1,790 research outputs found

### 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
$\hat{x}$ 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 $\rho_{1,2}$, conjectured by
Rastelli, Sen and Zwiebach to be left and right projectors on the sliver, are
indeed so.Comment: 27 pages; footnote adde

### 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

### Non-Douglas-Kazakov phase transition of two-dimensional generalized Yang-Mills theories

In two-dimensional Yang-Mills and generalized Yang-Mills theories for large
gauge groups, there is a dominant representation determining the thermodynamic
limit of the system. This representation is characterized by a density the
value of which should everywhere be between zero and one. This density itself
is determined through a saddle-point analysis. For some values of the parameter
space, this density exceeds one in some places. So one should modify it to
obtain an acceptable density. This leads to the well-known Douglas-Kazakov
phase transition. In generalized Yang-Mills theories, there are also regions in
the parameter space where somewhere this density becomes negative. Here too,
one should modify the density so that it remains nonnegative. This leads to
another phase transition, different from the Douglas-Kazakov one. Here the
general structure of this phase transition is studied, and it is shown that the
order of this transition is typically three. Using carefully-chosen parameters,
however, it is possible to construct models with phase-transition orders not
equal to three. A class of these non-typical models are also studied.Comment: 11 pages, accepted for publication in Eur. Phys. J.

### Siegel Gauge in Vacuum String Field Theory

We study the star algebra of ghost sector in vacuum string field theory
(VSFT). We show that the star product of two states in the Siegel gauge is BRST
exact if we take the BRST charge to be the one found in hep-th/0108150, and the
BRST exact states are nil factors in the star algebra. By introducing a new
star product defined on the states in the Siegel gauge, the equation of motion
of VSFT is characterized as the projection condition with respect to this new
product. We also comment on the comma form of string vertex in the ghost
sector.Comment: 13 pages, lanlmac; v3: comment adde

### Ghost Kinetic Operator of Vacuum String Field Theory

Using the data of eigenvalues and eigenvectors of Neumann matrices in the
3-string vertex, we prove analytically that the ghost kinetic operator of
vacuum string field theory obtained by Hata and Kawano is equal to the ghost
operator inserted at the open string midpoint. We also comment on the values of
determinants appearing in the norm of sliver state.Comment: 19 pages, 1 figure, lanlmac; v2: typos correcte

### The Spectrum of the Neumann Matrix with Zero Modes

We calculate the spectrum of the matrix M' of Neumann coefficients of the
Witten vertex, expressed in the oscillator basis including the zero-mode a_0.
We find that in addition to the known continuous spectrum inside [-1/3,0) of
the matrix M without the zero-modes, there is also an additional eigenvalue
inside (0,1). For every eigenvalue, there is a pair of eigenvectors, a
twist-even and a twist-odd. We give analytically these eigenvectors as well as
the generating function for their components. Also, we have found an
interesting critical parameter b_0 = 8 ln 2 on which the forms of the
eigenvectors depend.Comment: 25+1 pages, 3 Figures; typos corrected and some comments 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

### Dualities, Twists, and Gauge Theories with Non-Constant Non-Commutativity

We study the world volume theory of D3-branes wrapping the Melvin universe
supported by background NSNS B-field. In the appropriate decoupling limit, the
open string dynamics is that of non-commutative guage field theory with
non-constant non-commutativity. We identify this model as a simple Melvin twist
of flat D3 branes. Along similar lines, one recognizes the model of Hashimoto
and Sethi as being the Melvin null twist, and the model of Dolan and Nappi as
being the null Melvin twist, of the flat D3-brane. This construction therefore
offers a unified perspective on most of the known explicit constructions of
non-commutative gauge theories as a decoupled theory of D-branes in a B-field
background. We also describe the world volume theory on the D3-brane in Melvin
universe which is decaying via the nucleation of monopole anti-monopole pair.Comment: 18 pages, 1 figure, References added, typo correcte

### Open String Star as a Continuous Moyal Product

We establish that the open string star product in the zero momentum sector
can be described as a continuous tensor product of mutually commuting two
dimensional Moyal star products. Let the continuous variable $\kappa \in
[~0,\infty)$ parametrize the eigenvalues of the Neumann matrices; then the
noncommutativity parameter is given by $\theta(\kappa) =2\tanh(\pi\kappa/4)$.
For each $\kappa$, the Moyal coordinates are a linear combination of even
position modes, and the Fourier transform of a linear combination of odd
position modes. The commuting coordinate at $\kappa=0$ is identified as the
momentum carried by half the string. We discuss the relation to Bars' work, and
attempt to write the string field action as a noncommutative field theory.Comment: 30 pages, LaTeX. One reference adde

### The Origins of Phase Transitions in Small Systems

The identification and classification of phases in small systems, e.g.
nuclei, social and financial networks, clusters, and biological systems, where
the traditional definitions of phase transitions are not applicable, is
important to obtain a deeper understanding of the phenomena observed in such
systems. Within a simple statistical model we investigate the validity and
applicability of different classification schemes for phase transtions in small
systems. We show that the whole complex temperature plane contains necessary
information in order to give a distinct classification.Comment: 3 pages, 4 figures, revtex 4 beta 5, for further information see
http://www.smallsystems.d

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