
• Matrix Model and Stationary Problem in Toda Chain

Cited by in corpus (7)

• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• On Microscopic Origin of Integrability in Seiberg-Witten Theory
• Reconstructing 1/2 BPS Space-Time Metrics from Matrix Models and Spin Chains
• Notes on the algebraic curves in (p,q) minimal string theory
• Matrix Models, Complex Geometry and Integrable Systems. I
• On two-dimensional quantum gravity and quasiclassical integrable hierarchies
• Comments on Slavnov products, Temperley-Lieb open spin chains, and KP tau functions