Non commutative gravity from the ADS/CFT correspondence

Abstract

The exclusion principle of Maldacena and Strominger is seen to follow from deformed Heisenberg algebras associated with the chiral rings of S_N orbifold CFTs. These deformed algebras are related to quantum groups at roots of unity, and are interpreted as algebras of space-time field creation and annihilation operators. We also propose, as space-time origin of the stringy exclusion principle, that the $AD{S}_3\times S^3$ space-time of the associated six-dimensional supergravity theory acquires, when quantum effects are taken into account, a non-commutative structure given by $S{U}_q(1,1)\times S{U}_q(2)$. Both remarks imply that finite N effects are captured by quantum groups $S{L}_q(2)$ with $q=e^{\frac{i\pi }{N+1}}$. This implies that a proper framework for the theories in question is given by gravity on a non-commutative spacetime with a q-deformation of field oscillators. An interesting consequence of this framework is a holographic interpretation for a product structure in the space of all unitary representations of the non-compact quantum group $S{U}_q(1,1)$ at roots of unity.

28 pages in harvmac big ; v2: Minor corrections, ref added

Cited by in corpus (60)

• Large N Field Theories, String Theory and Gravity
• Noncommutative Black Holes, The Final Appeal To Quantum Gravity: A Review
• Giant Gravitons in Conformal Field Theory
• Comments on the Bagger-Lambert theory and multiple M2-branes
• Noncommutative Spacetime, Stringy Spacetime Uncertainty Principle, and Density Fluctuations
• Symmetry, Gravity and Noncommutativity
• Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua
• Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality
• Large-N Collective Fields and Holography
• On spherical harmonics for fuzzy spheres in diverse dimensions
• Gravity from CFT on $S^N(X)$ CFT: Symmetries and Interactions
• Comments on noncommutative gravity
• Noncommutative Gravity
• Vibration modes of giant gravitons
• Giant Graviton Correlators from Dual SU(N) super Yang-Mills Theory
• Giant Gravitons, BPS bounds and Noncommutativity
• Enhanced symmetries of gauge theory and resolving the spectrum of local operators
• M-theory branes and their interactions
• Higher Dimensional Geometries from Matrix Brane constructions
• Higher dimensional geometries related to fuzzy odd-dimensional spheres
• From counting to construction of BPS states in N=4 SYM
• A new twist on dS/CFT
• Geodesic equation in $k$-Minkowski spacetime
• Nonabelian Phenomena on D-branes
• Bi-local Construction of Sp(2N)/dS Higher Spin Correspondence
• Matrix Strings in Weakly Curved Background Fields
• Noncommutative $D_3$-brane, Black Holes and Attractor Mechanism
• Large N Expansion From Fuzzy AdS_2
• Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra
• Non-Abelian BIonic Brane Intersections
• Quantum Spacetimes and Finite N Effects in 4D Super Yang-Mills Theories
• Modular discretization of the AdS2/CFT1 Holography
• Exact operator bosonization of finite number of fermions in one space dimension
• Twisted Covariant Noncommutative Self-dual Gravity
• q-Deformed de Sitter/Conformal Field Theory Correspondence
• Finite N and the failure of bulk locality: Black holes in AdS/CFT
• Effects of Quantum Deformations on the Spectrum of Cosmological Perturbations
• Fuzzy Gravitons From Uncertain Spacetime
• Worldvolume Uncertainty Relations for D-Branes
• Free particles from Brauer algebras in complex matrix models
• Fluctuating Fuzzy Funnels
• Field Theory of Primaries in W_N Minimal Models
• Noncommutative brane-world, (Anti) de Sitter vacua and extra dimensions
• Dynamics of chiral primaries in $Ad{S}_3\times S^3\times T^4$
• CP^n Model on Fuzzy Sphere
• Tunneling between the giant gravitons in AdS5 x S5
• Quantum states to brane geometries via fuzzy moduli spaces of giant gravitons
• Noncommutative Effects in the Black Hole Evaporation in Two Dimensions
• Thresholds of Large N Factorization in CFT4 : Exploring bulk spacetime in AdS5
• Towards Gauge theory for a class of commutative and non-associative fuzzy spaces
• Stability and fluctuation modes of giant gravitons with NSNS B field
• Holography based on noncommutative geometry and the AdS/CFT correspondence
• Vibration modes of giant gravitons in the background of dilatonic D-branes
• Holography for Tensor models
• Strings on Plane Waves, Super-Yang Mills in Four Dimensions, Quantum Groups at Roots of One
• Statistical entropy of two-dimensional dilaton de Sitter space
• A Universal Behavior of Half BPS Probes in the Superstar Ensemble
• Duality and Combinatorics of Long Strings in ADS3
• dS-AdS structures in the non-commutative Minkowski spaces
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects