BPS M2M2-branes in AdS4×Q1,1,1AdS_4\times Q^{1, 1, 1} Dual to Loop Operators

In this paper, we first compute the Killing spinors of $AdS_4\times Q^{1, 1, 1}$ and its certain orbifolds. Based on this, two classes of $M2$-brane solutions are found. The first class of solutions includes $M2$-branes dual to Wilson loops in the fundamental representation as special cases. The second class includes the candidates of the holographic description of vortex loops in the dual field theories.Comment: v6, typoes fixed, 14 pages, no figure

Comments on Two-Loop Four-Particle Amplitude in Superstring Theory

It is shown that the four-particle amplitude of superstring theory at two loops obtained in [1,2] is equivalent to the previously obtained results in [3,4,5]. Here the ${\bf Z}_2$ symmetry in hyperelliptic Riemann surface plays an important role in the proof.Comment: 10 pages, Latex fil

Two-Loop Superstrings in Hyperelliptic Language III: the Four-Particle Amplitude

We compute explicitly the four-particle amplitude in superstring theories by using the hyperelliptic language and the newly obtained chiral measure of D'Hoker and Phong. Although the algebra of the intermediate steps is a little bit involved, we obtain a quite simple expression for the four-particle amplitude. As expected, the integrand is independent of all the insertion points. As an application of the obtained result, we show that the perturbative correction to the $R^4$ term in type II superstring theories is vanishing point-wise in (even) moduli space at two loops.Comment: v1, LaTex file, 33 pages; v2, 34 pages, add references and minor correction

New electromagnetic memories and soft photon theorems

In this paper, we present a new type of electromagnetic memory. It is a `magnetic' type, or B mode, radiation memory effect. Rather than a residual velocity, we find a position displacement of a charged particle induced by the B mode radiation with memory. We find two types of electromagnetic displacement (ordinary and null). We also show that the null electromagnetic memory formulas are nothing but a Fourier transformation of soft photon theorems.Comment: v2: interpretation improved and typos fixed, refs adde

Scattering Equations, Twistor-string Formulas and Double-soft Limits in Four Dimensions

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.Comment: 22 pages, 2 tables; v2: ref added, minor typos fixe