N=1 Superconformal Symmetry in Four-Dimensional Quantum Field Theory

Abstract

The implications of N = 1 superconformal symmetry for four dimensional quantum field theories are studied. Superconformal covariant expressions for two and three point functions of quasi-primary superfields of arbitrary spin are found and connected with the operator product expansion. The general formulae are specialised to cases involving a scalar superfield L, which contains global symmetry currents, and the supercurrent, which contains the energy momentum tensor, and the consequences of superconformal Ward identities are analysed. The three point function of L is shown to have unique completely antisymmetric or symmetric forms. In the latter case the superspace version of the axial anomaly equation is obtained. The three point function for the supercurrent is shown to have two linearly independent forms. A linear combination of the associated coefficients for the general expression is shown to be related to the scale of the supercurrent two point function through Ward identities. The coefficients are given for the two free field superconformal theories and are also connected with the parameters present in the supercurrent anomaly for supergravity backgrounds. Superconformal invariants, which are possible even in three point functions, are discussed.

Superconformal flavor simplified

“…However the enlarged symmetry group of a SCFT imposes additional constraints. In particular, J I and T µ become primary operators and their three-point function T µ (z 2 )T ν (z 3 )J I (z 1 ) is uniquely determined up to an overall constant by superconformal symmetry [60]. This immediately implies that Tr(RRF I ) and Tr(F I ) are proportional to each other, with a constant that's universal for any SCFT.…”

OPE methods for the holomorphic Higgs portal

“…Starting from the expressions of [18], where soft parameters are expressed in terms of two-point functions of hidden-sector operators, we will show, utilizing the general formalism of [24], that the approximate superconformal symmetry provides powerful constraints on the form of such terms. Our strategy is to use the (kinematically constrained) form of three-point functions in N = 1 superconformal theories to extract the OPE of the first two operators with the third.…”

On compactified harmonic/projective superspace, 5D superconformal theories, and all that

“…These relations define a projective multiplet, following the four-dimensional terminology [9]. Associated with φ(z, w) is its smile-conjugateφ 34) which is also a projective multiplet. Ifφ(z, w) = φ(z, w), the projective superfield is called real.…”

“…The concept of superconformal Killing vectors [28,29,30,31,32,21,33], has proved to be extremely useful for various studies of superconformal theories in four and six dimensions, see e.g. [34,35,36]. This paper is organized as follows.…”