1,222 research outputs found
Star Algebra Spectroscopy
The spectrum of the infinite dimensional Neumann matrices M^{11}, M^{12} and
M^{21} in the oscillator construction of the three-string vertex determines key
properties of the star product and of wedge and sliver states. We study the
spectrum of eigenvalues and eigenvectors of these matrices using the derivation
K_1 = L_1 + L_{-1} of the star algebra, which defines a simple infinite matrix
commuting with the Neumann matrices. By an exact calculation of the spectrum of
K_1, and by consideration of an operator generating wedge states, we are able
to find analytic expressions for the eigenvalues and eigenvectors of the
Neumann matrices and for the spectral density. The spectrum of M^{11} is
continuous in the range [-1/3, 0) with degenerate twist even and twist odd
eigenvectors for every eigenvalue except for -1/3.Comment: LaTeX, 30 pages, 2 figure
Some exact results on the matter star-product in the half-string formalism
We show that the D25 sliver wavefunction, just as the D-instanton sliver,
factorizes when expressed in terms of half-string coordinates. We also
calculate analytically the star-product of two zero-momentum eigenstates of
using the vertex in the oscillator basis, thereby showing that the
star-product in the matter sector can indeed be seen as multiplication of
matrices acting on the space of functionals of half strings. We then use the
above results to establish that the matrices , conjectured by
Rastelli, Sen and Zwiebach to be left and right projectors on the sliver, are
indeed so.Comment: 27 pages; footnote adde
Tunable ohmic environment using Josephson junction chains
We propose a scheme to implement a tunable, wide frequency-band dissipative
environment using a double chain of Josephson junctions. The two parallel
chains consist of identical SQUIDs, with magnetic-flux tunable inductance,
coupled to each other at each node via a capacitance much larger than the
junction capacitance. Thanks to this capacitive coupling, the system sustains
electromagnetic modes with a wide frequency dispersion. The internal quality
factor of the modes is maintained as high as possible, and the damping is
introduced by a uniform coupling of the modes to a transmission line, itself
connected to an amplification and readout circuit. For sufficiently long
chains, containing several thousands of junctions, the resulting admittance is
a smooth function versus frequency in the microwave domain, and its effective
dissipation can be continuously monitored by recording the emitted radiation in
the transmission line. We show that by varying in-situ the SQUIDs' inductance,
the double chain can operate as tunable ohmic resistor in a frequency band
spanning up to one GHz, with a resistance that can be swept through values
comparable to the resistance quantum R_q = (h/4e^2) ~ 6.5 k{\Omega}. We argue
that the circuit complexity is within reach using current Josephson junction
technology.Comment: 11 pages, 9 figure
Coherent dynamics in long fluxonium qubits
We analyze the coherent dynamics of a fluxonium device (Manucharyan et al
2009 Science 326 113) formed by a superconducting ring of Josephson junctions
in which strong quantum phase fluctuations are localized exclusively on a
single weak element. In such a system, quantum phase tunnelling by
occurring at the weak element couples the states of the ring with supercurrents
circulating in opposite directions, while the rest of the ring provides an
intrinsic electromagnetic environment of the qubit. Taking into account the
capacitive coupling between nearest neighbors and the capacitance to the
ground, we show that the homogeneous part of the ring can sustain
electrodynamic modes which couple to the two levels of the flux qubit. In
particular, when the number of Josephson junctions is increased, several
low-energy modes can have frequencies lower than the qubit frequency. This
gives rise to a quasiperiodic dynamics, which manifests itself as a decay of
oscillations between the two counterpropagating current states at short times,
followed by oscillation-like revivals at later times. We analyze how the system
approaches such a dynamics as the ring's length is increased and discuss
possible experimental implications of this non-adiabatic regime.Comment: 20 pages, 8 figures (new, substantially revised version
B field and squeezed states in Vacuum String Field Theory
We show that squeezed state solutions for solitonic lumps in Vacuum String
Field Theory still exist in the presence of a constant B field. We show in
particular that, just as in the B=0 case, we can write down a compact explicit
form for such solutions.Comment: 15 pages, Latex, typos corrected, final versio
Wedge states in string field theory
The wedge states form an important subalgebra in the string field theory. We
review and further investigate their various properties. We find in particular
a novel expression for the wedge states, which allows to understand their star
products purely algebraically. The method allows also for treating the matter
and ghost sectors separately. It turns out, that wedge states with different
matter and ghost parts violate the associativity of the algebra. We introduce
and study also wedge states with insertions of local operators and show how
they are useful for obtaining exact results about convergence of level
truncation calculations. These results help to clarify the issue of anomalies
related to the identity and some exterior derivations in the string field
algebra.Comment: 40 pages, 9 figures, v3: section 3.3 rewritten, few other
corrections, set in JHEP styl
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
Ratio of Tensions from Vacuum String Field Theory
We show analytically that the ratio of the norm of sliver states agrees with
the ratio of D-brane tensions. We find that the correct ratio appears as a
twist anomaly.Comment: 13 pages, lanlmac; version to appear in JHE
Star Algebra Projectors
Surface states are open string field configurations which arise from Riemann
surfaces with a boundary and form a subalgebra of the star algebra. We find
that a general class of star algebra projectors arise from surface states where
the open string midpoint reaches the boundary of the surface. The projector
property of the state and the split nature of its wave-functional arise because
of a nontrivial feature of conformal maps of nearly degenerate surfaces.
Moreover, all such projectors are invariant under constant and opposite
translations of their half-strings. We show that the half-string states
associated to these projectors are themselves surface states. In addition to
the sliver, we identify other interesting projectors. These include a butterfly
state, which is the tensor product of half-string vacua, and a nothing state,
where the Riemann surface collapses.Comment: 65 pages, 23 figures, LaTe
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