Conformal Regge theory

By M. Costa, V. Gonçalves, J. Penedones. 2012

340 citations recorded by the source corpus.

A bstractWe 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 $ \mathcal{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_{{\mathcal{OO}J}}} $ 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_{{\mathcal{LL}J}}} $ between two Lagrangians and the leading twist operators of spin J.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/94deda62204ea030227b2297c80291160d4d5371

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Citations in the corpus

Spinning AdS propagators (2014, methodology): “Another check of the result (164) is the property M(s, t) = M(−s− t, t), that follows from (7)See equation (132) of [46] for the flat space limit formula in the present conventions.”
Defects in conformal field theory (2016, methodology): “Many results are available for the conformal blocks in this case [50, 51, 52, 53, 54, 55, 56].”
Loops in AdS from conformal field theory (2016, background): “These obey an orthogonality relation [59], which can be written5 ∫ i∞”
Bounding the space of holographic CFTs with chaos (2016, methodology): “This is essentially a realization of conformal Regge theory [58].”
Witten diagrams revisited: the AdS geometry of conformal blocks (2015, background): “The polynomial boundedness is a signature of local AdS dynamics [25, 40].”
From correlation functions to event shapes (2013, methodology): “to inﬁnity (or equivalently τ− θ= ﬁxed and τ+ θ→ ∞, see Fig. 1). The 6It is interesting to note that in conformal OPE for correlation functions all conformal blocks admit a Mellin transform (see e.g. [23]). This suggests that our approachcan be employed to compute the charge ﬂow correlations in term”
How to succeed at holographic correlators without really trying (2017, background): “The s-channel exchange Witten diagram with an exchanged field of conformal dimension ∆ and spin J has a Mellin amplitude with the following simple analytic structure [44],”
A Mellin space approach to the conformal bootstrap (2016, methodology): “The Mack polynomials P (s) ν,` (s, t) are explicitly known [27, 30, 42], albeit in terms of a multiple sum”
Gravitational S-matrix from CFT dispersion relations (2017, background): “ace operators. Thus the double-discontinuity picks up precisely those terms dubbed \singular" in the preceding section. { 6 { The function ~c(‘;) encodes the s-channel OPE data through its poles [12,15]: if k is the dimension of the exchanged operator, then ~c(‘;) ! f2 ‘; k k : (3.3) where f2 ‘”
Hexagonalization of correlation functions (2016, background): “(1)Examples of such interesting physics discussed recently are the Regge limit [1], the emergence of the bulk locality [2] and chaos [3].”
Bootstrapping mixed correlators in the 3D Ising model (2014, background): “Other recent studies of global conformal blocks can be found in [12, 45, 46, 51, 52, 55–61], with connections to Mellin amplitudes in [62–71].”
Looking for a bulk point (2015, neutral): “, [48].”
Stringy effects in scrambling (2014, neutral): “(Some recent references include [63–65]).”
The analytic bootstrap and AdS superhorizon locality (2012, positive): “One inspiration for our approach was the structure of conformal blocks in Mellin space [23, 24, 29, 41, 54], where the blocks imitate the momentum-space partial waves of scattering amplitudes more transparently.”
The S-matrix bootstrap. Part I: QFT in AdS (2016, background): “09) where and lare the dimension and spin of the exchanged operator O k and ’s are OPE coecients. The residue is a Mack polynomial of degree lin the Mellin variable 13. We follow the conventions of [44], Q l;q( 13) = 2( + l)( 1) l 4 l ++ 12 2 12 2 + l+ 34 2 l 34 2 (110) Q l;q( 13) q! +d 2 + 1 q 1 2 ”
Bootstrapping inflationary correlators in Mellin space (2019, methodology): “The Mellin space representation of conformal correlators [5–13] and Harmonic Analysis for the Euclidean Conformal Group [12, 14–17] have proven instrumental in making this connection manifest, which encode bulk physics in a way which shares key similarities with the flat-space scattering amplitudes.”