Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM

In this paper we consider tree-level gauge invariant off-shell amplitudes (Wilson line form factors) in $\mathcal{N}=4$ SYM with arbitrary number of off-shell gluons or equivalently Wilson line operator insertions. We make a conjecture for the Grassmannian integral representation for such objects and verify our conjecture on several examples. It is remarkable that in our formulation one can consider situation when on-shell particles are not present at all, i.e. we have Grassmannian integral representation for purely off-shell object. In addition we show that off-shell amplitude with arbitrary number of off-shell gluons could be also obtained using quantum inverse scattering method for auxiliary $\mathfrak{gl}(4|4)$ super spin chain.Comment: 38 pages, 9 figures; v4: typos corrected, comment in section 3.2 adde

Ambitwistor strings and reggeon amplitudes in N=4 SYM

We consider the description of reggeon amplitudes (Wilson lines form factors) in N=4 SYM within the framework of four dimensional ambitwistor string theory. The latter is used to derive scattering equations representation for reggeon amplitudes with multiple reggeized gluons present. It is shown, that corresponding tree-level string correlation function correctly reproduces previously obtained Grassmannian integral representation of reggeon amplitudes in N=4 SYM.Comment: 18 page

Wilson lines, Grassmannians and gauge invariant off-shell amplitudes in N = 4 N=4 \mathcal{N}=4 SYM

In this paper we consider tree-level gauge invariant off-shell amplitudes (Wilson line form factors) in $\mathcal{N}=4$ SYM. For the off-shell amplitudes with one leg off-shell we present a conjecture for their Grassmannian integral representation in spinor helicity, twistor and momentum twistor parameterizations. The presented conjecture is successfully checked against BCFW results for MHV$_n$, NMHV$_4$ and NMHV$_5$ off-shell amplitudes. We have also verified that our Grassmannian integral representation correctly reproduces soft (on-shell) limit for the off-shell gluon momentum. It is shown that the (deformed) off-shell amplitude expressions could be also obtained using quantum inverse scattering method for auxiliary $gl(4|4)$ super spin chain

Diagnosis and treatment of hereditary angioedema with normal C1 inhibitor

Until recently it was assumed that hereditary angioedema is a disease that results exclusively from a genetic deficiency of the C1 inhibitor. In 2000, families with hereditary angioedema, normal C1 inhibitor activity and protein in plasma were described. Since then numerous patients and families with that condition have been reported. Most of the patients by far were women. In many of the affected women, oral contraceptives, hormone replacement therapy containing estrogens, and pregnancies triggered the clinical symptoms. Recently, in some families mutations in the coagulation factor XII (Hageman factor) gene were detected in the affected persons