BMN gauge theory as a quantum mechanical system
By N. Beisert, Charlotte Kristjansen, J. Plefka, M. Staudacher. 2002
165 citations recorded by the source corpus.
We rigorously derive an effective quantum mechanical Hamiltonian from N = 4 gauge theory in the BMN limit. Its eigenvalues yield the exact oneloop anomalous dimensions of scalar two-impurity BMN operators for all genera. It is demonstrated that this reformulation vastly simplifies computations. E.g. the known anomalous dimension formula for genus one is reproduced through a one-line calculation. We also efficiently evaluate the genus two correction, finding a non-vanishing result. We comment on multi-trace two-impurity operators and we conjecture that our quantum-mechanical reformulation could be extended to higher quantum loops and more impurities.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/4a8965fcacb5efcd66695f6d49d21bff0b96482f
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In Atomic and Molecular Physics, and Optics
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Citations in the corpus
- Planar N=4 Gauge Theory and the Inozemtsev Long Range Spin Chain (2004, methodology): “In particular, powerful techniques for the efficient computation of one-loop anomalous dimensions of N = 4 composite operators containing a large number of scalar fields were developed [5].”
- Rotating string solutions: AdS/CFT duality in non-supersymmetric sectors (2003, background): “Remarkably, the two recent developments on the SYM [2,3,4,5] and the string [6,7] sides have converged to provide such non-trivial tests.”
- Pulsating strings on Ads(5) x S(5) (2004, background): “it (e.g. by taking both J1 and J2 to be large) have since been studied extensively [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], and are reviewed in [18]. Studies of the corresponding gauge theory [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29] (see also[30,31])were simplified andextended by theobser”
- The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability (2004, methodology): “A radiative correction to the dilatation operator in the context of N = 4 SYM has first been computed in [48, 35].”
- Multi-spin string solutions in AdS5×S5 (2003, background): “0619λ, but comparison with the results of [9] shows that it belongs to [2,4,2] representation.”
- The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory (2003, methodology): “After multiplication with g(2) YMN/8π 2 this is exactly the effective vertex found in [20] and yields the dilatation generators in [25,22,23].”
- Stringing Spins and Spinning Strings (2003, background): “Remarkably, these results can be directly related to a string calculation on AdS5×S5 [23,24,25,26,27,28,29,30,31,32,33,34,35,36], since one can choose λ large but L also large such that λ′ = λ/L2 is small.”
- The factorized S-matrix of CFT/AdS (2004, background): “and may be expressed with the help of the permutation operator Px,x+1 which exchanges the partons at sites x and x+1, as first noticed in [1, 40].”
- Tiny graviton matrix theory: DLCQ of IIB plane-wave string theory, a conjecture (2004, background): “ for perturbative dynamics of fundamental type IIB closed strings. The first is obtained by summarizing the information coming from the N = 4,D= 4 gauge theory calculations in the BMN sector, e.g. see [11, 22]. The second one is the Verlinde’s String Bit model [23]. We will comment on the possible re”
- The dilatation operator of conformal N=4 super-Yang–Mills theory (2003, background): “While many of the recently obtained new results on N = 4 in principle could have been derived a long time ago, the AdS/CFT correspondence clearly helped immensely in formulating the right questions.”