14556916
Universal Subleading Spectrum of Effective String Theory
We analyse the spectrum of the D-dimensional Poincare invariant effective string model of Polchinski and Strominger. It is shown that the leading terms beyond the Casimir term in the long distance expansion of the spectrum have a universal character which follows from the constraint of Poincare invariance.
9351073
Superconformal invariants or how to relate four-point AdS amplitudes
Abstract Using the form of N = 2 superconformal invariants we derive the explicit relation between the bottom and top components of the correlator of four stress-tensor multiplets in N = 4 super-Yang–Mills. The result is given in terms of an eighth order differential operator acting on the function of two variables which characterises these correlators. It allows us to show a non-trivial consistency relation between the known results for the corresponding supergravity amplitudes on AdS 5 .
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.
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.
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.
119252785
New differential equations for on-shell loop integrals
We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several infinite series of integrals satisfying such iterative differential equations. The differential operators we use are best written using momentum twistor space. The use of the latter was advocated in recent papers discussing loop integrals in $ \mathcal{N} = 4 $ super Yang-Mills. One of our motivations is to provide a tool for deriving analytical results for scattering amplitudes in this theory. We show that the integrals needed for planar MHV amplitudes up to two loops can be thought of as deriving from a single master topology. The master integral satisfies our differential equations, and so do most of the reduced integrals. A consequence of the differential equations is that the integrals we discuss are not arbitrarily complicated transcendental functions. For two specific two-loop integrals we give the full analytic solution. The simplicity of the integrals appearing in the scattering amplitudes in planar $ \mathcal{N} = 4 $ super Yang-Mills is strongly suggestive of a relation to the conjectured underlying integrability of the theory. We expect these differential equations to be relevant for all planar MHV and non-MHV amplitudes. We also discuss possible extensions of our method to more general classes of integrals.
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.