411 research outputs found
Poisson Structures of Calogero-Moser and Ruijsenaars-Schneider Models
We examine the Hamiltonian structures of some Calogero-Moser and
Ruijsenaars-Schneider N-body integrable models. We propose explicit
formulations of the bihamiltonian structures for the discrete models, and
field-theoretical realizations of these structures. We discuss the relevance of
these realizations as collective-field theory for the discrete models.Comment: 15 pages, no figures; v2 references added, typos correcte
Large N WZW Field Theory Of N=2 Strings
We explore the quantum properties of self-dual gravity formulated as a large
two-dimensional WZW sigma model. Using a non-trivial classical background,
we show that a space-time is generated. The theory contains an infinite
series of higher point vertices. At tree level we show that, in spite of the
presence of higher than cubic vertices, the on-shell 4 and higher point
functions vanish, indicating that this model is related with the field theory
of closed N=2 strings. We examine the one-loop on-shell 3-point amplitude and
show that it is ultra-violet finite.Comment: This is the final version. By editorial mistake at Phys.Lett.B an
older version was published in prin
Large-N Collective Fields and Holography
We propose that the euclidean bilocal collective field theory of critical
large-N vector models provides a complete definition of the proposed dual
theory of higher spin fields in anti de-Sitter spaces. We show how this bilocal
field can be decomposed into an infinite number of even spin fields in one more
dimension. The collective field has a nontrivial classical solution which leads
to a O(N) thermodynamic entropy characteristic of the lower dimensional theory,
as required by general considerations of holography. A subtle cancellation of
the entropy coming from the bulk fields in one higher dimension with O(1)
contributions from the classical solution ensures that the subleading terms in
thermodynamic quantities are of the expected form. While the spin components of
the collective field transform properly under dilatational, translational and
rotational isometries of , special conformal transformations mix fields of
different spins indicating a need for a nonlocal map between the two sets of
fields. We discuss the nature of the propagating degrees of freedom through a
hamiltonian form of collective field theory and argue that nonsinglet states
which are present in an euclidean version are related to nontrivial
backgrounds.Comment: 27 pages, harvmac. v2: references adde
Equivalence of Two Dimensional QCD and the Matrix Model
We consider two dimensional QCD with the spatial dimension compactified to a
circle. We show that the states in the theory consist of interacting strings
that wind around the circle and derive the Hamiltonian for this theory in the
large limit, complete with interactions. Mapping the winding states into
momentum states, we express this Hamiltonian in terms of a continuous field.
For a gauge group with a background source of Wilson loops, we recover
the collective field Hamiltonian found by Das and Jevicki for the matrix
model, except the spatial coordinate is on a circle. We then proceed to show
that two dimensional QCD with a gauge group can be reduced to a one-
dimensional unitary matrix model and is hence equivalent to a theory of
free nonrelativistic fermions on a circle. A similar result is true for the
group , but the fermions must be modded out by the center of mass
coordinate.Comment: 15 pages, CERN-TH 6843/93, UVA-HET-93-0
Generalized Conformal Symmetry in D-Brane Matrix Models
We study in detail the extension of the generalized conformal symmetry
proposed previously for D-particles to the case of supersymmetric Yang-Mills
matrix models of Dp-branes for arbitrary p. It is demonstrated that such a
symmetry indeed exists both in the Yang-Mills theory and in the corresponding
supergravity backgrounds produced by Dp-branes. On the Yang-Mills side, we
derive the field-dependent special conformal transformations for the collective
coordinates of Dp-branes in the one-loop approximation, and show that they
coincide with the transformations on the supergravity side. These
transformations are powerful in restricting the forms of the effective actions
of probe D-branes in the fixed backgrounds of source D-branes. Furthermore, our
formalism enables us to extend the concept of (generalized) conformal symmetry
to arbitrary configurations of D-branes, which can still be used to restrict
the dynamics of D-branes. For such general configurations, however, it cannot
be endowed a simple classical space-time interpretation at least in the static
gauge adopted in the present formulation of D-branes.Comment: 26 pages, no figure
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.
The Collective Field Theory of a Singular Supersymmetric Matrix Model
The supersymmetric collective field theory with the potential is studied, motivated by the matrix model proposed by Jevicki
and Yoneya to describe two dimensional string theory in a black hole
background. Consistency with supersymmetry enforces a two band solution. A
supersymmetric classical configuration is found, and interpreted in terms of
the density of zeros of certain Laguerre polynomials. The spectrum of the model
is then studied and is seen to correspond to a massless scalar and a majorana
fermion. The space eigenfunctions are constructed and expressed in terms of
Chebyshev polynomials. Higher order interactions are also discussed.Comment: Revtex 8 pages, Submitted to Phys. Rev. D. References and preprint
numbers have been adde
Lumps and P-branes in Open String Field Theory
We describe numerical methods for constructing lump solutions in open string
field theory. According to Sen, these lumps represent lower dimensional
Dp-Branes and numerical evaluation of their energy can be compared with the
expected value for the tension. We take particular care of all higher
derivative terms inherent in Witten's version of open string field theory. The
importance of these terms for off shell phenomena is argued in the text.
Detailed numerical calculations done for the case of general brane show
very good agreement with Sen's conjectured value. This gives credence to the
conjecture itself and establishes further the usefulness of Witten's version of
SFT .Comment: 11 pages, 1 figure, 1 table; v2: small typos correcte
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