Umkehr Maps Patched via the Compactified Cleavage Operad

Via a compactification of the cleavage operad, we describe two actions on the mapping spaces from spheres into compact, oriented manifolds. The map from the compactified version of the cleavage operad provides a version of intersection theory along the underlying base manifold lifted to the mapping space. The other action map only works for the uncompactified cleavage operad, and gives a homotopy theoretic version of higher dimensional string topology.Comment: This paper is under revision since there is a mistake not taking twistings into account. An upcoming paper with a different scope solves this problem in a geometric fashion. The statements on the compactifications in this paper will be reformulated accordingl

Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory

Constraints of the osp(6|4) symmetry on tree-level scattering amplitudes in N=6 superconformal Chern-Simons theory are derived. Supplemented by Feynman diagram calculations, solutions to these constraints, namely the four- and six-point superamplitudes, are presented and shown to be invariant under Yangian symmetry. This introduces integrability into the amplitude sector of the theory.Comment: 50 pages. v2, v3: References added, minor correction

New Relations for Three-Dimensional Supersymmetric Scattering Amplitudes

We provide evidence for a duality between color and kinematics in three-dimensional supersymmetric Chern-Simons matter theories. We show that the six-point amplitude in the maximally supersymmetric, N=8, theory can be arranged so that the kinematic factors satisfy the fundamental identity of three-algebras. We further show that the four- and six-point N=8 amplitudes can be "squared" into the amplitudes of N=16 three-dimensional supergravity, thus providing evidence for a hidden three-algebra structure in the dynamics of the supergravity.Comment: 8 pages, 2 figure

The Two-Loop Symbol of all Multi-Regge Regions

We study the symbol of the two-loop n-gluon MHV amplitude for all Mandelstam regions in multi-Regge kinematics in N=4 super Yang-Mills theory. While the number of distinct Mandelstam regions grows exponentially with n, the increase of independent symbols turns out to be merely quadratic. We uncover how to construct the symbols for any number of external gluons from just two building blocks which are naturally associated with the six- and seven-gluon amplitude, respectively. The second building block is entirely new, and in addition to its symbol, we also construct a prototype function that correctly reproduces all terms of maximal functional transcendentality.Comment: 20 pages, v2: include details on functions f and g, make appendix consistent with main text, typesetting (published version

Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory

We study Yangian-invariant deformations of scattering amplitudes in 4d N=4 supersymmetric Yang-Mills theory and 3d N=6 Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. In particular, we obtain the deformed Grassmannian integral for 4d N=4 super Yang-Mills theory, both in momentum and momentum-twistor space. For 3d ABJM theory, we initiate the study of deformed scattering amplitudes. We investigate general deformations of on-shell diagrams, and find the deformed Grassmannian integral for this theory. We furthermore introduce the algebraic R-matrix construction of deformed Yangian invariants for ABJM theory.Comment: 39 pages, 9 figures; v2: references added, typos fixed, section 3.4 improved, published versio

Handling Handles: Nonplanar Integrability in N=4\mathcal{N}=4 Supersymmetric Yang-Mills Theory

We propose an integrability setup for the computation of correlation functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at higher orders in the large $N_{\text{c}}$ genus expansion and at any order in the 't Hooft coupling $g_{\text{YM}}^2N_{\text{c}}$. In this multi-step proposal, one polygonizes the string worldsheet in all possible ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over all hexagon junctions to obtain the full correlator. We test our integrability-based conjecture against a non-planar four-point correlator of large half-BPS operators at one and two loops.Comment: 6 pages, 4 figures; v2: updated references, typos, minor improvements (published version

Thermoelastic study of nanolayered structures using time-resolved x-ray diffraction at high repetition rate

We investigate the thermoelastic response of a nanolayered sample composed of a metallic SrRuO3 (SRO) electrode sandwiched between a ferroelectric Pb(Zr0.2Ti0.8)O3 (PZT) film with negative thermal expansion and a SrTiO3 substrate. SRO is rapidly heated by fs-laser pulses with 208 kHz repetition rate. Diffraction of x-ray pulses derived from a synchrotron measures the transient out-of-plane lattice constant c of all three materials simultaneously from 120 ps to 5 mus with a relative accuracy up to Delta c/c = 10^-6. The in-plane propagation of sound is essential for understanding the delayed out of plane expansion.Comment: 5 pages, 3 figure

Simultaneous dynamic characterization of charge and structural motion during ferroelectric switching

Monitoring structural changes in ferroelectric thin films during electric field-induced polarization switching is important for a full microscopic understanding of the coupled motion of charges, atoms and domain walls. We combine standard ferroelectric test-cycles with time-resolved x-ray diffraction to investigate the response of a nanoscale ferroelectric oxide capacitor upon charging, discharging and switching. Piezoelectric strain develops during the electronic RC time constant and additionally during structural domain-wall creep. The complex atomic motion during ferroelectric polarization reversal starts with a negative piezoelectric response to the charge flow triggered by voltage pulses. Incomplete screening limits the compressive strain. The piezoelectric modulation of the unit cell tweaks the energy barrier between the two polarization states. Domain wall motion is evidenced by a broadening of the in-plane components of Bragg reflections. Such simultaneous measurements on a working device elucidate and visualize the complex interplay of charge flow and structural motion and challenges theoretical modelling