104 research outputs found
Perturbation Theory in Two Dimensional Open String Field Theory
In this paper we develop the covariant string field theory approach to open
2d strings. Upon constructing the vertices, we apply the formalism to calculate
the lowest order contributions to the 4- and 5- point tachyon--tachyon tree
amplitudes. Our results are shown to match the `bulk' amplitude calculations of
Bershadsky and Kutasov. In the present approach the pole structure of the
amplitudes becomes manifest and their origin as coming from the higher string
modes transparent.Comment: 26 page
Exact Solution of the One-Dimensional Non-Abelian Coulomb Gas at Large N
The problem of computing the thermodynamic properties of a one-dimensional
gas of particles which transform in the adjoint representation of the gauge
group and interact through non-Abelian electric fields is formulated and solved
in the large limit. The explicit solution exhibits a first order
confinement-deconfinement phase transition with computable properties and
describes two dimensional adjoint QCD in the limit where matter field masses
are large.Comment: 8 pages, late
Classical Solutions in Two-Dimensional String Theory and Gravitational Collapse
A general solution to the 1-loop beta functions equations including
tachyonic back reaction on the metric is presented. Dynamical black hole
(classical) solutions representing gravitational collapse of tachyons are
constructed. A discussion on the correspondence with the matrix-model approach
is given.Comment: 7 pages, UTTG-31-9
Systematic corrections for bosonic and fermionic vector models without auxiliary fields
In this paper, colorless bilocal fields are employed to study the large
limit of both fermionic and bosonic vector models. The Jacobian associated with
the change of variables from the original fields to the bilocals is computed
exactly, thereby providing an exact effective action. This effective action is
shown to reproduce the familiar perturbative expansion for the two and four
point functions. In particular, in the case of fermionic vector models, the
effective action correctly accounts for the Fermi statistics. The theory is
also studied non-perturbatively. The stationary points of the effective action
are shown to provide the usual large gap equations. The homogeneous
equation associated with the quadratic (in the bilocals) action is simply the
two particle Bethe Salpeter equation. Finally, the leading correction in
is shown to be in agreement with the exact matrix of the model.Comment: 24 pages, uses REVTEX macros. Replaced with final version to appear
in Phys. Rev.
Algebraic Structures and Eigenstates for Integrable Collective Field Theories
Conditions for the construction of polynomial eigen--operators for the
Hamiltonian of collective string field theories are explored. Such
eigen--operators arise for only one monomial potential in the
collective field theory. They form a --algebra isomorphic to the
algebra of vertex operators in 2d gravity. Polynomial potentials of orders only
strictly larger or smaller than 2 have no non--zero--energy polynomial
eigen--operators. This analysis leads us to consider a particular potential
. A Lie algebra of polynomial eigen--operators is then
constructed for this potential. It is a symmetric 2--index Lie algebra, also
represented as a sub--algebra of Comment: 27 page
On the spectrum of QCD(1+1) with large numbers of flavours N_F and colours N_C near N_F/N_C = 0
QCD(1+1) in the limit of a large number of flavours N_F and a large number of
colours N_C is examined in the small N_F/N_C regime. Using perturbation theory
in N_F/N_C, stringent results for the leading behaviour of the spectrum
departing from N_F/N_C = 0 are obtained. These results provide benchmarks in
the light of which previous truncated treatments of QCD(1+1) at large N_F and
N_C are critically reconsidered.Comment: 6 revtex page
One-dimensional classical adjoint SU(2) Coulomb Gas
The equation of state of a one-dimensional classical nonrelativistic Coulomb
gas of particles in the adjoint representation of SU(2) is given. The problem
is solved both with and without sources in the fundamental representation at
either end of the system. The gas exhibits confining properties at low
densities and temperatures and deconfinement in the limit of high densities and
temperatures. However, there is no phase transition to a regime where the
string tension vanishes identically; true deconfinement only happens for
infinite densities and temperatures. In the low density, low temperature limit,
a new type of collective behavior is observed.Comment: 6 pages, 1 postscript figur
Numerical Simulations of N=(1,1) SYM{1+1} with Large Supersymmetry Breaking
We consider the SYM theory that is obtained by dimensionally
reducing SYM theory in 2+1 dimensions to 1+1 dimensions and discuss soft
supersymmetry breaking. We discuss the numerical simulation of this theory
using SDLCQ when either the boson or the fermion has a large mass. We compare
our result to the pure adjoint fermion theory and pure adjoint boson DLCQ
calculations of Klebanov, Demeterfi, and Bhanot and of Kutasov. With a large
boson mass we find that it is necessary to add additional operators to the
theory to obtain sensible results. When a large fermion mass is added to the
theory we find that it is not necessary to add operators to obtain a sensible
theory. The theory of the adjoint boson is a theory that has stringy bound
states similar to the full SYM theory. We also discuss another theory of
adjoint bosons with a spectrum similar to that obtained by Klebanov, Demeterfi,
and Bhanot.Comment: 12 pages, 4 figure
A Note on Background (In)dependence
In general quantum systems there are two kinds of spacetime modes, those that
fluctuate and those that do not. Fluctuating modes have normalizable
wavefunctions. In the context of 2D gravity and ``non-critical'' string theory
these are called macroscopic states. The theory is independent of the initial
Euclidean background values of these modes. Non-fluctuating modes have
non-normalizable wavefunctions and correspond to microscopic states. The theory
depends on the background value of these non-fluctuating modes, at least to all
orders in perturbation theory. They are superselection parameters and should
not be minimized over. Such superselection parameters are well known in field
theory. Examples in string theory include the couplings (including the
cosmological constant) in the matrix models and the mass of the two-dimensional
Euclidean black hole. We use our analysis to argue for the finiteness of the
string perturbation expansion around these backgrounds.Comment: 16 page
-Dimensional Large QCD coupled to Adjoint Fermions
We consider 1+1-dimensional QCD coupled to Majorana fermions in the adjoint
representation of the gauge group . Pair creation of partons (fermion
quanta) is not suppressed in the large- limit, where the glueball-like bound
states become free. In this limit the spectrum is given by a linear \lc\ Schr\"
odinger equation, which we study numerically using the discretized \lcq. We
find a discrete spectrum of bound states, with the logarithm of the level
density growing approximately linearly with the mass. The wave function of a
typical excited state is a complicated mixture of components with different
parton numbers. A few low-lying states, however, are surprisingly close to
being eigenstates of the parton number, and their masses can be accurately
calculated by truncated diagonalizations.Comment: 22 pages + 9 figures (available by request from
[email protected]), uses phyzzx.tex + tables.tex PUPT-1413,
IASSNS-HEP-93/4
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