929 research outputs found
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 He and role of He impurities
We analyze the complex phenomenology of the Non-Classical Rotational Inertia
(NCRI) observed at low temperature in solid He within the context of a two
dimensional Berezinski-Kosterlitz-Thouless transition in a premelted He
film at the grain boundaries. We show that both the temperature and 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 He
impurities and we provide a simple power-law relation between the NCRIF and the
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
(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 -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
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
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
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