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

Challenges of D=6 N=(1,1) SYM Theory

Maximally supersymmetric Yang-Mills theories have several remarkable properties, among which are the cancellation of UV divergences, factorization of higher loop corrections and possible integrability. Much attention has been attracted to the N=4 D=4 SYM theory. The N=(1,1) D=6 SYM theory possesses similar properties but is nonrenomalizable and serves as a toy model for supergravity. We consider the on-shell four point scattering amplitude and analyze its perturbative expansion within the spin-helicity and superspace formalism. The integrands of the resulting diagrams coincide with those of the N=4 D=4 SYM and obey the dual conformal invariance. Contrary to 4 dimensions, no IR divergences on mass shell appear. We calculate analytically the leading logarithmic asymptotics in all loops. Their summation leads to a Regge trajectory which is calculated exactly. The leading powers of s are calculated up to six loops. Their summation is performed numerically and leads to a smooth function of s. The leading UV divergences are calculated up to 5 loops. The result suggests the geometrical progression which ends up in a finite expression. This leads us to a radical point of view on nonrenormalizable theories.Comment: 11 pages, 2 figures, Late

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

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

UV Divergences, RG Equations and High Energy Behaviour of the Amplitudes in the Wess-Zumino Model with Quartic Interaction

We analyse the UV divergences for the scattering amplitude in the Wess-Zumino SUSY model with the quartic superpotential. Within the superfield formalism, we calculate the corresponding Feynman diagrams and evaluate their leading divergences up to 4 loop order of PT. Then we construct recurrence relations that connect the leading UV divergences in subsequent orders of perturbation theory. These recurrence relations allow us to calculate the leading divergences in a pure algebraic way starting from the one loop contribution. We check that the obtained relations correctly reproduce the lower order diagrams evaluated explicitly. At last, we convert the recurrence relations into the RG equations that have integro-differential form. Solving these equations for a particular sequence of diagrams, we find out the high energy behaviour of the amplitude. We then argue that the full amplitude has a similar behaviour with the key feature of the existence of a pole in the s-channel corresponding to a state with a mass ~1/g, where g is the original dimensionfull coupling of the theory. We find out the this state is actually a ghost one similar to the Landau pole in scalar theory.Comment: 26 pages, 5 figure