210160917
The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N = 4 SYM
We provide an analytic formula for the (rescaled) one-loop six-dimensional scalar hexagon integral Φ̃6 with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals appearing in oneand two-loop amplitudes in planar N = 4 super-Yang-Mills theory, Ω(1) and Ω(2). The derivative of Ω(2) with respect to one of the conformal invariants yields Φ̃6, while another first-order differential operator applied to Φ̃6 yields Ω (1). We also introduce some kinematic variables that rationalize the arguments of the polylogarithms, making it easy to verify the latter differential equation. We also give a further example of a six-dimensional integral relevant for amplitudes in N = 4 super-Yang-Mills theory.
3185569
Codimension zero superembeddings
Superembeddings which have bosonic codimension zero are studied in three, four and six dimensions. The worldvolume multiplets of these branes are off-shell vector multiplets in these dimensions, and their self-interactions include a Born-Infeld term. It is shown how they can be written in terms of standard vector multiplets in flat superspace by working in the static gauge. The action formula is used to determine both Green-Schwarz-type actions and superfield actions.
119108460
Simple loop integrals and amplitudes in N=4 SYM
We use momentum twistors to evaluate planar loop integrals. Infrared divergences are regulated by the recently proposed AdS-inspired mass regulator. We show that two-loop amplitudes in N = 4 super Yang-Mills can be expanded in terms of basis integrals having twistor numerators. We argue that these integrals are considerably simpler compared to the ones conventionally used. Our case in point is the two-loop six-point MHV amplitude. We present analytical results for the remainder function in a kinematical limit, and find agreement with a recent Wilson loop computation. We also provide two-loop evidence that the logarithm of MHV amplitudes can be written in terms of simple twistor space integrals.
17229527
The one-loop six-dimensional hexagon integral with three massive corners
We compute the six-dimensional hexagon integral with three non-adjacent external masses analytically. After a simple rescaling, it is given by a function of six dual conformally invariant cross-ratios. The result can be expressed as a sum of 24 terms involving only one basic function, which is a simple linear combination of logarithms, dilogarithms, and trilogarithms of uniform degree three transcendentality. Our method uses differential equations to determine the symbol of the function, and an algorithm to reconstruct the latter from its symbol. It is known that six-dimensional hexagon integrals are closely related to scattering amplitudes in N = 4 super Yang-Mills theory, and we therefore expect our result to be helpful for understanding the structure of scattering amplitudes in this theory, in particular at two loops.
18684844
Reply to hep-th/0606265
In hep-th/0411017 the Polchinski-Strominger effective string model was examined and it was shown there that the spectrum of excitations is universal up to and including terms of order $R^{-3}$ in the long distance expansion. Subsequently the same result was claimed in hep-th/0606265 where certain criticisms of the earlier work were made. In this note we demonstrate that the criticisms are wrong and the methods and results of the earlier work are perfectly correct. In particular we address the issue of higher order corrections to the action and show that they were correctly given already in hep-th/0411017.
119226686
The Yangian origin of the Grassmannian integral
In this paper we analyse formulas which reproduce leading singularities of scattering amplitudes in N = 4 super Yang-Mills theory through a Grassmannian integral. Recently their Yangian invariance has been proved directly by using the explicit expression of the Yangian level-one generators. The specific cyclic structure of the form integrated over the Grassmannian enters in a crucial way in demonstrating the symmetry. Here we show that the Yangian symmetry fixes this structure uniquely.
18119323
Generalised integrable Hubbard models
We construct the XX and Hubbard-like models based on unitary superalgebras gl(N |M) generalizing Shastry's and Maassarani's approach. We introduce the R-matrix of the gl(N |M) XX-type model; the one of the Hubbard-like model is defined by "coupling" two independent XX models. In both cases, we show that the R-matrices satisfy the Yang-Baxter equation. We derive the corresponding local Hamiltonian in the transfer matrix formalism and we determine its symmetries. A perturbative calculation "`a la Klein and Seitz" is performed. Some explicit examples are worked out. We give a description of the two-particle scattering.