D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes

By G. Mack. 2009

319 citations recorded by the source corpus.

The Euklidean correlation functions and vacuum expectation values of products of field operators of some Lorentz spin and dimension are expressed through Mellin amplitudes which depend on complex dimensions subject to linear constraints. The constraints can be solved in terms of conserved momenta whose squares are given by the field dimensions, and related Mandelstam variables s. The Mellin amplitudes furnish a universal representation of conformal field theories without explicit reference to D. The costumary principles of quantum field theory plus conformal invariance and operator product expansions (OPE) say that the Mellin amplitudes are amplitudes of dual resonance models with exact duality and a form of factorization which follows from OPE. Fields in the OPE with spin l and dimension d produce simple poles in the scalar 4-point Mellin amplitude at s=d-l+2n, n=0,1,2,3... with polynomial residues. The leading pole determines the satellites n=1,2,3...

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/90e6cae2ad4870444978f0c1149c54778294ee46

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

All point correlation functions in SYK (2017, background): “Mellin space Mellin space is useful for large N CFTs [35, 30].”
Spinning conformal correlators (2011, background): “Another motivation for this work is the recently found analogy between CFT correlation functions written in the Mellin representation and scattering amplitudes [7, 8].”
Bootstrapping the O(N ) vector models (2013, background): “The sum over poles may also be particularly interesting from the perspective of Mellin amplitudes [58–66].”
Causality constraints in conformal field theory (2015, background): “Equivalently, for each flat-space scalar S-matrix, there is a corresponding crossing-symmetric CFT correlator in Mellin space [26,28,34,35].”
Writing CFT correlation functions as AdS scattering amplitudes (2010, methodology): “A Mellin integration measure The precise definition of the integration measure dδij in (2) was given in [8, 10].”
$$ \mathcal{N} $$ = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization (2019, background): “e u= 2p s t, and where the two integration contours in (2.12) include all poles of the Gamma functions on one side or the other of the contour. (These poles are associated with double-trace operators [61].) The reason for considering the Mellin space representation is that, in Mellin space, tree-lev”
Spinning AdS propagators (2014, methodology): “To see that, we first use the relation between the residues of the conformal partial amplitudes bl(ν) and OPE coefficients [45, 48, 46].”
Quartic AdS interactions in higher-spin gravity from Conformal Field Theory (2015, background): “This extension is based on numerous results indicating the similarity of Mellin amplitudes for Witten diagrams in AdS with flat amplitudes in Minkowski space [70, 71, 101].”
From correlation functions to event shapes (2013, methodology): “For our purposes, a very eﬃcient way to carry out the required analytic continuation is through the Mellin space representation of the correlation functions [11].”
A natural language for AdS/CFT correlators (2011, background): “In those cases M(δij) must not only have additional poles accounting for the multi-trace operators but also zeroes to cancel off the poles from the Γ(δij) factors [1].”
Analyticity and the holographic S-matrix (2011, background): “On very general grounds, the Mellin amplitude is expected [4, 5, 2] to have only simple poles on the real axis, so the more intricate analytic structure of the S-Matrix must emerge from the coalescence and resummation of the poles of the Mellin amplitude.”
Spinning conformal blocks (2011, background): “Additional progress has been made at understanding the constraints of unitarity in this context [9], as well as in exploring the recently found analogy between CFT correlation functions in the Mellin representation and scattering amplitudes [10–13].”