Conformal Invariance = Finiteness and Beta Deformed N=4 SYM Theory

We claim that if by a choice of the couplings the theory can be made conformally invariant (vanishing of the beta functions) it is automatically finite and vice versa. This is demonstrated by explicit example in supersymmetric gauge theory. The formalism is then applied to the beta deformed ${\cal N}=4$ SYM theory and it is shown that the requirement of conformal invariance = finiteness can be achieved for any complex parameter of deformations.Comment: 15 pages, Latex, 1 figure axodraw styl

Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions

The main aim of this paper is to study the scattering amplitudes in gauge field theories with maximal supersymmetry in dimensions D=6,8 and 10. We perform a systematic study of the leading ultraviolet divergences using the spinor helicity and on-shell momentum superspace framework. In D=6 the first divergences start at 3 loops and we calculate them up to 5 loops, in D=8,10 the first divergences start at 1 loop and we calculate them up to 4 loops. The leading divergences in a given order are the polynomials of Mandelstam variables. To be on the safe side, we check our analytical calculations by numerical ones applying the alpha-representation and the dedicated routines. Then we derive an analog of the RG equations for the leading pole that allows us to get the recursive relations and construct the generating procedure to obtain the polynomials at any order of (perturbation theory) PT. At last, we make an attempt to sum the PT series and derive the differential equation for the infinite sum. This equation possesses a fixed point which might be stable or unstable depending on the kinematics. Some consequences of these fixed points are discussed.Comment: 43 pages, 13 figures, pdf LaTex, v2 minor changes and references adde

Infrared Finite Observables in N=8 Supergravity

Using the algorithm of constructing the IR finite observables suggested and discussed in details in our previous publications, we consider construction of such observables in N=8 SUGRA in NLO of PT. In general, contrary to the amplitudes defined in the presence of some IR regulator, such observables do not reveal any simple structure

Readout and Control of a Power-recycled Interferometric Gravitational-wave Antenna

Interferometric gravitational wave antennas are based on Michelson interferometers whose sensitivity to small differential length changes has been enhanced by adding multiple coupled optical resonators. The use of optical cavities is essential for reaching the required sensitivity, but sets challenges for the control system which must maintain the cavities near resonance. The goal for the strain sensitivity of the Laser Interferometer Gravitational-wave Observatory (LIGO) is 10^-21 rms, integrated over a 100 Hz bandwidth centered at 150 Hz. We present the major design features of the LIGO length and frequency sensing and control system which will hold the differential length to within 5 10^-14 m of the operating point. We also highlight the restrictions imposed by couplings of noise into the gravitational wave readout signal and the required immunity against them.Comment: Presentation at ICALEPCS 2001, San Jose, November 2001, (WECT003), 3 page

Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory

In this paper we give all the details of the calculation that we presented in our previous paper ArXiv:0908.0387 where the infrared structure of the MHV gluon amplitudes in the planar limit for ${\cal N}=4$ super Yang-Mills theory was considered in the next-to-leading order of perturbation theory. Explicit cancellation of the infrared divergencies in properly defined inclusive cross-sections is demonstrated first in a toy model example of "conformal QED" and then in the real ${\cal N}=4$ SYM theory. We give the full-length details both for the calculation of the real emission and for the diagrams with splitting in initial and final states. The finite parts for some inclusive differential cross-sections are presented in an analytical form. In general, contrary to the virtual corrections, they do not reveal any simple structure. An example of the finite part containing just the log functions is presented. The dependence of inclusive cross-section on the external scale related to the definition of asymptotic states is discussed.Comment: 49 pages, LATEX, 6 eps figures; Minor changes, Refs adde