In N ≥ 2 superconformal Chern-Simons-matter theories we construct the infinite family of Bogomol’nyi-Prasad-Sommerfield (BPS) Wilson loops featured by constant parametric couplings to scalar and fermion matter, including both line Wilson loops in Minkowski spacetime and circle Wilson loops in Euclidean space. We find that the connection of the most general BPS Wilson loop cannot be decomposed in terms of double-node connections. Moreover, if the quiver contains triangles, it cannot be interpreted as a super-matrix inside a superalgebra. However, for particular choices of the parameters it reduces to the well-known connections of 1/6 BPS Wilson loops in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory and 1/4 BPS Wilson loops in N = 4 orbifold ABJM theory. In the particular case of N = 2 orbifold ABJM theory we identify the gravity duals of a subset of operators. We investigate the cohomological equivalence of fermionic and bosonic BPS Wilson loops at quantum level by studying their expectation values, and find strong evidence that the cohomological equivalence holds quantum mechanically, at framing one. Finally, we discuss a stronger formulation of the cohomological equivalence, which implies non-trivial identities for correlation functions of composite operators in the defect CFT defined on the Wilson contour and allows to make novel predictions on the corresponding unknown integrals that call for a confirmation.

We compute the two-loop anomalous dimension matrix in the scalar sector of planar N=3 flavored ABJM theory. Using coordinate Bethe ansatz, we obtain the reflection matrices and confirm that the boundary Yang-Baxter equations are satisfied. This establishes the integrability of this theory in the scalar sector at the two-loop order.

We study scattering equations and formulas for tree amplitudes of various theories in four dimensions, in terms of spinor helicity variables and on-shell superspace for supersymmetric theories. As originally obtained in Witten’s twistor string theory and other twistor-string models, the equations can take either polynomial or rational forms, and we clarify the simple relation between them. We present new, four-dimensional formulas for all tree amplitudes in the non-linear sigma model, a special Galileon theory and the maximally supersymmetric completion of the Dirac-Born-Infeld theory. Furthermore, we apply the formulas to study various double-soft theorems in these theories, including the emissions of a pair of soft photons, fermions and scalars for super-amplitudes in super-DBI theory.

We show that generic three-dimensional N=2 quiver super Chern–Simons-matter theories admit Bogomol'nyi–Prasad–Sommerfield (BPS) Drukker–Trancanelli (DT) type Wilson loops. We investigate both Wilson loops along timelike infinite straight lines in Minkowski spacetime and circular Wilson loops in Euclidean space. In Aharnoy–Bergman–Jafferis–Maldacena theory, we find that generic BPS DT type Wilson loops preserve the same number of supersymmetries as Gaiotto–Yin type Wilson loops. There are several free parameters for generic BPS DT type Wilson loops in the construction, and supersymmetry enhancement for Wilson loops happens for special values of the parameters.

We investigate the supersymmetric Wilson loops in d = 3 N=4 super Chern-Simons-matter theory obtained from non-chiral orbifold of ABJM theory. We work in both Minkowski spacetime and Euclidean space, and we construct 1/4 and 1/2 BPS Wilson loops. We also provide a complete proof that the difference between 1/4 and 1/2 Wilson loops is Q-exact with Q being some supercharge that is preserved by both the 1/4 and 1/2 Wilson loops. This plays an important role in applying the localization techniques to compute the vacuum expectation values of Wilson loops. We also study the M-theory dual of the 1/2 BPS circular Wilson loop.

In this paper, we study the semi-classical strings in AdS4 × CP3 spacetime. We construct various kinds of string solutions, including the point-like, circular, folded and pulsating strings. For the circular and folded strings, we figure out their field theory dual operators. In particular, we discuss the anomalous dimensions of the corresponding operators from decoupled SU(2) × SU(2) spin chain. We find that in the large angular momentum limit, the field theory and string theory results are in very good agreement up to an interpolating function of coupling constant.

The Cachazo-Svrcek-Witten approach to perturbative gauge theory is extended to gauge theories with quarks and gluinos. All googly amplitudes with quark-antiquark pairs and gluinos are computed and shown to agree with the previously known results. The computations of the non-MHV or non-googly amplitudes are also briefly discussed, in particular the purely fermionic amplitude with 3 quark-antiquark pairs.

The generic googly amplitudes in gauge theory are computed by using the Cachazo-Svrcek-Witten approach to perturbative calculation in gauge theory and the results are in agreement with the previously well-known ones. Within this approach we also discuss the parity transformation, charge conjugation and the dual Ward identity. We also extend this calculation to include fermions and the googly amplitudes with a single quark-anti-quark pair are obtained correctly from fermionic MHV vertices. At the end we briefly discuss the possible extension of this approach to gravity.