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Lectures on the plane‐wave string/gauge theory duality
Author(s) -
Plefka J.C.
Publication year - 2004
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.200310121
Subject(s) - physics , superstring theory , string duality , string (physics) , s duality , non critical string theory , string theory , green–schwarz mechanism , gauge theory , string field theory , duality (order theory) , scaling limit , light cone gauge , mathematical physics , supersymmetry , theoretical physics , quantum mechanics , relationship between string theory and quantum field theory , scaling , quantum , quantum gravity , mathematics , geometry , pure mathematics
These lectures give an introduction to the novel duality relating type IIB string theory in a maximally supersymmetric plane‐wave background to = 4, d = 4, U ( N ) super Yang‐Mills theory in a particular large N and large R‐charge limit due to Berenstein, Maldacena and Nastase. In the first part of these lectures the duality is derived from the AdS/CFT correspondence by taking a Penrose limit of the AdS 5 × S 5 geometry and studying the corresponding double‐scaling limit on the gauge theory side. The resulting free plane‐wave superstring is then quantized in light‐cone gauge. On the gauge theory side of the correspondence the composite super Yang‐Mills operators dual to string excitations are identified, and it is shown how the string spectrum can be mapped to the planar scaling dimensions of these operators. In the second part of these lectures we study the correspondence at the interacting respectively non‐planar level. On the gauge theory side it is demonstrated that the large N large R‐charge limit in question preserves contributions from Feynman graphs of all genera through the emergence of a new genus counting parameter – in agreement with the string genus expansion for non‐zero g s . Effective quantum mechanical tools to compute higher genus contributions to the scaling dimensions of composite operators are developed and explicitly applied in a genus one computation. We then turn to the interacting string theory side and give an elementary introduction into light‐cone superstring field theory in a plane‐wave background and point out how the genus one prediction from gauge theory can be reproduced. Finally, we summarize the present status of the plane‐wave string/gauge theory duality.