We study supersymmetric Wilson loop operators in ABJM theory from both sides of the AdS 4 /CF T 3 correspondence. We first construct some supersymmetric Wilson loops. The perturbative computations are performed in the field theory side at the first two orders. A fundamental string solution ending on a circular loop is also studied.

Abstract: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.

In this paper we construct and classify novel Drukker-Trancanelli (DT) type BPS Wilson loops along infinite straight lines and circles in N = 2, 3 quiver superconformal Chern-Simons-matter theories, Aharony-Bergman-Jafferis-Maldacena (ABJM) theory, and N = 4 orbifold ABJM theory. Generally we have four classes of Wilson loops, and all of them preserve the same supersymmetries as the BPS Gaiotto-Yin (GY) type Wilson loops. There are several free complex parameters in the DT type BPS Wilson loops, and for two classes of Wilson loops in ABJM theory and N = 4 orbifold ABJM theory there are supersymmetry enhancements at special values of the parameters. We check that the differences of the DT type and GY type Wilson loops are Q-exact with Q being some supercharges preserved by both the DT type and GY type Wilson loops. The results would be useful to calculate vacuum expectation values of the DT type Wilson loops in matrix models if they are still BPS quantum mechanically. * ouyangh@ihep.ac.cn † wujb@ihep.ac.cn ‡ jjzhang@ihep.ac.cn1 Introduction BPS (Bogomol'nyi-Prasad-Sommerfield) Wilson loops are important nonlocal objects in supersymmetric gauge theories, and in AdS/CFT correspondence [1-3] they are dual to probe F-strings/membranes in string/M theory [4-7], when they are in fundamental representation of the gauge group. BPS Wilson loops in three-dimensional quiver superconformal Chern-Simons-matter (CSM) theories are more complex than those in four-dimensional super Yang-Mills theories. One can use only bosonic fields and Note that the two equations are consistent, since they are complex conjugates of each other. In this case we haveThe Wilson loop is global SU (3) R-symmetry invariant. Whenᾱ 2 = 0, it is just Wilson loop that was constructed in [9].So for general parameters the Wilson loop with (4.26) is 1/6 BPS, and the preserved supersymmetries are (4.19). When there is also (4.33), the Wilson loop is enhanced to 1/2 BPS, and the preserved supersymmetries are (4.34). Class IIIn the second solution the calculation is parallel to that of the first one. We havē α 1,2 = β 1,2 = 0, (4.36)

Abstract:We investigate the supersymmetric Wilson loops in d = 3 N = 4 super ChernSimons-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.

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Abstract:We investigate the short interval expansion of the Rényi entropy for twodimensional conformal field theory (CFT) on a torus. We require the length of the interval to be small with respect to the spatial and temporal sizes of the torus. The operator product expansion of the twist operators allows us to compute the short interval expansion of the Rényi entropy at any temperature. In particular, we pay special attention to the large c CFTs dual to the AdS 3 gravity and its cousins. At both low and high temperature limits, we read the Rényi entropies to order 6 , and find good agreements with holographic results. Moreover, the expansion allows us to read 1/c contribution, which is hard to get by expanding the thermal density matrix. We generalize the study to the case with the chemical potential as well.

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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.