Silvia Penati

Non(anti)commutative superspace

We investigate the most general non(anti)commutative geometry in N = 1 four-dimensional superspace, invariant under the classical (i.e., undeformed) supertranslation group. We find that a nontrivial non(anti)commutative superspace geometry compatible with supertranslations exists with non(anti)commutation parameters which may depend on the spinorial coordinates. The algebra is in general nonassociative. Imposing associativity introduces additional constraints which, however, allow for nontrivial commutation relations involving fermionic coordinates. We obtain explicitly the first three terms of a series expansion in the deformation parameter for a possible associative -product. We also consider the case of N = 2 Euclidean superspace where the different conjugation relations among spinorial coordinates allow for a more general supergeometry.

Exact results in planar Script N = 1 superconformal Yang-Mills theory

In the β-deformed = 4 supersymmetric SU(N) Yang-Mills theory we study the class of operators J = Tr(ΦiJΦk), i≠k and compute their exact anomalous dimensions for N,J→∞. This leads to a prediction for the masses of the corresponding states in the dual string theory sector. We test the exact formula perturbatively up to two loops. The consistency of the perturbative calculation with the exact result indicates that in the planar limit the one-loop condition g2 = h for superconformal invariance is indeed sufficient to insure the exact superconformal invariance of the theory. We present a direct proof of this point in perturbation theory. The J sector of this theory shares many similarities with the BMN sector of the = 4 theory in the large R-charge limit.

Wave equations for arbitrary spin from quantization of the extended supersymmetric spinning particle

Abstract We present the action for a relativistic particle with a gauged N-extended line supersymmetry and show that, upon quantization, it yields a relativistic wave equation for pure spin 1 2 N . A curved-space background is compatible with worldline supersymmetry only for N⩽2.

Two-loop renormalization for nonanticommutative N = 1/2 supersymmetric WZ model

We study systematically, through two loops, the divergence structure of the supersymmetric WZ model defined on the N = 1/2 nonanticommutative superspace. By introducing a spurion field to represent the supersymmetry breaking term F3 we are able to perform our calculations using conventional supergraph techniques. Divergent terms proportional to F, F2 and F3 are produced (the first two are to be expected on general grounds) but no higher-point divergences are found. By adding ab initio F and F2 terms to the original lagrangian we render the model renormalizable. We determine the renormalization constants and beta functions through two loops, thus making it possible to study the renormalization group flow of the nonanticommutation parameter.

Two-point correlators in the beta-deformed N=4 SYM at the next-to-leading order.

We compute two-point functions of lowest weight operators at the next-to-leading order in the couplings for the β-deformed = 4SU(N) SYM. In particular we focus on the CPO Tr(Φ12) and the operator Tr(Φ1Φ2) not presently listed as BPS. We find that for both operators no anomalous dimension is generated at this order, then confirming the results recently obtained at lowest order in [5]. However, in both cases a finite correction to the two-point function appears.

SCATTERING AMPLITUDES/WILSON LOOP DUALITY IN ABJM THEORY

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More on correlators and contact terms in N=4 SYM at order g(4)

\mathcal{N} = 6

From correlators to Wilson loops in Chern-Simons matter theories

superconformal Chern-Simons-matter theories in three dimensions, by a direct superspace Feynman diagram approach, we compute the two-loop four-point scattering amplitude with external chiral matter fields. We find that the result is in perfect agreement with the two-loop result for a light-like four-polygon Wilson loop. This is the first non-trivial evidence that an amplitudes/Wilson loop duality might work in three dimensions. Moreover, both the IR divergent and the finite parts of our two-loop result agree with a BDS-like ansatz for all-loop amplitudes where the scaling function is given in terms of the