Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.Comment: 10 pages, 2 figure

A Consistent Meson-Field-Theoretical Description of PP-Bremsstrahlung

A parameter-free and relativistic extension of the RuhrPot meson-baryon model is used to define the dominant isoscalar meson-exchange currents. We compute pp-bremsstrahlung observables below the $\pi-$production threshold using a relativistic hadronic current density that includes impulse, wave function re-orthonormalization, meson-recoil, $\bar{{\rm N}}$N creation and annihilation, $\rho\pi\gamma$ + $\omega\pi\gamma$ + $\rho\eta\gamma$ + $\omega\eta\gamma$ vector-meson decay and N$\Delta\gamma(\pi,\rho)$ exchange currents. We obtain a good description of the available data. The N$\Delta\gamma(\pi)$ current is shown to dominate the large two-body contributions and closed-form expressions for various non-relativistic approximations are analyzed. An experimental sensitivity to the admixture of pseudo-scalar and pseudo-vector admixture of the NN$\pi$ interaction is demonstrated. We examine the Lorentz invariance of the NN$\rightleftharpoons$NN $t$-matrices and show a dominantly pseudo-vector NN$\pi$ coupling renders impulse approximation calculations without boost operators to be essentially exact. Conversely, a similar analysis of the $\Delta{\rm N}\rightleftharpoons$NN transitions shows that boost operators and the two-body $N\Delta\gamma$ wave function re-orthonormalization meson-recoil currents are required in NN, $\Delta$N and $\Delta\Delta$ coupled channel $t$-matrix applications. The need for additional data is stressed.Comment: 34 pages of uuencoded REVTeX using multicol.sty with 21 figures inlined using epsf.sty. This revision adds section IV.

Four-point correlators of BPS operators in N=4 SYM at order g^4

We study the large N degeneracy in the structure of the four-point amplitudes of 1/2-BPS operators of arbitrary weight k in perturbative N=4 SYM theory. At one loop (order g^2) this degeneracy manifests itself in a smaller number of independent conformal invariant functions describing the amplitude, compared to AdS_5 supergravity results. To study this phenomenon at the two-loop level (order g^4) we consider a particular N=2 hypermultiplet projection of the general N=4 amplitude. Using the formalism of N=2 harmonic superspace we then explicitly compute this four-point correlator at two loops and identify the corresponding conformal invariant functions. In the cases of 1/2-BPS operators of weight k=3 and k=4 the one-loop large N degeneracy is lifted by the two-loop corrections. However, for weight k > 4 the degeneracy is still there at the two-loop level. This behavior suggests that for a given weight k the degeneracy will be removed if perturbative corrections of sufficiently high order are taken into account. These results are in accord with the AdS/CFT duality conjecture.Comment: 45 pages, latex, 14 figure

Unstable particle's wave-function renormalization prescription

We strictly define two set Wave-function Renormalization Constants (WRC) under the LSZ reduction formula for unstable particles at the first time. Then by introducing antiparticle's WRC and the CPT conservation law we obtain a new wave-function renormalization condition which can be used to totally determine the two set WRC. We calculate two physical processes to manifest the consistence of the present wave-function renormalization prescription with the gauge theory in standard model. We also prove that the conventional wave-function renormalization prescription which discards the imaginary part of unstable particle's WRC leads to physical amplitude gauge dependent.Comment: 10 pages, 3 figure

Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials

We study initial boundary value problems for the convective Cahn-Hilliard equation \Dt u +\px^4u +u\px u+\px^2(|u|^pu)=0. It is well-known that without the convective term, the solutions of this equation may blow up in finite time for any $p>0$. In contrast to that, we show that the presence of the convective term u\px u in the Cahn-Hilliard equation prevents blow up at least for $0<p<\frac49$. We also show that the blowing up solutions still exist if $p$ is large enough ($p\ge2$). The related equations like Kolmogorov-Sivashinsky-Spiegel equation, sixth order convective Cahn-Hilliard equation, are also considered

Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators

We consider folded spinning strings in AdS_5xS^5 (with one spin component S in AdS_5 and J in S^5) corresponding to the Tr(D^S Z^J) operators in the sl(2) sector of the N=4 SYM theory in the special scaling limit in which both the string mass M ~ \sqrt \lambda \ln S and J are sent to infinity with their ratio fixed. Expanding in the parameter \el= J/M we compute the 2-loop string sigma model correction to the string energy and show that it agrees with the expression proposed by Alday and Maldacena in arxiv:0708.0672. We suggest that a resummation of the logarithmic \el^2 \ln^n \el terms is necessary in order to establish an interpolation to the weakly coupled gauge theory results. In the process, we set up a general framework for the calculation of higher loop corrections to the energy of multi-spin string configurations. In particular, we find that in addition to the direct 2-loop term in the string energy there is a contribution from lower loop order due to a finite ``renormalization'' of the relation between the parameters of the classical solution and the fixed spins, i.e. the charges of the SO(2,4) x SO(6) symmetry.Comment: 31 pages, Latex. v2:minor corrections; few comments and references added v3: typos correcte

EGF receptor trafficking: consequences for signaling and cancer

The ligand-stimulated epidermal growth factor receptor (EGFR) has been extensively studied in the analysis of molecular mechanisms regulating endocytic traffic and the role of that traffic in signal transduction. Although such studies have largely focused on mitogenic signaling and dysregulated traffic in tumorigenesis, there is growing interest in the potential role of EGFR traffic in cell survival and the consequent response to cancer therapy. Here we review recent advances in our understanding of molecular mechanisms regulating ligand-stimulated EGFR activation, internalization, and post-endocytic sorting. The role of EGFR overexpression/mutation and new modulators of EGFR traffic in cancer and the response to cancer therapeutics are also discussed. Finally, we speculate on the relationship between EGFR traffic and cell survival

New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators

We consider correlation functions of the stress-tensor or a conserved current in AdS_{d+1}/CFT_d computed using the Hilbert or the Yang-Mills action in the bulk. We introduce new recursion relations to compute these correlators at tree level. These relations have an advantage over the BCFW-like relations described in arXiv:1102.4724 and arXiv:1011.0780 because they can be used in all dimensions including d=3. We also introduce a new method of extracting flat-space S-matrix elements from AdS/CFT correlators in momentum space. We show that the (d+1)-dimensional flat-space amplitude of gravitons or gluons can be obtained as the coefficient of a particular singularity of the d-dimensional correlator of the stress-tensor or a conserved current; this technique is valid even at loop-level in the bulk. Finally, we show that our recursion relations automatically generate correlators that are consistent with this observation: they have the expected singularity and the flat-space gluon or graviton amplitude appears as its coefficient.Comment: 22+6 pages (v2) typos fixe