International Journal of Modern Physics A

We review the use of simple currents in constructing modular invariant partition functions and the problem of resolving their fixed points. We present some new results, in particular regarding fixed point resolution. Additional empirical evidence is provided in support of our conjecture that fixed points are always related to some conformal field theory. We complete the identification of the fixed point conformal field theories for all simply laced and most non-simply laced Kac-Moody algebras, for which the fixed point CFT’s turn out to be Kac-Moody algebras themselves. For the remaining non-simply laced ones we obtain spectra that appear to correspond to new non-unitary conformal field theories. The fusion rules of the simplest unidentified example are computed.

We discuss a continuous extension of the Sugawara construction in two-dimensional conformal field theory proposed earlier. The extension which is built on the SL(2)₄ Kač-Moody algebra is shown to describe the standard c=1 series corresponding to a free bosonic field defined on a circle. The radius of the circle as a function of the continuous parameter existing in the model is found. We also present a continuous Sugawara series referring to SL(3)₄. The latter is closely related to the case of SL(2)₄.

The peculiar velocity of quasars is among the most sought data of observational cosmology. This paper discusses a method of determining an upper limit to the peculiar velocity of quasars by means of a statistical analysis on quasar pairs. A preliminary conclusion is that the peculiar velocity in the direction along the line joining the two quasars in a pair may not exceed, on average, one thousand km/sec.

We will solve some constrained systems by regularizing them, compare them with the known results, and apply this regularization method to the superparticle system.

Some Calabi-Yau manifolds leading to three generations of chiral fermions in the heterotic E₈×E₈ some superstring theory are endowed with a freely acting discrete symmetry Z₃, which when mapped homomorphically into the E₆ subgroup of the first E₈ causes it to break to (SU(3))³ or SU(6)×U(1). The same discrete group can be mapped homomorphically into the second E₈ and can result in its breaking. We obtain some of the maximal subgroups of E₈ and present the breaking directions in weight space for some breakings. Flux-tubes arise in these theories and their significance in cosmology is briefly discussed.

The determinant formula for N-soliton solutions of the Bullough-Dodd-Jiber-Shabat equation on a finite-gap background is obtained. Nonsingularity conditions for them and their asymptotics are investigated.

A quantum Hamiltonian, defined on the half-line, will typically not lead to unitary time evolution unless the domain of the Hamiltonian is carefully specified. Different choices of the domain result in different Green’s functions. For a wide class of non-relativistic Hamiltonians we show how to define the functional integral on the half-line in a way which matches the various Green’s functions. To do so we analytically continue, in time, functional integrals constructed with real measures that give weight to paths on the half-line according to how much time they spend near the origin.

The free energy of the heterotic string is calculated in the covariant lattice formalism. It is shown that requiring modular invariance and correct statistics leads to a unique answer, which agrees with the known result obtained by path integral methods.

We discuss N=2, U(1) supermodular transformation on supertorus. For a special case when the U(1) parameter turns off, we obtain the supermodular transformation and we derive the Green function on supertorus. Further, we show that general supermodular transformation cannot be obtained from the Crane and Rabin approach. However, for the case of the U(1) parameter= pure soul, we obtain the general N=2 supermodular transformation.