New exact results on density matrix for XXX spin chain

Using the fermionic basis we obtain the expectation values of all \slt-invariant and $C$-invariant local operators on 10 sites for the anisotropic six-vertex model on a cylinder with generic Matsubara data. This is equivalent to the generalised Gibbs ensemble for the XXX spin chain. In the case when the \slt and $C$ symmetries are not broken this computation is equivalent to finding the entire density matrix up to 10 sites. As application, we compute the entanglement entropy without and with temperature, and compare the results with CFT predictions.Comment: 20 pages, 4 figure

Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators

We present an algorithm for the analytical evaluation of dimensionally regularized massless on-shell double box Feynman diagrams with arbitrary polynomials in numerators and general integer powers of propagators. Recurrence relations following from integration by parts are solved explicitly and any given double box diagram is expressed as a linear combination of two master double boxes and a family of simpler diagrams. The first master double box corresponds to all powers of the propagators equal to one and no numerators, and the second master double box differs from the first one by the second power of the middle propagator. By use of differential relations, the second master double box is expressed through the first one up to a similar linear combination of simpler double boxes so that the analytical evaluation of the first master double box provides explicit analytical results, in terms of polylogarithms \Li{a}{-t/s}, up to $a=4$, and generalized polylogarithms $S_{a,b}(-t/s)$, with $a=1,2$ and $b=2$, dependent on the Mandelstam variables $s$ and $t$, for an arbitrary diagram under consideration.Comment: LaTeX, 16 pages; misprints in ff. (8), (24), (30) corrected; some explanations adde

Analytic Results for Massless Three-Loop Form Factors

We evaluate, exactly in d, the master integrals contributing to massless three-loop QCD form factors. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin--Barnes representation, and the PSLQ algorithm. Using our results for the master integrals we obtain analytical expressions for two missing constants in the ep-expansion of the two most complicated master integrals and present the form factors in a completely analytic form.Comment: minor revisions, to appear in JHE

Analytical Result for Dimensionally Regularized Massless Master Double Box with One Leg off Shell

The dimensionally regularized massless double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e. with non-zero q^2=p_1^2, and three legs on shell, p_i^2=0, i=2,3,4, is analytically calculated for general values of q^2 and the Mandelstam variables s and t. An explicit result is expressed through (generalized) polylogarithms, up to the fourth order, dependent on rational combinations of q^2,s and t, and a one-dimensional integral with a simple integrand consisting of logarithms and dilogarithms.Comment: 10 pages, LaTeX with axodraw.sty, one reference is correcte

The Leading Power Regge Asymptotic Behaviour of Dimensionally Regularized Massless On-Shell Planar Triple Box

The leading power asymptotic behaviour of the dimensionally regularized massless on-shell planar triple box diagram in the Regge limit t/s -> 0 is analytically evaluated.Comment: 9 pages, LaTeX with axodraw.st

Analytical Result for Dimensionally Regularized Massless On-Shell Planar Triple Box

The dimensionally regularized massless on-shell planar triple box Feynman diagram with powers of propagators equal to one is analytically evaluated for general values of the Mandelstam variables s and t in a Laurent expansion in the parameter \ep=(4-d)/2 of dimensional regularization up to a finite part. An explicit result is expressed in terms of harmonic polylogarithms, with parameters 0 and 1, up to the sixth order. The evaluation is based on the method of Feynman parameters and multiple Mellin-Barnes representation. The same technique can be quite similarly applied to planar triple boxes with any numerators and integer powers of the propagators.Comment: 8 pages, LaTeX with axodraw.st

On the Resolution of Singularities of Multiple Mellin-Barnes Integrals

One of the two existing strategies of resolving singularities of multifold Mellin-Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, is formulated in a modified form. The corresponding algorithm is implemented as a Mathematica code MBresolve.mComment: LaTeX, 10 page

The Four-Loop Dressing Phase of N=4 SYM

We compute the dilatation generator in the su(2) sector of planar N=4 super Yang-Mills theory at four-loops. We use the known world-sheet scattering matrix to constrain the structure of the generator. The remaining few coefficients can be computed directly from Feynman diagrams. This allows us to confirm previous conjectures for the leading contribution to the dressing phase which is proportional to zeta(3).Comment: 19 pages, v2: referenced adde

Evaluating multiloop Feynman integrals by Mellin-Barnes representation

The status of analytical evaluation of double and triple box diagrams is characterized. The method of Mellin-Barnes representation as a tool to evaluate master integrals in these problems is advocated. New MB representations for massive on-shell double boxes with general powers of propagators are presented.Comment: 5 pages, Talk given at the 7th DESY workshop on Elementary Particle Theory, "Loops and Legs in Quantum Field Theory", April 25-30, 2004, Zinnowitz, Germany, to appear in the proceeding