Large N Reductions and Holography

Abstract

The large $N$ reductions in gauge theories are identified with dimensional reductions with homogeneous distribution of the eigenvalues of the gauge field, and it is used to identify the corresponding closed string descriptions in the Maldacena duality. When one does not take the zero-radii limit, the large $N$ reductions are naturally extended to the equivalences between the gauge theories and the "generalized" reduced models, which naturally contain the notion of T-dual equivalence. In the dual gravitational description, T-duality relates two type IIB supergravity solutions, the near horizon geometry of D3-branes, and the near horizon geometry of D-instantons densely and homogeneously distributing on the dual torus. This is the holographic description of the generalized large $N$ reductions. A new technique for calculating correlation functions of local gauge invariant single trace operators from the reduced models is also given.

REVTeX4 v2: simple mistake in eq.(1) corrected. footnote 4 in v1 expanded in the main body. conflicting notations for the dilaton below eq.(6) (in v1) fixed. 6 pages, 5 figures v3: corrected typo v4: presentation improved with explanations and clarifications. results unchanged. refs added. 8pages

References in corpus (34)

• The Large N Limit of Superconformal Field Theories and Supergravity
• The World as a Hologram
• M Theory As A Matrix Model: A Conjecture
• Wilson loops in large N field theories
• The Bethe-Ansatz for N=4 Super Yang-Mills
• A Large-N Reduced Model as Superstring
• Black Strings and p-Branes are Unstable
• The N=4 SYM Integrable Super Spin Chain
• The AdS/CFT Correspondence and a New Positive Energy Conjecture for General Relativity
• Wilson-Polyakov Loop at Finite Temperature in Large N Gauge Theory and Anti-de Sitter Supergravity
• The Instability of Charged Black Strings and p-Branes
• D-brane field theory on compact spaces
• Space-Time Structures from IIB Matrix Model
• Instantons and seven-branes in type IIB superstring theory
• Gluino Condensate and Magnetic Monopoles in Supersymmetric Gluodynamics
• Dynamical Aspects of Large N Reduced Models
• Black hole-black string phase transitions in thermal 1+1-dimensional supersymmetric Yang-Mills theory on a circle
• Simplifying superstring action on AdS_5 x S^5
• From Free Fields to $AdS$
• Phase Transitions for Flat adS Black Holes
• Monopoles, affine algebras and the gluino condensate
• Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory
• From Free Fields to $AdS$ -- III
• Vacua of M-theory and string theory
• The Phase Structure of Low Dimensional Large N Gauge Theories on Tori
• From Free Fields to AdS -- II
• On Stringy Thresholds in SYM/AdS Thermodynamics
• Black Holes and the SYM Phase Diagram
• Black Holes and the Super Yang-Mills diagram. II
• Exact Results in N_c=2 IIB Matrix Model
• Winding tachyons in asymptotically supersymmetric black strings
• From Free Fields to AdS -- Thermal Case
• Configurations of two D-instantons
• On The Field Theory Limit Of D-Instantons

Cited by in corpus (7)

• A Matrix Model for Black Hole Thermalization
• Phase structure of matrix quantum mechanics at finite temperature
• Inheritance principle and Non-renormalization theorems at finite temperature
• AdS/CFT and large-N volume independence
• Confined Phase In The Real Time Formalism And The Fate Of The World Behind The Horizon
• Lectures On AdS-CFT At Weak 't Hooft Coupling At Finite Temperature
• Equivalence of large-$N$ gauge theories on a group manifold and its coset space