Operator product expansion of the lowest weight CPOs in N=4 SYM 4 at strong coupling

By G. Arutyunov, S. Frolov, A. Petkou. 2000

147 citations recorded by the source corpus.

Abstract We present a detailed analysis of the 4-point functions of the lowest weight chiral primary operators O I ∼ tr (φ (i φ j) ) in N =4 SYM 4 at strong coupling and show that their structure is compatible with the predictions of AdS/CFT correspondence. In particular, all power-singular terms in the 4-point functions exactly coincide with the contributions coming from the conformal blocks of the CPOs, the R -symmetry current and the stress tensor. Operators dual to string modes decouple at strong coupling. We compute the anomalous dimensions and the leading 1/N 2 corrections to the normalization constants of the 2- and 3-point functions of scalar and vector double-trace operators with approximate dimensions 4 and 5, respectively. We also find that the conformal dimensions of certain towers of double-trace operators in the 105 , 84 and 175 irreps are non-renormalized. We show that, despite the absence of a non-renormalization theorem for the double-trace operator in the 20 irrep, its anomalous dimension vanishes. As by-products of our investigation, we derive explicit expressions for the conformal block of the stress tensor, and for the conformal partial wave amplitudes of a conserved current and of a stress tensor in d dimensions.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/32fe3bea9bfaa8cd20826f9ba8a741c0ad63443f

How researchers see this paper

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

In Mathematical Physics

In Nuclear and High Energy Physics

Citations in the corpus

On Four-Point Functions of Half-BPS Operators in General Dimensions (2004, result): “usion in [7] that the single-variable function does not receive quantum corrections (a phenomenon called “partial non-renormalization”), in excellent agreement with results from AdS5 ×S5 supergravity [9] and from perturbative ﬁeld theory [10]. Later on, in [11] the same Ward identities were derived,”
$$ \mathcal{N} $$ = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization (2019, background): “nately for the strong coupling limit we are interested in, the Konishi operator is known to develop a large anomalous dimension and eectively decouples from the operator algebra in the 1 expansion [63,64]. Consequently for our purpose, we may eectively set L= Cin (3.5). 3.1.2 N= 2 Coulomb branch ch”
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.”
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].”
On short and semi-short representations for four-dimensional superconformal symmetry (2002, unknown): “In addition there are various short superm ultiplets in which the num - ber ofstates involve factors 2p,p 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 6 ,7,8,9,10,11].”
Superconformal symmetry, correlation functions and the operator product expansion (2001, methodology): “9 With a different normalisation these were given in [ 12 ].”
The dilatation operator of conformal N=4 super-Yang–Mills theory (2003, background): “Assuming that the integrability structure extends to more than two loops, we determine the planar three-loop contribution to the dilatation operator.”
Supersymmetric gauge theories and the AdS / CFT correspondence (2002, background): “T correspondence, κ2 5 may be related to Nby κ2 5 = 4π 2/N2. This system was ﬁrst examined in [131] and [132]. An investigation directly of the correlator of half-BPS chiral primaries may be found in [133]. viiActually, the possible intermediary ﬁelds and operators are restricted by the full SU(2,2|”
Effective conformal theory and the flat-space limit of AdS (2010, unknown): “[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 4, 15].”
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].”
The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory (2003, unknown): “ 2 ∂ k ′ 3 ∂ n−k 4 k!(n− k)!k′!(n −k′)! (r − s)Φ(r,s) x2 13x 2 24 (B.8) where r,s are the conformal cross ratios r = x2 12x 2 34 x2 13x 2 24 , s = x2 14x 2 23 x2 13x 2 24 . (B.9) We use the expansion [26] of Φ in the limit x2 → x1, x4 → x3 (r → 0,s → 1) Φ(r,s) = − X∞ n,m=0 (n+m)!2 m!(1 +2n+m)! rn(1−”
Rigorous limits on the interaction strength in quantum field theory (2009, background): “It should be noted that this conclusion is nontrivial only for small Nc, since at large Nc the OPE O1 × O2 is known to factorize, with the composite “multi-trace” fields : O1O2 : appearing with the coefficient 1 +O(1/N(2) c ) while all other fields 1/Nc suppressed [23].”
From correlation functions to event shapes (2013, background): “presentation of the correlation functions [37, 38, 39]. The Mellin representation is a natural language for the description of CFT correlators and came into widespread use in recent years (see, e.g., [40, 41, 42, 43]). For the connected part of the four-point Euclidean correlation function16 it read”