RD-flatness and RD-injectivity

It is proved that every commutative ring whose RD-injective modules are $\Sigma$-RD-injective is the product of a pure semi-simple ring and a finite ring. A complete characterization of commutative rings for which each artinian (respectively simple) module is RD-injective, is given. These results can be obtained by using the properties of RD-flat modules and RD-coflat modules which are respectively the RD-relativization of flat modules and fp-injective modules. It is also shown that a commutative ring is perfect if and only if each RD-flat module is RD-projective.Comment: A new section is added to the version published in Communications in Algebra where a complete proof of Theorem 3.1 is give

Symmetry breaking boundary conditions and WZW orbifolds

Symmetry breaking boundary conditions for WZW theories are discussed. We derive explicit formulae for the reflection coefficients in the presence of boundary conditions that preserve only an orbifold subalgebra with respect to an involutive automorphism of the chiral algebra. The characters and modular transformations of the corresponding orbifold theories are computed. Both inner and outer automorphisms are treated.Comment: 39 pages, LaTeX2

Schnabl's L_0 Operator in the Continuous Basis

Following Schnabl's analytic solution to string field theory, we calculate the operators ${\cal L}_0,{\cal L}_0^\dagger$ for a scalar field in the continuous $\kappa$ basis. We find an explicit and simple expression for them that further simplifies for their sum, which is block diagonal in this basis. We generalize this result for the bosonized ghost sector, verify their commutation relation and relate our expressions to wedge state representations.Comment: 1+16 pages. JHEP style. Typos correcte

On the validity of the solution of string field theory

We analyze the realm of validity of the recently found tachyon solution of cubic string field theory. We find that the equation of motion holds in a non trivial way when this solution is contracted with itself. This calculation is needed to conclude the proof of Sen's first conjecture. We also find that the equation of motion holds when the tachyon or gauge solutions are contracted among themselves.Comment: JHEP style, 9+1 pages. Typos correcte

Criteria for Continuous-Variable Quantum Teleportation

We derive an experimentally testable criterion for the teleportation of quantum states of continuous variables. This criterion is especially relevant to the recent experiment of Furusawa et al. [Science 282, 706-709 (1998)] where an input-output fidelity of $0.58 \pm 0.02$ was achieved for optical coherent states. Our derivation demonstrates that fidelities greater than 1/2 could not have been achieved through the use of a classical channel alone; quantum entanglement was a crucial ingredient in the experiment.Comment: 12 pages, to appear in Journal of Modern Optic

Ghost story. III. Back to ghost number zero

After having defined a 3-strings midpoint-inserted vertex for the bc system, we analyze the relation between gh=0 states (wedge states) and gh=3 midpoint duals. We find explicit and regular relations connecting the two objects. In the case of wedge states this allows us to write down a spectral decomposition for the gh=0 Neumann matrices, despite the fact that they are not commuting with the matrix representation of K1. We thus trace back the origin of this noncommutativity to be a consequence of the imaginary poles of the wedge eigenvalues in the complex k-plane. With explicit reconstruction formulas at hand for both gh=0 and gh=3, we can finally show how the midpoint vertex avoids this intrinsic noncommutativity at gh=0, making everything as simple as the zero momentum matter sector.Comment: 40 pages. v2: typos and minor corrections, presentation improved in sect. 4.3, plots added in app. A.1, two refs added. To appear in JHE

Ghost story. II. The midpoint ghost vertex

We construct the ghost number 9 three strings vertex for OSFT in the natural normal ordering. We find two versions, one with a ghost insertion at z=i and a twist-conjugate one with insertion at z=-i. For this reason we call them midpoint vertices. We show that the relevant Neumann matrices commute among themselves and with the matrix $G$ representing the operator K1. We analyze the spectrum of the latter and find that beside a continuous spectrum there is a (so far ignored) discrete one. We are able to write spectral formulas for all the Neumann matrices involved and clarify the important role of the integration contour over the continuous spectrum. We then pass to examine the (ghost) wedge states. We compute the discrete and continuous eigenvalues of the corresponding Neumann matrices and show that they satisfy the appropriate recursion relations. Using these results we show that the formulas for our vertices correctly define the star product in that, starting from the data of two ghost number 0 wedge states, they allow us to reconstruct a ghost number 3 state which is the expected wedge state with the ghost insertion at the midpoint, according to the star recursion relation.Comment: 60 pages. v2: typos and minor improvements, ref added. To appear in JHE

Analysis and interpretation of new low-energy Pi-Pi scattering data

The recently published E865 data on charged K_e4 decays and Pi-Pi phases are reanalyzed to extract values of the two S-wave scattering lengths, of the subthreshold parameters alpha and beta, of the low-energy constants l3-bar and l4-bar as well as of the main two-flavour order parameters: and F_pi in the limit m_u = m_d = 0 taken at the physical value of the strange quark mass. Our analysis is exclusively based on direct experimental information on Pi-Pi phases below 800 MeV and on the new solutions of the Roy equations by Ananthanarayan et al. The result is compared with the theoretical prediction relating 2 a_0^0 - 5 a_0^2 and the scalar radius of the pion, which was obtained in two-loop Chiral Perturbation Theory. A discrepancy at the 1-sigma level is found and commented upon.Comment: Published version, to appear in Eur. Phys. J.