A New Double-Scaling Limit of N = 4 Super Yang-Mills Theory and PP-Wave Strings

By C. Kristjansen, J. Plefka, G. Semenoff, M. Staudacher. 2002

312 citations recorded by the source corpus.

Abstract The metric of a spacetime with a parallel plane (pp)-wave can be obtained in a certain limit of the space AdS5 × S5. According to the AdS/CFT correspondence, the holographic dual of superstring theory on that background should be the analogous limit of N =4 supersymmetric Yang–Mills theory. In this paper we shall show that, contrary to widespread expectation, non-planar diagrams survive this limiting procedure in the gauge theory. Using matrix model techniques as well as combinatorial reasoning it is demonstrated that a subset of diagrams of arbitrary genus survives and that a non-trivial double scaling limit may be defined. We exactly compute two- and three-point functions of chiral primaries in this limit. We also carefully study certain operators conjectured to correspond to string excitations on the pp-wave background. We find non-planar linear mixing of these proposed operators, requiring their redefinition. Finally, we show that the redefined operators receive non-planar corrections to the planar one-loop anomalous dimension.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/3ac749d0eef6b71f1c3963890e24e6d1129d3971

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In Nuclear and High Energy Physics

1. N. Beisert
2. M. Staudacher
3. A. Tseytlin
4. S. Frolov
5. K. Zarembo
6. D. Berenstein
7. G. Arutyunov
8. R. Roiban

Citations in the corpus

• A toy model for the AdS/CFT correspondence (2004, background): “Explicit results for the appropriate normalizations have been found to all orders in 1/N for all n in [20] in which they needed explicit expressions to understand the light cone string theory in the plane wave geometry [21].”
• Stringing Spins and Spinning Strings (2003, background): “The result for this particular [J, 0, J ] operator is smaller than the anomalous dimension derived by Frolov and Tseytlin [hep-th/0304255] for a semiclassical string configuration which is the dual of a gauge invariant operator in the same representation.”
• Branes, anti-branes and Brauer algebras in gauge-gravity duality (2007, unknown): “1y.kimura@qmul.ac.uk 2s.ramgoolam@qmul.ac.uk”
• Open Strings from N=4 Super Yang-Mills (2002, background): “N small to suppress the non-planar contributions anomalous dimensions [ 24 , 25].”
• BMN Correlators and Operator Mixing in N=4 Super Yang-Mills Theory (2002, methodology): “As was already discussed in detail in [8, 10], on the torus the operators eq.”
• Operators with Large R-Charge in N=4 Yang-Mills Theory (2002, background): “ wave background were discussed in [25] where propagators and closed string vertices were constructed. First steps towards the derivation of the string interactions from the field theory were taken in [26]. The interesting question of holography in plane wave background was attacked from various pers”
• The N=4 SYM Integrable Super Spin Chain (2003, unknown): “Pq”
• Large N BPS states and emergent quantum gravity (2005, background): “ge as well (let us say of order N2) where the planar approximation usually breaks down. In fact, the failure of orthogonality of traces starts to become of order one when the energy E is of order √ N [10, 11], which is much smaller than the size of the matrices. This was discovered by carrying out t”
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills (2004, background): “gress was achieved in dealing with both problems. It was understood, initially for a scalar subsector of the fields, that the computation can be quite generally reformulated in a combinatorial fashion [1], and that this combinatorics may be efficiently treated by Hamiltonian methods [2,3]. At one loop,”
• The su(2|3) dynamic spin chain (2003, methodology): “In particular, the BMN correspondence [3] has attracted attention to scaling dimensions of local operators and efficient methods for their computation have been developed [4].”
• Superstring interactions in a pp -wave background (2002, background): “[4]). It has recently been proposed [ 5-7 ] to extend this duality to include string interactions.”