Integrability and maximally helicity violating diagrams in n=4 supersymmetric yang-mills theory.

We apply maximally helicity violating (MHV) diagrams to the derivation of the one-loop dilatation operator of N=4 supersymmetric Yang-Mills theory in the SO(6) sector. We find that in this approach the calculation reduces to the evaluation of a single MHV diagram in dimensional regularization. This provides the first application of MHV diagrams to an off-shell quantity. We also discuss other applications of the method and future directions

Multi - instantons, supersymmetry and topological field theories

In this letter we argue that instanton-dominated Green's functions in N=2 Super Yang-Mills theories can be equivalently computed either using the so-called constrained instanton method or making reference to the topological twisted version of the theory. Defining an appropriate BRST operator (as a supersymmetry plus a gauge variation), we also show that the expansion coefficients of the Seiberg-Witten effective action for the low-energy degrees of freedom can be written as integrals of total derivatives over the moduli space of self-dual gauge connections

Fermion BMN operators, the dilatation operator of N = 4 SYM, and pp-wave string interactions

The goal of this paper is to study the BMN correspondence in the fermionic sector. On the field theory side, we compute matrix elements of the dilatation operator in = 4 Super Yang-Mills for BMN operators containing two fermion impurities. Our calculations are performed up to and including (λ') in the 't Hooft coupling and (g2) in the Yang-Mills genus counting parameter. On the string theory side, we compute the corresponding matrix elements of the interacting string hamiltonian in string field theory, using the three-string interaction vertex constructed by Spradlin and Volovich (and subsequently elaborated by Pankiewicz and Stefanski). In string theory we use the natural string basis, and in field theory the basis which is isomorphic to it. We find that the matrix elements computed in field theory and the corresponding string amplitudes derived from the three-string vertex are, in all cases, in perfect agreement

Quantum MHV diagrams

Over the past two years, the use of on-shell techniques has deepened our understanding of the S-matrix of gauge theories and led to the calculation of many new scattering amplitudes. In these notes we review a particular on-shell method developed recently, the quantum MHV diagrams, and discuss applications to one-loop amplitudes. Furthermore, we briefly discuss the application of D-dimensional generalised unitarity to the calculation of scattering amplitudes in non-supersymmetric Yang-Mills

Lp−Lq Estimates for Orbital Measures and Radon Transforms on Compact Lie Groups and Lie Algebras

AbstractLet μ be an invariant measure on a regular orbit in a compact Lie group or in a Lie algebra. We prove sharp Lp − Lq estimates for the convolution operators defined through μ. We also obtain similar results for the related Radon transform on the Lie algebra

On higher-derivative effects on the gravitational potential and particle bending

Using modern amplitude techniques we compute the leading classical and quantum corrections to the classical gravitational potential between two massive scalars induced by adding an $R^3$ term to Einstein gravity. We then study the scattering of massless scalars, photons and gravitons off a heavy scalar in the presence of the same $R^3$ deformation, and determine the bending angle in the three cases from the non-analytic component of the scattering amplitude. Similarly to the Einstein-Hilbert case, we find that the classical contribution to the bending angle is universal, but unlike that case, universality is preserved also by the first quantum correction. Finally we extend our analysis to include a deformation of the form $\Phi R^2$, where $\Phi$ is the dilaton, which arises in the low-energy effective action of the bosonic string in addition to the $R^3$ term, and compute its effect on the graviton bending.Comment: 23 pages, 4 figures. v2: typos corrected, one reference added, several comments and clarifications added in Section 2. v3: JHEP version. v4: typos correcte