119117490
Nonplanarity through unitarity in the ABJM theory
We use unitarity techniques to compute the two-loop non-planar corrections to the Sudakov form factor and the four-point amplitude in ABJM theory. We start by reconstructing non-planar integrals from two-particle cuts in three dimensions. This causes ambiguities, due to the one-loop four-point amplitude being subleading in dimensional regularization. We provide a prescription to circumvent them and show that it leads to the correct results, as checked against the recent Feynman diagram computation. For the amplitude we point out an alternative basis of integrals, including a non-planar double-box with a numerator inspired by color-kinematics duality. We reproduce the result using a combination thereof with the coefficients fixed by generalized unitarity. For BLG theory we propose that this gives the form of the amplitude satisfying color-kinematics duality. Finally, we compute the complete two-loop amplitude of three-dimensional N = 8 SYM, and the corresponding four-point amplitude in N = 16 supergravity as a double copy.
123488833
Scattering amplitudes in three-dimensional superconformal field theory
Recent progress in computation of loop amplitudes in three-dimensional superconformal models is reviewed.
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.
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.
54031010
Two-loop cusp anomaly in ABJM at strong coupling
A bstractWe compute the null cusp anomalous dimension of ABJM theory at strong coupling up to two-loop order. This is done by evaluating corrections to the corresponding superstring partition function, weighted by the AdS4 × ℂℙ3 action in AdS light-cone gauge. We compare our result, where we use an anomalous shift in the AdS4 radius, with the cusp anomaly of N$$ \mathcal{N} $$ = 4 SYM, and extract the two-loop contribution to the non-trivial integrable coupling h(λ) of ABJM theory. It coincides with the strong coupling expansion of the exact expression for h(λ) recently conjectured by Gromov and Sizov. Our work provides thus a non-trivial perturbative check for the latter, as well as evidence for two-loop UV-finiteness and quantum integrability of the Type IIA AdS4 × ℂℙ3 superstring in this gauge.
7025247
Discrete torsion in non-geometric orbifolds and their open-string descendants
Abstract We discuss some Z N L × Z N R orbifold compactifications of the type IIB superstring to D =4,6 dimensions and their type I descendants. Although the Z N L × Z N R generators act asymmetrically on the chiral string modes, they result into left–right symmetric models that admit sensible unorientable reductions. We carefully work out the phases that appear in the modular transformations of the chiral amplitudes and identify the possibility of introducing discrete torsion. We propose a simplifying ansatz for the construction of the open-string descendants in which the transverse-channel Klein-bottle, annulus and Mobius-strip amplitudes are numerically identical in the proper parametrization of the world-sheet. A simple variant of the ansatz for the Z 2 L × Z 2 R orbifold gives rise to models with supersymmetry breaking in the open-string sector.
12505991
Precision spectroscopy and higher spin symmetry in the ABJM model
We revisit Kaluza-Klein compactification of 11-d supergravity on $ {{{{S^7}}} \left/ {{{\mathbb{Z}_k}}} \right.} $ using group theory techniques that may find application in other flux vacua with internal coset spaces. Among the SO(2) neutral states, we identify marginal deformations and fields that couple to the recently discussed world-sheet instanton of Type IIA on $ \mathbb{C}{\mathbb{P}^3} $. We also discuss charged states, dual to monopole operators, and the $ {\mathbb{Z}_k} $ projection of the Osp(8|4) singleton and its tensor products. In particular, we show that the doubleton spectrum may account for $ \mathcal{N} = 6 $ higher spin symmetry enhancement in the limit of vanishing ’t Hooft coupling in the boundary Chern-Simons theory.
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.
123407983
On the ADHM construction on ALE gravitational backgrounds
Abstract In this letter we report on the explicit construction of self-dual connections on Asymptotically Locally Euclidean spaces following the approach of Kronheimer and Nakajima. Restricting ourselves to the simplest case of an SU (2) connection with the lowest Chern class on the Eguchi-Hanson gravitational background, we study the wave operators for scalar, spinor and vector fields in the adjoint representation of the gauge group and verify that the metric on the moduli space coincides with the metric on the base manifold.
197424879
1994 status report RD9: A Demonstrator analog signal processing circuit in a radiation hard SOI-CMOS technology