From free fields to AdS. III

2005/04/30 by Rajesh Gopakumar · 108 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Duality (order theory) #Mathematical physics #Mathematics #Matrix (chemical analysis) #Moduli space #Non-critical string theory #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum mechanics #Relationship between string theory and quantum field theory #String (physics) #String duality #String theory #hep-th

paper · pdf · doi:10.1103/physrevd.72.066008

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 72(6) (American Physical Society) · 30 pages, 6 figures, harvmac; v2: references added

arxiv created 2005/05/13 · openalex publication_date 2005/09/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In previous work, we have shown that large N field theory amplitudes, in Schwinger parametrized form, can be organized into integrals over the stringy moduli space M_g,n\ifmmode×\else\texttimes\fiR₊ⁿ. Here we flesh this out into a concrete implementation of open-closed string duality. In particular, we propose that the closed string world sheet is reconstructed from the unique Strebel quadratic differential that can be associated to (the dual of) a field theory skeleton graph. We are led, in the process, to identify the inverse Schwinger proper times (\ensuremathσ_i=1/\ensuremathτ_i) with the lengths of edges of the critical graph of the Strebel differential. Kontsevich's matrix model derivation of the intersection numbers in moduli space provides a concrete example of this identification. It also exhibits how closed string correlators emerge very naturally from the Schwinger parameter integrals. Finally, to illustrate the utility of our approach to open-closed string duality, we outline a method by which a world sheet operator product expansion can be directly extracted from the field theory expressions. Limits of the Strebel differential for the four punctured sphere play a key role.

Citations

• Open-Closed String Duality at Tree Level
• Notes On Higher Spin Symmetries
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• Strebel differentials on stable curves and Kontsevich's proof of Witten's conjecture
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• Aspects of semiclassical strings in AdS5
• Open/closed string duality for topological gravity with matter
• String theory beyond the Planck scale
• 3D interacting CFTs and generalized Higgs phenomenon in higher spin theories on AdS
• A Googly Amplitude from the B-model in Twistor Space
• Large-Ncollective fields and holography
• Free field theory as a string theory?
• Evaluating the AdS dual of the criticalO(N) vector model
• A planar diagram theory for strong interactions
• The Large-N Limit of Superconformal Field Theories and Supergravity
• An alternative string theory
• The large N limit of superconformal field theories and supergravity

Cited by

• From Symmetric Product CFTs to \rm AdS₃
• Extremal correlators and Hurwitz numbers in symmetric product orbifolds