Energy from the gauge invariant observables

For a classical solution |Psi> in Witten's cubic string field theory, the gauge invariant observable is conjectured to be equal to the difference of the one-point functions of the closed string state corresponding to V, between the trivial vacuum and the one described by |Psi>. For a static solution |Psi>, if V is taken to be the graviton vertex operator with vanishing momentum, the gauge invariant observable is expected to be proportional to the energy of |Psi>. We prove this relation assuming that |Psi> satisfies equation of motion and some regularity conditions. We discuss how this relation can be applied to various solutions obtained recently.Comment: 27 pages; v5: minor revision in section 2, results unchange

The off-shell Veneziano amplitude in Schnabl gauge

We give a careful definition of the open string propagator in Schnabl gauge and present its worldsheet interpretation. The propagator requires two Schwinger parameters and contains the BRST operator. It builds surfaces by gluing strips of variable width to the left and to the right of off-shell states with contracted or expanded local frames. We evaluate explicitly the four-point amplitude of off-shell tachyons. The computation involves a subtle boundary term, crucial to enforce the correct exchange symmetries. Interestingly, the familiar on-shell physics emerges even though string diagrams produce Riemann surfaces more than once. Off-shell, the amplitudes do not factorize over intermediate on-shell states.Comment: 48 pages, 10 figures. v2:acknowledgments adde

Once more on extra quark-lepton generations and precision measurements

Precision measurements of $Z$-boson parameters and $W$-boson and $t$-quark masses put strong constraints on non $SU(2)\times U(1)$ singlet New Physics. We demonstrate that one extra generation passes electroweak constraints even when all new particle masses are well above their direct mass bounds.Comment: Dedicated to L.B. Okun's 80th birthda

Recent Developments in Precision Electroweak Physics

Developments in precision electroweak physics in the two years since the symposium are briefly summarized.Comment: Update on recent developments, prepared for the publication of the Proceedings of Alberto Sirlin Symposium, New York University, October 2000. 10 pages, 1 figur

The Experimental Status of the Standard Electroweak Model at the End of the LEP-SLC Era

A method is proposed to calculate the confidence level for agreement of data with the Standard Model (SM) by combining information from direct and indirect Higgs Boson searches. Good agreement with the SM is found for $m_H \simeq 120$ GeV using the observables most sensitive to $m_H$: $A_l$ and $m_W$. In particular, quantum corrections, as predicted by the SM, are observed with a statistical significance of forty-four standard deviations. However, apparent deviations from the SM of 3.7$\sigma$ and 2.8$\sigma$ are found for the Z$\nu \bar{\nu}$ and right-handed Zb$\bar{{\rm b}}$ couplings respectively. The maximum confidence level for agreement with the SM of the entire data set considered is $\simeq 0.006$ for $m_H \simeq 180$ GeV. The reason why confidence levels about an order of magnitude higher than this have been claimed for global fits to similar data sets is explained.Comment: 47 pages, 8 figures, 24 tables. An in-depth study of statistical issues related to the comparison of precision EW data to the S

Fluctuations around the Tachyon Vacuum in Open String Field Theory

We consider quadratic fluctuations around the tachyon vacuum numerically in open string field theory. We work on a space ${\cal H}_N^{{\rm vac}}$ spanned by basis string states used in the Schnabl's vacuum solution. We show that the truncated form of the Schnabl's vacuum solution on ${\cal H}_N^{{\rm vac}}$ is well-behaved in numerical work. The orthogonal basis for the new BRST operator $\tilde Q$ on ${\cal H}_N^{{\rm vac}}$ and the quadratic forms of potentials for independent fields around the vacuum are obtained. Our numerical results support that the Schnabl's vacuum solution represents the minimum energy solution for arbitrary fluctuations also in open string field theory.Comment: 16 pages, 2 figures, some comments and one table added, version to appear in JHE