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Register a new userDemystifying the twistor construction of composite operators in N=4 super-Yang-Mills theory
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We explain some details of the construction of composite operators in N=4 SYM that we have elaborated earlier in the context of Lorentz harmonic chiral (LHC) superspace. We give a step-by-step elementary derivation and show that the result coincides with the recent hypothesis put forward in arXiv:1603.04471 within the twistor approach. We provide the appropriate LHC-to-twistors dictionary.
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We study event shapes in N=4 SYM describing the angular distribution of energy and R-charge in the final states created by the simplest half-BPS scalar operator. Applying the approach developed in the companion paper arXiv:1309.0769, we compute these observables using the correlation functions of certain components of the N=4 stress-tensor supermultiplet: the half-BPS operator itself, the R-symmetry current and the stress tensor. We present master formulas for the all-order event shapes as convolutions of the Mellin amplitude defining the correlation function of the half-BPS operators, with a coupling-independent kernel determined by the choice of the observable. We find remarkably simple relations between various event shapes following from N=4 superconformal symmetry. We perform thorough checks at leading order in the weak coupling expansion and show perfect agreement with the conventional calculations based on amplitude techniques. We extend our results to strong coupling using the correlation function of half-BPS operators obtained from the AdS/CFT correspondence.
We review a recent progress in constructing low-energy effective action in N=4 super Yang-Mills theories. Using harmonic superspace approach we consider N=4 SYM in terms of unconstrained N=2 superfield and apply N=2 background field method to finding effective action for N=4 SU(n) SYM broken down to U(1)^(n-1). General structure of leading low-energy corrections to effective action is discussed.
We study modular invariants arising in the four-point functions of the stress tensor multiplet operators of the ${cal N} = 4$ $SU(N)$ super-Yang-Mills theory, in the limit where $N$ is taken to be large while the complexified Yang-Mills coupling $tau$ is held fixed. The specific four-point functions we consider are integrated correlators obtained by taking various combinations of four derivatives of the squashed sphere partition function of the ${cal N} = 2^*$ theory with respect to the squashing parameter $b$ and mass parameter $m$, evaluated at the values $b=1$ and $m=0$ that correspond to the ${cal N} = 4$ theory on a round sphere. At each order in the $1/N$ expansion, these fourth derivatives are modular invariant functions of $(tau, bar tau)$. We present evidence that at half-integer orders in $1/N$, these modular invariants are linear combinations of non-holomorphic Eisenstein series, while at integer orders in $1/N$, they are certain generalized Eisenstein series which satisfy inhomogeneous Laplace eigenvalue equations on the hyperbolic plane. These results reproduce known features of the low-energy expansion of the four-graviton amplitude in type IIB superstring theory in ten-dimensional flat space and have interesting implications for the structure of the analogous expansion in $AdS_5times S^5$.
There is evidence that one can compute tree level super Yang-Mills amplitudes using either connected or completely disconnected curves in twistor space. We argue that the two computations are equivalent, if the integration contours are chosen in a specific way, by showing that they can both be reduced to the same integral over a moduli space of singular curves. We also formulate a class of new ``intermediate prescriptions to calculate the same amplitudes.
We argue that the scattering amplitudes in the maximally supersymmetric N=4 super-Yang-Mills theory possess a new symmetry which extends the previously discovered dual conformal symmetry. To reveal this property we formulate the scattering amplitudes as functions in the appropriate dual superspace. Rewritten in this form, all tree-level MHV and next-to-MHV amplitudes exhibit manifest dual superconformal symmetry. We propose a new, compact and Lorentz covariant formula for the tree-level NMHV amplitudes for arbitrary numbers and types of external particles. The dual conformal symmetry is broken at loop level by infrared divergences. However, we provide evidence that the anomalous contribution to the MHV and NMHV superamplitudes is the same and, therefore, their ratio is a dual conformal invariant function. We identify this function by an explicit calculation of the six-particle amplitudes at one loop. We conjecture that these properties hold for all, MHV and non-MHV, superamplitudes in N=4 SYM both at weak and at strong coupling.
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