Direct solution of the hard pomeron problem for arbitrary conformal weight

A new method is applied to solve the Baxter equation for the one dimensional system of noncompact spins. Dynamics of such an ensemble is equivalent to that of a set of reggeized gluons exchanged in the high energy limit of QCD amplitudes. The technique offers more insight into the old calculation of the intercept of hard Pomeron, and provides new results in the odderon channel.Comment: Contribution to the ICHEP96 Conference, July 1996, Warsaw, Poland. LaTeX, 4 pages, 3 epsf figures, includes modified stwol.sty file. Some references were revise

Solution of the Odderon Problem

The intercept of the odderon trajectory is derived, by finding the spectrum of the second integral of motion of the three reggeon system in high energy QCD. When combined with earlier solution of the appropriate Baxter equation, this leads to the determination of the low lying states of that system. In particular, the energy of the lowest state gives the intercept of the odderon alpha_O(0)=1-0.2472 alpha_s N_c/pi.Comment: 11 pages, 2 Postscript figure

Summing free unitary random matrices

I use quaternion free probability calculus - an extension of free probability to non-Hermitian matrices (which is introduced in a succinct but self-contained way) - to derive in the large-size limit the mean densities of the eigenvalues and singular values of sums of independent unitary random matrices, weighted by complex numbers. In the case of CUE summands, I write them in terms of two "master equations," which I then solve and numerically test in four specific cases. I conjecture a finite-size extension of these results, exploiting the complementary error function. I prove a central limit theorem, and its first sub-leading correction, for independent identically-distributed zero-drift unitary random matrices.Comment: 17 pages, 15 figure

Non-lattice simulation for supersymmetric gauge theories in one dimension

Lattice simulation of supersymmetric gauge theories is not straightforward. In some cases the lack of manifest supersymmetry just necessitates cumbersome fine-tuning, but in the worse cases the chiral and/or Majorana nature of fermions makes it difficult to even formulate an appropriate lattice theory. We propose to circumvent all these problems inherent in the lattice approach by adopting a non-lattice approach in the case of one-dimensional supersymmetric gauge theories, which are important in the string/M theory context.Comment: REVTeX4, 4 pages, 3 figure