We present and prove a formula for the MHV scattering amplitude of n gravitons at tree level.Some of the more interesting features of the formula, which set it apart as being significantly different from many more familiar formulas, include the absence of any vestigial reference to a cyclic ordering of the gravitons-making it in a sense a truly gravitational formula, rather than a recycled Yang-Mills result, and the fact that it simultaneously manifests both S n−2 symmetry as well as large-z behavior that is O(1/z 2 ) term-by-term, without relying on delicate cancellations.The formula is seemingly related to others by an enormous simplification provided by O(n n ) iterated Schouten identities, but our proof relies on a complex analysis argument rather than such a brute force manipulation. We find that the formula has a very simple link representation in twistor space, where cancellations that are non-obvious in physical space become manifest.
Evidence has recently emerged for a hidden symmetry of planar scattering amplitudes in N 4 superYang-Mills theory called dual conformal symmetry. At weak coupling the presence of this symmetry has been observed through five loops, while at strong coupling the symmetry has been shown to have a natural interpretation in terms of a T-dualized AdS 5 . In this paper we study dual conformally invariant off-shell four-point Feynman diagrams. We classify all such diagrams through four loops and evaluate 10 new offshell integrals in terms of Mellin-Barnes representations, also finding explicit expressions for their infrared singularities.
We show that for a class of model Hamiltonians for which certain trial quantum Hall wavefunctions are exact ground states, there is a single spectral density function which controls all two-point correlation functions of density, current and stress tensor components. From this we show that the static structure factors of these wavefunctions behaves at long wavelengths as s4k 4 where the coefficient s4 is directly related to the shift: s4 = (S − 1)/8.
We propose nonabelian higher-rank gauge theories in 2+1D and 3+1D. The gauge group is constructed from the volume-preserving diffeomorphisms of space. We show that the intriguing physics of the lowest Landau level (LLL) limit can be interpreted as the consequences of the symmetry. We derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term within our formalism. Using the gauge symmetry in 2+1D, we derive the LLL effective action of vortex crystal in rotating Bose gas as well as Wigner crystal of electron in an applied magnetic field. We show that the nonlinear sigma models of ferromagnets in 2+1D and 3+1D exhibit the higher-rank gauge symmetries that we introduce in this paper. We interpret the fractonic behavior of the excitations on the lowest Landau level and of skyrmions in ferromagnets as the consequence of the higher-rank gauge symmetry.
The quantum Hall effect in curved space has been the subject of many theoretical investigations in the past, but devising a physical system to observe this effect is hard. Many works have indicated that electronic excitations in strained graphene realize Dirac fermions in curved space in the presence of a background pseudo-gauge field, providing an ideal playground for this. However, the absence of a direct matching between a numerical, strained tight-binding calculation of an observable and the corresponding curved space prediction has hindered realistic predictions. In this work, we provide this matching by deriving the low-energy Hamiltonian from the tight-binding model analytically to second order in the strain and mapping it to the curved-space Dirac equation. Using a strain profile that produces a constant pseudo-magnetic field and a constant curvature, we compute the Landau level spectrum with real-space numerical tight-binding calculations and find excellent agreement with the prediction of the quantum Hall effect in curved space. We conclude discussing experimental schemes for measuring this effect.
Thieno[3,thiophene is a structural motif that can be found in many important organic materials. A number of mono-, diand tetraarylthieno [3,2-b]thiophenes are reported herein. [1]benzothiophene (C 13 BTBT) were shown to demonstrate a very high thin film mobility of 3.1 cm 2 /Vs and 17.2 cm 2 /Vs, respectively, in VD-OFETs. 4b,c Due to intermolecular sulfur-sulfur interactions, materials containing thieno[3,2-b]thiophene may increase the electronic transport between neighboring molecules. The introduction of substituents into the core structure of materials may change electronic properties, solubility as well as molecular packing. 2m For tuning electronic properties, heterocycles have been widely functionalized by many methods, especially, by palladium(0)-catalyzed cross-coupling reactions. 5 It was previously shown that polyhalogenated heterocycles can be regioselectively functionalized by palladium-catalyzed crosscoupling reactions at the carbon-halogen bonds adjacent to the heteroatom. 5 These were controlled by both electronic and steric factors. We recently reported the methodologies for functionalization of N-methyltetrabromopyrrole, 6 tetrabromothiophene, 6 tetrabromoselenophene 7 and tetrabromofuran, 8 based on site-selective palladium(0)-catalyzed Suzuki reactions. Due to the importance of thieno[3,2-b]thiophene in materials science, we were interested in developing a sequential process for the functionalization of thieno [3,2-b]thiophene via site-selective palladium(0)-catalyzed Suzuki reactions of tetrabromothieno[3,2-b]thiophene with boronic acids. We report herein an efficient synthesis of mono-, di-and tetraarylthieno[3,2-b]thiophene using this strategy.The Suzuki-Miyaura reactions of 1 9 (1.0 equiv) with a series of boronic acids (1.2 equiv) resulted in a site-selective formation of 2-aryl-3,5,6-tribromothieno[3,2-b]thiophenes 2a-j 5 in 25-80% yields (Scheme 1 and Table 1). The conditions used were optimized with regard to temperature, solvent, base additive, and water additive. Pd(PPh 3 ) 4 was found to be an efficient catalyst for the current reaction. Other well-known catalyst systems, such as Pd(OAc) 2 /X-Phos, resulted in lower yields of the desired products. All reactions were carried out at 90-110 °C in 4-6 hours. Table 1).
One of the many remarkable features of MHV scattering amplitudes is their conjectured equality to lightlike polygon Wilson loops, which apparently holds at all orders in perturbation theory as well as non-perturbatively. This duality is usually expressed in terms of purely four-dimensional quantities obtained by appropriate subtraction of the IR and UV divergences from amplitudes and Wilson loops respectively. In this paper we demonstrate, by explicit calculation, the completely unanticipated fact that the equality continues to hold at two loops through O(ǫ) in dimensional regularization for both the four-particle amplitude and the (parity-even part of the) five-particle amplitude.
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