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Register a new userConformal Invariance in the Leigh-Strassler deformed N=4 SYM Theory
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We consider a full Leigh-Strassler deformation of the ${cal N}=4$ SYM theory and look for conditions under which the theory would be conformally invariant and finite. Applying the algorithm of perturbative adjustments of the couplings we construct a family of theories which are conformal up to 3 loops in the non-planar case and up to 4 loops in the planar one. We found particular solutions in the planar case when the conformal condition seems to be exhausted in the one loop order. Some of them happen to be unitary equivalent to the real beta-deformed ${cal N}=4$ SYM theory, while others are genuine. We present the arguments that these solutions might be valid in any loop order.
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We study the cal{N}=1 SU(N) SYM theory which is a marginal deformation of the cal{N}=4 theory, with a complex deformation parameter beta. We consider the large N limit and study perturbatively the conformal invariance condition. We find that finiteness requires reality of the deformation parameter beta.
We consider gluon and gluino scattering amplitudes in large N beta-deformed N=4 SYM with real beta. A direct inspection of the planar diagrams shows that the scattering amplitudes to all orders in perturbation theory are the same as in the undeformed N=4 SYM theory. Using the dual sigma-model description, we find the same equality at strong coupling to all orders in the sigma-model loop expansion. Finally, we show that the same analysis holds for gluon scattering amplitudes in a three-parameter deformation of planar N=4 SYM that breaks all the supersymmetry.
We study the gamma-deformation of the planar N=4 super Yang-Mills theory which breaks all supersymmetries but is expected to preserve integrability of the model. We focus on the operator Tr$(phi_1phi_1)$ built from two scalars, whose integrability description has been questioned before due to contributions from double-trace counterterms. We show that despite these subtle effects, the integrability-based Quantum Spectral Curve (QSC) framework works perfectly for this state and in particular reproduces the known 1-loop prediction. This resolves an earlier controversy concerning this operator and provides further evidence that the gamma-deformed model is an integrable CFT at least in the planar limit. We use the QSC to compute the first 5 weak coupling orders of the anomalous dimension analytically, matching known results in the fishnet limit, and also compute it numerically all the way from weak to strong coupling. We also utilize this data to extract a new coefficient of the beta function of the double-trace operator couplings.
We compute four-point correlation functions of scalar composite operators in the N=4 supercurrent multiplet at order g^4 using the N=1 superfield formalism. We confirm the interpretation of short-distance logarithmic behaviours in terms of anomalous dimensions of unprotected operators exchanged in the intermediate channels and we determine the two-loop contribution to the anomalous dimension of the N=4 Konishi supermultiplet.
Recent studies of scattering amplitudes in planar N=4 SYM theory revealed the existence of a hidden dual superconformal symmetry. Together with the conventional superconformal symmetry it gives rise to powerful restrictions on the planar scattering amplitudes to all loops. We study the general form of the invariants of both symmetries. We first construct an integral representation for the most general dual superconformal invariants and show that it allows a considerable freedom in the choice of the integration measure. We then perform a half-Fourier transform to twistor space, where conventional conformal symmetry is realized locally, derive the resulting conformal Ward identity for the integration measure and show that it admits a unique solution. Thus, the combination of dual and conventional superconformal symmetries, together with invariance under helicity rescalings, completely fixes the form of the invariants. The expressions obtained generalize the known tree and one-loop superconformal invariants and coincide with the recently proposed coefficients of the leading singularities of the scattering amplitudes as contour integrals over Grassmannians.
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