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Register a new userExploring the ground state spectrum of gamma-deformed N=4 SYM
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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.
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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 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.
The spectrum of IIB supergravity on AdS${}_5 times S^5$ contains a number of bound states described by long double-trace multiplets in $mathcal{N}=4$ super Yang-Mills theory at large t Hooft coupling. At large $N$ these states are degenerate and to obtain their anomalous dimensions as expansions in $tfrac{1}{N^2}$ one has to solve a mixing problem. We conjecture a formula for the leading anomalous dimensions of all long double-trace operators which exhibits a large residual degeneracy whose structure we describe. Our formula can be related to conformal Casimir operators which arise in the structure of leading discontinuities of supergravity loop corrections to four-point correlators of half-BPS operators.
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 construct the complete spectral curve for an arbitrary local operator, including fermions and covariant derivatives, of one-loop N=4 gauge theory in the thermodynamic limit. This curve perfectly reproduces the Frolov-Tseytlin limit of the full spectral curve of classical strings on AdS_5xS^5 derived in hep-th/0502226. To complete the comparison we introduce stacks, novel bound states of roots of different flavors which arise in the thermodynamic limit of the corresponding Bethe ansatz equations. We furthermore show the equivalence of various types of Bethe equations for the underlying su(2,2|4) superalgebra, in particular of the type Beauty and Beast.
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