Partial non-renormalisation of the stress-tensor four-point function in /N=4 SYM and AdS/CFT

By B. Eden, A. Petkou, C. Schubert, E. Sokatchev. 2000

141 citations recorded by the source corpus.

Abstract We show that, although the correlator of four stress-tensor multiplets in N=4 SYM is known to have radiative corrections, certain linear combinations of its components are protected from perturbative renormalisation and remain at their free-field values. This result is valid for weak as well as for strong coupling and for any gauge group. Our argument uses Intriligator's insertion formula, and includes a proof that the possible contact term contributions cannot change the form of the amplitudes. Combining this new non-renormalisation theorem with Maldacena's conjecture allows us to make a prediction for the structure of the corresponding correlator in AdS supergravity. This is verified by first considerably simplifying the strong coupling expression obtained by recent supergravity calculations, and then showing that it does indeed exhibit the expected structure.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/169952dc9f10f5300bc1c40ec1949775cfbbc30d

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Citations in the corpus

Witten diagrams revisited: the AdS geometry of conformal blocks (2015, methodology): “crossing symmetry, non-renormalization), and for N = 4 SYM in particular, was performed in [4, 47,52–62].”
Superconformal symmetry, correlation functions and the operator product expansion (2001, methodology): “This was demonstrated by Eden et al [10] by direct calculation starting from D1111(u, v) = Φ ((1))(u, v) , (D.”
On Four-Point Functions of Half-BPS Operators in General Dimensions (2004, background): “2.1 Conformal cross-ratios and related variables 7 2.2 R symmetry invariant variables 9 2.2.1 The cases SO(5), SO(6) and SO(8) 9 2.2.2 The case SO(3) 10 2.3 Two-, three- and four-point functions 11 2.3.1 Two- and three-point functions 11 2.3.2 Four-point functions 13”
Superconformal Ward identities and their solution (2004, background): “In particular for the N = 4 superconformal SU(N) gauge theory, to which the AdS/CFT correspondence is most directly applicable, many new and exciting results have been obtained.”
How to succeed at holographic correlators without really trying (2017, background): “The function Φ obeys the following differential relations [72], ∂zΦ = − 1 z − z̄ Φ− 1 z(z − z̄) log(−1 + z)(−1 + z̄) + 1 (−1 + z)(z − z̄) log(zz̄) ,”
From correlation functions to scattering amplitudes (2010, background): “As shown in [41, 48, 49], this factorization of the loop corrections is a universal feature, called “partial non-renormalization”.”
An Index for 4 Dimensional Super Conformal Theories (2005, background): “Indeed this operator was studied in [47,48,49] and a proof that it is protected was was given in [50,51,52], based on the non-renormalization theorem in [53].”
$$ \mathcal{N} $$ = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization (2019, background): “(See, for instance, [15–22] for earlier results.”
Infinite Chiral Symmetry in Four Dimensions (2013, background): “The fact that the left-hand side of this equation is a meromorphic function of the operator insertion points is a consequence of the cohomological arguments of the previous sections, but it is also precisely the final form of the superconformal Ward identities for such a correlation function [11–16]”
Conformal partial wave expansions for N=4 chiral four-point functions (2004, methodology): “Gn,n(u, v). However this is an inefficient procedure even for determining �I,1 except if there is no degeneracy and it is sufficient to restrict ton = 1. Such perturbative expansions were first applied for conformal O(N) sigma models in dimensions 2 8 ,9,10,11].”
Correlation functions and massive Kaluza-Klein modes in the AdS//CFT correspondence (2002, background): “The action of the derivatives on Φ is given by [19]”
From correlation functions to event shapes (2013, background): “8) is known explicitly in terms of functions with known Mellin representation up to two loops [58,53,59,60], and up to six loops in terms of basis integrals [56], which were successfully computed at three-loop order [61].”
Notes on the scattering amplitude — Wilson loop duality (2010, methodology): “It was used to prove non-renormalization theorems [41] and also as an efficient tool for 2-loop computations [42].”