Solving Open String Field Theory with Special Projectors

Schnabl recently found an analytic expression for the string field tachyon condensate using a gauge condition adapted to the conformal frame of the sliver projector. We propose that this construction is more general. The sliver is an example of a special projector, a projector such that the Virasoro operator \L_0 and its BPZ adjoint \L*_0 obey the algebra [\L_0, \L*_0] = s (\L_0 + \L*_0), with s a positive real constant. All special projectors provide abelian subalgebras of string fields, closed under both the *-product and the action of \L_0. This structure guarantees exact solvability of a ghost number zero string field equation. We recast this infinite recursive set of equations as an ordinary differential equation that is easily solved. The classification of special projectors is reduced to a version of the Riemann-Hilbert problem, with piecewise constant data on the boundary of a disk.Comment: 64 pages, 6 figure

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

Finite size Berezinski-Kosterlitz-Thouless transition at grain boundaries in solid 4^4He and role of 3^3He impurities

We analyze the complex phenomenology of the Non-Classical Rotational Inertia (NCRI) observed at low temperature in solid $^4$He within the context of a two dimensional Berezinski-Kosterlitz-Thouless transition in a premelted $^4$He film at the grain boundaries. We show that both the temperature and $^3$He doping dependence of the NCRI fraction (NCRIF) can be ascribed to finite size effects induced by the finite grain size. We give an estimate of the average size of the grains which we argue to be limited by the isotopic $^3$He impurities and we provide a simple power-law relation between the NCRIF and the $^3$He concentration.Comment: Final version, as appearing on prin

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

Comments on Schnabl's analytic solution for tachyon condensation in Witten's open string field theory

Schnabl recently constructed an analytic solution for tachyon condensation in Witten's open string field theory. The solution consists of two pieces. Only the first piece is involved in proving that the solution satisfies the equation of motion when contracted with any state in the Fock space. On the other hand, both pieces contribute in evaluating the kinetic term to reproduce the value predicted by Sen's conjecture. We therefore need to understand why the second piece is necessary. We evaluate the cubic term of the string field theory action for Schnabl's solution and use it to show that the second piece is necessary for the equation of motion contracted with the solution itself to be satisfied. We also present the solution in various forms including a pure-gauge configuration and provide simpler proofs that it satisfies the equation of motion.Comment: 33 pages, 4 figures, LaTeX2e; v2: minor changes, version published in JHE

On surface states and star-subalgebras in string field theory

We elaborate on the relations between surface states and squeezed states. First, we investigate two different criteria for determining whether a matter sector squeezed state is also a surface state and show that the two criteria are equivalent. Then, we derive similar criteria for the ghost sector. Next, we refine the criterion for determining whether a surface state is in H_{\kappa^2}, the subalgebra of squeezed states obeying [S,K_1^2]=0. This enables us to find all the surface states of the H_{\kappa^2} subalgebra, and show that it consists only of wedge states and (hybrid) butterflies. Finally, we investigate generalizations of this criterion and find an infinite family of surface states subalgebras, whose surfaces are described using a "generalized Schwarz-Christoffel" mapping.Comment: 38 pages, 6 figures, JHEP style; typos corrected, ref. adde

Chan-Paton factors and Higgsing from Vacuum String Field Theory

We give a description of open strings stretched between N parallel D-branes in VSFT. We show how higgsing is generated as the branes are displaced: the shift in the mass formula for on-shell states stretched between different branes is due to a twist anomaly, a contribution localized at the midpoint.Comment: 20 pages, JHEP clas

(1+1)-dimensional separation of variables

In this paper we explore general conditions which guarantee that the geodesic flow on a 2-dimensional manifold with indefinite signature is locally separable. This is equivalent to showing that a 2-dimensional natural Hamiltonian system on the hyperbolic plane possesses a second integral of motion which is a quadratic polynomial in the momenta associated with a 2nd-rank Killing tensor. We examine the possibility that the integral is preserved by the Hamiltonian flow on a given energy hypersurface only (weak integrability) and derive the additional requirement necessary to have conservation at arbitrary values of the Hamiltonian (strong integrability). Using null coordinates, we show that the leading-order coefficients of the invariant are arbitrary functions of one variable in the case of weak integrability. These functions are quadratic polynomials in the coordinates in the case of strong integrability. We show that for $(1+1)$-dimensional systems there are three possible types of conformal Killing tensors, and therefore, three distinct separability structures in contrast to the single standard Hamilton-Jacobi type separation in the positive definite case. One of the new separability structures is the complex/harmonic type which is characterized by complex separation variables. The other new type is the linear/null separation which occurs when the conformal Killing tensor has a null eigenvector.Comment: To appear on Journal of Mathematical Physic

Mechanical lattice instability and thermodynamical properties in classical solids

In this paper we revisit the onset of the instability of the solid state in classical systems within self-consistent phonon theory (SCPT). Spanning the whole phase diagram versus volume and versus pressure, we identify two different kinds of mechanism: one mainly relevant at constant volume, associated with the vanishing of the SCPT solution; and one related to the disappearing at a spinodal temperature of the solid phase as a metastable energy minimum. We show how the first mechanism occurs at extremely high temperatures and it is not reflected in any singular behavior of the thermodynamical properties. In contrast, the second one appears at physical temperatures which correlate well with the melting temperature and it is signalized by the divergence of the thermal compressibility as well as of the the lattice expansion coefficient.Comment: (submitted to PRB

Proof of vanishing cohomology at the tachyon vacuum

We prove Sen's third conjecture that there are no on-shell perturbative excitations of the tachyon vacuum in open bosonic string field theory. The proof relies on the existence of a special state A, which, when acted on by the BRST operator at the tachyon vacuum, gives the identity. While this state was found numerically in Feynman-Siegel gauge, here we give a simple analytic expression.Comment: 19 pages, 4 figures; v2: references adde