Superconformal symmetry, correlation functions and the operator product expansion

By F. Dolan, H. Osborn. 2001

261 citations recorded by the source corpus.

Abstract Superconformal transformations are derived for the N =2,4 supermultiplets corresponding to the simplest chiral primary operators. These are applied to two-, three- and four-point correlation functions. When N =4 , results are obtained for the three-point function of various descendant operators, including the energy–momentum tensor and SU (4) current. For both N =2 or 4 superconformal identities are derived for the functions of the two conformal invariants appearing in the four-point function for the chiral primary operator. These are solved in terms of a single arbitrary function of the two conformal invariants and one or three single variable functions. The results are applied to the operator product expansion using the exact formula for the contribution of an operator in the operator product expansion in four dimensions to a scalar four-point function. Explicit expressions representing exactly the contribution of both long and possible short supermultiplets to the chiral primary four-point function are obtained. These are applied to give the leading perturbative and large N corrections to the scale dimensions of long supermultiplets.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7d0999310ec46a1bc6acf998eef151e5e3df015a

How researchers see this paper

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

In Nuclear and High Energy Physics

Citations in the corpus

Conformal partial wave expansions for N=4 chiral four-point functions (2004, background): “esults (4.2), (4.3) and (4.4). The coeﬃcients of lnuin the large Nresults for Anm(u,v) 23 may also be expanded to give results for large N anomalous dimensions, for p= 2 and p= 3 these were quoted in [25] and [19] respectively, for p= 4 see [26]. 5. Perturbation Theory Results In order to express th”
Bounds on 4D conformal and superconformal field theories (2010, methodology): “To our knowledge, this expression has not yet appeared in the literature, though analogous results for N = 2 and N = 4 theories are known [ 37 ].”
$$ \mathcal{N} $$ = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization (2019, methodology): “The superconformal Ward identities relating the S i p to one another [31], given in Appendix B, are identical for any p.”
Superconformal Ward identities and their solution (2004, background): “Such results have also been extended more recently to chiral primary operators with p = 3, 4 [5,6,7].”
Higher Spin Symmetry and N = 4 SYM (2004, methodology): “rent multiplet V 0 = V 2,0 [0†,0†][0†,2,0†] . The remaining multiplets V 2n acquire anomalous dimensions which violate the conservation of their HS currents at the quantum level. At one-loop, one has [49,21] γ 1−loop(2n) = g2 YM N 2π2 h(2n), h(j) = Xj k=1 1 k , (5.2) This elegant (’number theoretic’”
Convexity and liberation at large spin (2012, methodology): “By plugging ∆ = 4 into our formula we correctly reproduce 96 N2 ! For other computations of the anomalous dimensions of double-trace operators in theories with gravity duals see [48,49].”
On short and semi-short representations for four-dimensional superconformal symmetry (2002, unknown): “PACS no:11.25.”
From correlation functions to scattering amplitudes (2010, background): “The knowledge of these quantum corrections allowed one to extract the spectrum of anomalous dimensions of the Konishi operator [25], and later on of all twist-two operators up to two loops by means of a conformal operator product expansion (OPE) [26].”
Gravitational S-matrix from CFT dispersion relations (2017, methodology): “, discussed so far, to that in the singlet representation. This relation has a nontrivial prefactor, which shifts the spin by 4 in some of the blocks, see eq. (8.1) and the third line of eq. (8.7) of [35]. This shift is important because for spins two and higher the Froissart-Gribov integral is guar”
The N=2$$ \mathcal{N}=2 $$ superconformal bootstrap (2014, background): “0 6R62. We denote these contributions as aX iR (u;v). For this particular four-point function the coecients of the conventional conformal blocks are all related by the superconformal Ward identities [107], and we end up with just a single undetermined OPE coecient (squared) for each superconformal b”
Correlation functions and massive Kaluza-Klein modes in the AdS//CFT correspondence (2002, background): “where the coefficients e ∆,m,n, f (`) ∆,m,n are given in [26] and are positive.”
Projectors, shadows, and conformal blocks (2012, background): “In particular, it would be interesting to apply it to superconformal theories, perhaps providing a way to bypass the complicated superconformal block calculations in [14, 42, 43].”