Exact Seiberg-Witten Map and Induced Gravity from Noncommutativity

Abstract

We find a closed form for Seiberg-Witten (SW) map between ordinary and noncommutative (NC) Dirac-Born-Infeld actions. We show that NC Maxwell action after the exact SW map can be regarded as ordinary Maxwell action coupling to a metric deformed by gauge fields. We also show that reversed procedure by inverse SW map leads to a similar interpretation in terms of induced NC geometry. This implies that noncommutativity in field theory can be interpreted as field dependent fluctuations of spacetime geometry, which genuinely realizes an interesting idea recently observed by Rivelles.

12 pages, Latex; version to appear in Mod. Phys. Lett. A

References in corpus (7)

• Exact Seiberg-Witten Map, Induced Gravity and Topological Invariants in Noncommutative Field Theories
• Seiberg-Witten-type Maps for Currents and Energy-Momentum Tensors in Noncommutative Gauge Theories
• Gravitational Instantons from Gauge Theory
• ALE spaces from noncommutative U(1) instantons via exact Seiberg-Witten map
• U(1) gauge invariant noncommutative Schrödinger theory and gravity
• A new approach to the analysis of a noncommutative Chern-Simons theory
• Can a Nonsymmetric Metric mimic NCQFT in $e^{+}{e}^{-}\to \gamma \gamma$ ?

Cited by in corpus (45)

• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Emergent Gravity from Noncommutative Gauge Theory
• Emergent Gravity from Noncommutative Spacetime
• Exact Seiberg-Witten Map, Induced Gravity and Topological Invariants in Noncommutative Field Theories
• Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
• On The Correspondence Between Noncommuative Field Theory And Gravity
• Noncommutative Conformally Coupled Scalar Field Cosmology and its Commutative Counterpart
• Emergent Spacetime and The Origin of Gravity
• Instantons and Emergent Geometry
• On the quantum structure of space-time, gravity, and higher spin in matrix models
• Emergent Geometry and Quantum Gravity
• ALE spaces from noncommutative U(1) instantons via exact Seiberg-Witten map
• Towards A Background Independent Quantum Gravity
• Gauge Theories on Deformed Spaces
• Emergent Geometry from Quantized Spacetime
• Maps for currents and anomalies in noncommutative gauge theories
• Test of Emergent Gravity
• U(1) gauge invariant noncommutative Schrödinger theory and gravity
• Quantum Gravity from Noncommutative Spacetime
• An Efficient Representation of Euclidean Gravity I
• Instantons, Twistors, and Emergent Gravity
• Quantization of Emergent Gravity
• Notes on Emergent Gravity
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Noncommutative Tachyon Kinks as D$(p-1)$-branes from Unstable D$p$-brane
• On the question of deconfinement in noncommutative Schwinger Model
• Poisson structure on a space with linear SU(2) fuzziness
• Canonical Noncommutativity Algebra for the Tetrad Field in General Relativity
• Non-commutativity from the double sigma model
• Ambiguities in the Seiberg-Witten Map and Emergent Gravity
• A note on graviton exchange in emergent gravity scenario
• Particle Dynamics And Emergent Gravity
• Remarks on an Exact Seiberg-Witten map
• Quantized Kähler Geometry and Quantum Gravity
• Novel Ambiguities in the Seiberg-Witten Map and the Emergent Gravity
• The Hierarchy Problem: From the Fundamentals to the Frontiers
• Contravariant geometry and emergent gravity from noncommutative gauge theories
• Towards Axiomatization and General Results on Strong Emergence Phenomena Between Lagrangian Field Theories
• Can a Nonsymmetric Metric mimic NCQFT in $e^{+}{e}^{-}\to \gamma \gamma$ ?
• Diffeomorphism-invariant noncommutative gravity with twisted local Lorentz invariance
• Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism
• An Axiomatization Proposal and a Global Existence Theorem for Strong Emergence Between Parameterized Lagrangian Field Theories
• Noncommutative Theories, Seiberg-Witten Map and Gravity
• Aspects of noncommutativity in field theory, strings and membranes
• Covariant Star Product on Semi-Conformally Flat Noncommutative Calabi-Yau Manifolds and Noncommutative Topological Index Theorem