DGLAP and BFKL Equations in N = 4 Supersymmetric Gauge Theory
By Anatoly V. Kotikov, L. Lipatov, V. Velizhanin. 2002
287 citations recorded by the source corpus.
We show the results for the DGLAP and BFKL evolution equations in the N =4s upersymmetric gauge theory obtained earlier in the next-to-leading approximation. The eigenvalue of the BFKL kernel in this model turns out to be an analytic function of the conformal spin |n|. The corresponding kernel for the Bethe–Salpeter equation has the property of the Hermitian separability. The anomalous dimension matrix can be transformed to a triangle form with the use of the similarity transformation for the diagonalization of the anomalous dimension matrix in the leading order. The eigenvalues of these matrices can be expressed in terms of a universal function by an integer shift of its argument. We also investigate in this approximation possible relations between the DGLAP and BFKL equations.
View Paper: https://www.semanticscholar.org/paper/3c84b847e483aeb44af1abff2668b909a3946f37
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Citations in the corpus
- Four loop twist two, BFKL, wrapping and strings (2008, methodology): “up to 3 loops [29] and using the maximum transcendentality conjecture [30] the corresponding answer in N = 4 SYM has been extracted [31, 32, 33].”
- SPINNING STRINGS AND AdS/CFT DUALITY (2003, background): “Also, it appears that the observation of [22, 23] that the 1-loop dilatation operator of N = 4 SYM theory is related to a Hamiltonian of an integrable spin chain (see also [65, 66]) should have generalizations to other N = 1, 2 supersymmetric theories [64].”
- Dressing and wrapping (2007, methodology): “According to the hypothesis formulated in the articles [32, 21], one can calculate the anomalous dimension γ near other non-physical points M = j−2 = −r (r = 2, 3, .”
- Deep inelastic scattering at strong coupling from gauge/string duality: the saturation line (2007, background): “For instance, it is known that the entropy of strongly coupled N = 4 SYM theory at finite temperature, which is a direct measure of the number of states, differs only by a factor 3/4 from the entropy of the corresponding ideal gas, where all the states are associated with free fundamental fields.”
- Scattering Amplitudes and the Positive Grassmannian (2012, background): “This has long been conjectured to be true for MHV amplitudes in connection to the maximal transcendentality principle of [155].”
- Five-loop anomalous dimension of twist-two operators (2009, background): “the eigenvalue equation for the reggeon Hamiltonian, takes a particularly simple form [7].”
- Integrability and transcendentality (2006, methodology): “The O(g 4 ) two-loop answer was found in [7] [8], and the O(g 6 ) three-loop one, inspired by a full-fledged computation in QCD [9], in [10].”
- The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability (2004, background): “If the discovered integrable structures are not accidental, we should expect that the so(6) results of [48] and the sl(2) results suggested from one-loop QCD [54,55] (see also [43,57]) can be combined and ‘lifted’ to a full psu(2, 2|4) super spin chain.”
- Conformal Regge theory (2012, background): “11Our definition of ν differs from that used in [22] by a factor of 2.”
- Transcendentality and crossing (2006, methodology): “In addition, the solution preserves the Kotikov-Lipatov transcendentality principle [14] to arbitrary loop order.”
- The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory (2003, methodology): “Using methods of QCD deep inelastic scattering, the DGLAP and BFKL equations, as well as by means of computer algebra systems developed for higher loop computations in the standard model, this result has been generalised to two-loops [14].”
- Wrapping interactions at strong coupling: The giant magnon (2007, unknown): “22 08 ∗e-mail: ufrjanik@if.uj.edu.pl †e-mail: tomaszlukowski@gmail.com”