102332810
Scattering amplitudes/Wilson loop duality in ABJM theory
A bstractFor $$ \mathcal{N} = 6 $$ 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 $$ \mathcal{N} = 4 $$ SYM one, according to the conjectured Bethe equations for ABJM. Consequently, we are able to make a prediction for the four-loop correction to the amplitude. We also discuss the dual conformal invariance of the two-loop result.
52023598
On the ABJM four-point amplitude at three loops and BDS exponentiation
A bstractWe study the three-loop four-point amplitude in ABJM theory. We determine the dual conformal invariant integrals with highest number of propagators and fix their coefficients by two-particle cuts. Evaluating such a combination of integrals in dimensional regularization we provide evidence for exponentiation of the amplitude, including the finite terms. In addition we show that the three-loop amplitude can be expressed in terms of classical polylogarithms of uniform degree of transcendentality.
119108513
The 1/2 BPS Wilson loop in ABJ(M) at two loops: the details
A bstractWe compute the expectation value of the 1/2 BPS circular Wilson loop operator in ABJ(M) theory at two loops in perturbation theory. Our result turns out to be in exact agreement with the weak coupling limit of the prediction coming from localization, including finite N contributions associated to non-planar diagrams. It also confirms the identification of the correct framing factor that connects framing-zero and framing one expressions, previously proposed. The evaluation of the 1/2 BPS operator is made technically difficult in comparison with other observables of ABJ(M) theory by the appearance of integrals involving the coupling between fermions and gauge fields, which are absent for instance in the 1/6 BPS case. We describe in detail how to analytically solve these integrals in dimensional regularization with dimensional reduction (DRED). By suitably performing the physical limit to three dimensions we clarify the role played by short distance divergences on the final result and the mechanism of their cancellation.
56038769
BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
A bstractWe study a family of circular BPS Wilson loops in $ \mathcal{N} $ = 6 super Chern-Simons-matter theories, generalizing the usual 1/2-BPS circle. The scalar and fermionic couplings depend on two deformation parameters and these operators can be considered as the ABJ(M) counterpart of the DGRT latitudes defined in $ \mathcal{N} $ = 4 SYM. We perform a complete two-loop analysis of their vacuum expectation value, discuss the appearance of framing-like phases and propose a general relation with cohomologically equivalent bosonic operators. We make an all-loop proposal for computing the Bremsstrahlung function associated to the 1/2-BPS cusp in terms of these generalized Wilson loops. When applied to our two-loop result it reproduces the known expression. Finally, we comment on the generalization of this proposal to the bosonic 1/6-BPS case.
54173371
One loop amplitudes in ABJM
A bstractFor three dimensional $ \mathcal{N} = 6 $ superconformal field theories we compute oneloop scattering amplitudes for any number of external particles. We focus on a particular subsector of $ \mathcal{N} = 2 $ invariant superamplitudes for which the ordinary perturbative evaluation becomes very easy. The result we obtain is in general non-vanishing. For six external particles our findings are sufficient for determining the complete expression of the $ \mathcal{N} = 6 $ superamplitude at this order. We discuss the symmetries of the result and its anomalous variation under superconformal generators.
119238771
Scattering in ABJ theories
A bstractWe study the correspondence between scattering amplitudes and Wilson loops in three-dimensional Chern-Simons matter theories. In particular, using $ \mathcal{N} = {2} $ superspace formalism, we compute at one loop the whole spectrum of four-point superamplitudes for generic $ \mathcal{N} \geqslant {2} $ supersymmetric theories and find a vanishing result for $ \mathcal{N} = {6} $ ABJ(M) and $ \mathcal{N} = {8} $ BLG models. This restricts the possible range of theories for which Wilson loops/scattering amplitudes duality might work. At two loops, we present the computation of the four-point ABJ scattering amplitude for external chiral superfields. Extending the known result for the ABJM Wilson loop to the ABJ case we find perfect agreement. We also discuss the dual conformal invariance of our results and the relationship between the Feynman diagram computation and unitarity methods. While for the ABJM theory dual conformally invariant integrals exactly reproduce the amplitude, for the ABJ case this happens only up to a residual constant depending on the parity-violating parameter. Finally we propose a BDS-like exponentiation for the amplitude based on an analogy with the four dimensional $ \mathcal{N} = {4} $ SYM case, and discuss its strong coupling dual counterpart.
53865790
Scattering higher spins off D-branes
A bstractWe study scattering amplitudes of higher spin closed-string states off D-branes. For states in the ‘first Regge trajectory’ we find remarkable simplifications both at tree level and at one loop. We discuss the high energy behavior in the Regge limit and comment on the validity of the eikonal approximation in this regime.
16348662
Unoriented D-brane instantons vs heterotic worldsheet instantons
We discuss Fermi interactions of four hyperini generated by "stringy" instan- tons in a Type I / Heterotic dual pair on T 4 /Z2.
14592640
Deep Inelastic Scattering in Improved Lattice QCD. II. The second moment of structure functions
In this paper we present the 1-loop perturbative computation of the renormalization constants and mixing coefficients of the lattice quark operators of rank three whose hadronic elements enter in the determination of the second moment of Deep Inelastic Scattering (DIS) structure functions. 
We have employed in our calculations the nearest-neighbor improved ``clover-leaf'' lattice QCD action. The interest of using this action in Monte Carlo simulations lies in the fact that all terms which in the continuum limit are effectively of order $a$ ($a$ being the lattice spacing) have been demonstrated to be absent from on-shell hadronic lattice matrix elements. We have limited our computations to the quenched case, in which quark operators do not mix with gluon operators. 
We have studied the transformation properties under the hypercubic group of the operators up to the rank five (which are related to moments up to the fourth of DIS structure functions), and we discuss the choice of the operators considered in this paper together with the feasibility of lattice computations for operators of higher ranks. 
To perform the huge amount of calculations required for the evaluation of all the relevant Feynman diagrams, we have extensively used the symbolic manipulation languages Schoonschip and Form.
15960683
Properties of the Konishi multiplet in N=4 SYM theory
We study perturbative and non-perturbative properties of the Konishi multiplet in = 4 SYM theory in D = 4 dimensions. We compute two-, three- and four-point Green functions with single and multiple insertions of the lowest component of the multiplet, 1, and of the lowest component of the supercurrent multiplet, 20'. These computations require a proper definition of the renormalized operator, 1, and lead to an independent derivation of its anomalous dimension. The O(g2) value found in this way is in agreement with previous results. We also find that instanton contributions to the above correlators vanish. From our results we are able to identify some of the lowest dimensional gauge-invariant composite operators contributing to the OPE of the correlation functions we have computed. We thus confirm the existence of an operator belonging to the representation 20', which has vanishing anomalous dimension at order g2 and g4 in perturbation theory as well as at the non-perturbative level, despite the fact that it does not obey any of the known shortening conditions.
18962115
Anomalous dimensions in N=4 SYM theory at order g4
Abstract 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.