Conformal Regge theory

Abstract

We generalize Regge theory to correlation functions in conformal field theories. This is done by exploring the analogy between Mellin amplitudes in AdS/CFT and S-matrix elements. In the process, we develop the conformal partial wave expansion in Mellin space, elucidating the analytic structure of the partial amplitudes. We apply the new formalism to the case of four point correlation functions between protected scalar operators in N=4 Super Yang Mills, in cases where the Regge limit is controlled by the leading twist operators associated to the pomeron-graviton Regge trajectory. At weak coupling, we are able to predict to arbitrary high order in the 't Hooft coupling the behaviour near J=1 of the OPE coefficients C_{OOJ} between the external scalars and the spin J leading twist operators. At strong coupling, we use recent results for the anomalous dimension of the leading twist operators to improve current knowledge of the AdS graviton Regge trajectory - in particular, determining the next and next to next leading order corrections to the intercept. Finally, by taking the flat space limit and considering the Virasoro-Shapiro S-matrix element, we compute the strong coupling limit of the OPE coefficient C_{LLJ} between two Lagrangians and the leading twist operators of spin J.Comment: 27 + 24 pages, 7 figures; v2 Typos corrected, references added; v3 Typo corrected; v4 Typos corrected, references adde

Computing three-point functions for short operators

“…For related references, see e.g. [39][40][41][42][43]. It can be hoped that the methods used here will also be useful for higher-point correlators.…”

“…Likewise, information from the four-point correlation functions of protected operators can be used to check the validity of our results. For example, in [43] there is a prediction for the structure constant between two operators dual to the dilaton and a third operator dual to a higher-spin state on the graviton Regge trajectory. It would be interesting to find their result for the spin 4 operator, which is at the first massive level, using the methods here.…”

Inclusive production through AdS/CFT

“…Other phenomenological applications include inclusive production in other kinematical regions where the consequences of conformality can appear, 21 such as the triple-Regge limit, explore heavy quark production in the central region, 22 and tetra quark production. 23 Also interesting would be the study of two-point correlations, such as γ * → c 1 + c 2 + X or a + b → X 1 + c 1 + c 2 + X 2 . Study in some of these issues are currently underway.…”

“…See [110] and references therein. 23 Although quark contributions are 1/N suppressed holographically-the ∆ = 4 tetra quark contribution [111][112][113], which has already been investigated holographically [114], could compete with a scalar glueball. Figure 8.…”

“…Although strictly speaking QCD itself is not a CFT, it is closely related to N = 4 super Yang-Mills, which is conformal, and the two theories are similar enough that a great deal can be learned from the conformal limit [9][10][11][12]. The effects of conformal symmetry on QCD have previously been studied in inclusive scattering in both the fixed-angle [13,14] and in the near-forward limits [15][16][17][18][19][20][21][22][23][24][25]. Here, we will focus on central production at the LHC.…”