Superconformal Ward identities and their solution

By Michael Nirschl, H. Osborn. 2004

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Abstract Superconformal Ward identities are derived for the four point functions of chiral primary BPS operators for N = 2 , 4 superconformal symmetry in four dimensions. Manipulations of arbitrary tensorial fields are simplified by introducing a null vector so that the four point functions depend on two internal R-symmetry invariants as well as two conformal invariants. The solutions of these identities are interpreted in terms of the operator product expansion and are shown to accommodate long supermultiplets with free scale dimensions and also short and semi-short multiplets with protected dimensions. The decomposition into R-symmetry representations is achieved by an expansion in terms of two variable harmonic polynomials which can be expressed also in terms of Legendre polynomials. Crossing symmetry conditions on the four point functions are also discussed.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5dea3fa290ca069f66c8f9c106671fba8c1bc78c

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In Nuclear and High Energy Physics

Citations in the corpus

Infinite Chiral Symmetry in Four Dimensions (2013, background): “The full collection of four-point functions can be conveniently packaged by introducing two-component SU(2)R vectors u(yi) = (1, yi) and defining contracted operators that depend on the auxiliary variable y as follows [15, 16]”
How to succeed at holographic correlators without really trying (2017, background): “Finally the overall constant can be determined by comparing with the free field result after restricting the R-symmetry cross ratios to a special slice [73] (this is related the chiral algebra twist [79]).”
All tree-level correlators in AdS5×S5 supergravity: hidden ten-dimensional conformal symmetry (2018, background): “This led to various conjectures for correlators [14, 15].”
Large spin systematics in CFT (2015, unknown): “The corresponding super-conformal blocks have been worked out in [13].”
Bootstrapping mixed correlators in the 3D Ising model (2014, background): “Superconformal extensions have been studied in [6, 22, 76–83].”
The (2, 0) superconformal bootstrap (2015, unknown): “2 3 + m; ‘+ 34 2 3 + m; ‘ 6 + 2m;z (z !z) : The harmonic functions for the various so(5) Rirreducible representation appearing in the decomposition of the four-point function (4.2) are given by [49,122] Y[4;0](;) = ˙2 + ˝2 + 4˙˝ 8(˙+ ˝) 9 + 8 63 ; Y[2;2](;) = ˙2 ˝2 4(˙ ˝) 7 ; Y[0;4](;) = ˙2 + ˝2 2”
The N=2$$ \mathcal{N}=2 $$ superconformal bootstrap (2014, methodology): “For the Higgs branch chiral ring, the structure of many relevant four-point functions and superconformal blocks have already been worked out in [111, 112].”
Exact correlators of BPS Operators from the 3d superconformal bootstrap (2014, unknown): “, [64]), one can show that”
Conformal Partial Waves: Further Mathematical Results (2011, background): “which play a role [23] in the decomposition of correlation functions.”
On Four-Point Functions of Half-BPS Operators in General Dimensions (2004, methodology): “s [21]. The Ward identities constraining these four-point functions take a very simple and universal form for all dimensions d, upon making a judicious choice of variables parametrizing the 1See also [15] where similar results are obtained in a component ﬁeld approach. 2See also some comments about ”