180 research outputs found
Scattering amplitudes of regularized bosonic strings
We compute scattering amplitudes of the regularized bosonic Nambu-Goto string
in the mean-field approximation, disregarding fluctuations of the Lagrange
multiplier and an independent metric about their mean values. We use the
previously introduced Lilliputian scaling limit to recover the Regge behavior
of the amplitudes with the usual linear Regge trajectory in space-time
dimensions d>2. We demonstrate a stability of this minimum of the effective
action under fluctuations for d<26.Comment: 11 pages, v2: typos corrected, to appear in PR
Stability of the nonperturbative bosonic string vacuum
Quantization of the bosonic string around the classical, perturbative vacuum
is not consistent for spacetime dimensions 2<d<26. Recently we have showed that
at large d there is another so-called mean field vacuum. Here we extend this
mean field calculation to finite d and show that the corresponding mean field
vacuum is stable under quadratic fluctuations for 2<d<26. We point out the
analogy with the two-dimensional O(N)-symmetric sigma-model, where the
1/N-vacuum is very close to the real vacuum state even for finite N, in
contrast to the perturbative vacuum.Comment: v2: 6pp, section about vacuum instability/stability added, to appear
in PL
The use of Pauli-Villars' regularization in string theory
The proper-time regularization of bosonic string reproduces the results of
canonical quantization in a special scaling limit where the length in target
space has to be renormalized. We repeat the analysis for the Pauli-Villars
regularization and demonstrate the universality of the results. In the
mean-field approximation we compute the susceptibility anomalous dimension and
show it equals 1/2. We discuss the relation with the previously known results
on lattice strings.Comment: 1+22 p
Strings, Matrix Models, and Meanders
I briefly review the present status of bosonic strings and discretized random
surfaces in D>1 which seem to be in a polymer rather than stringy phase. As an
explicit example of what happens, I consider the Kazakov-Migdal model with a
logarithmic potential which is exactly solvable for any D (at large D for an
arbitrary potential). I discuss also the meander problem and report some new
results on its representation via matrix models and the relation to the
Kazakov-Migdal model. A supersymmetric matrix model is especially useful for
describing the principal meanders.Comment: 12 pages, 4 Latex figures, uses espcrc2.sty Talk at the 29th
Ahrenshoop Symp., Buckow, Germany, Aug.29 - Sep.2, 199
Implementation of the Duality between Wilson loops and Scattering Amplitudes in QCD
We generalize modern ideas about the duality between Wilson loops and
scattering amplitudes in =4 SYM to large-N (or quenched) QCD. We show
that the area-law behavior of asymptotically large Wilson loops is dual to the
Regge-Veneziano behavior of scattering amplitudes at high energies and fixed
momentum transfer, when quark mass is small and/or the number of particles is
large. We elaborate on this duality for string theory in a flat space,
identifying the asymptotes of the disk amplitude and the Wilson loop of large-N
QCD.Comment: REVTex, 6 pages, 1 figure; v3: refs added; v4pp. to appear in PR
Generalized multicritical one-matrix models
We show that there exists a simple generalization of Kazakov's multicritical
one-matrix model, which interpolates between the various multicritical points
of the model. The associated multicritical potential takes the form of a power
series with a heavy tail, leading to a cut of the potential and its derivative
at the real axis, and reduces to a polynomial at Kazakov's multicritical
points. From the combinatorial point of view the generalized model allows
polygons of arbitrary large degrees (or vertices of arbitrary large degree,
when considering the dual graphs), and it is the weight assigned to these large
order polygons which brings about the interpolation between the multicritical
points in the one-matrix model.Comment: 25 page
Supersymmetric matrix models and branched polymers
We solve a supersymmetric matrix model with a general potential. While matrix
models usually describe surfaces, supersymmetry enforces a cancellation of
bosonic and fermionic loops and only diagrams corresponding to so-called
branched polymers survive. The eigenvalue distribution of the random matrices
near the critical point is of a new kind.Comment: xx pages, Latex, no macros neede
Perturbed generalized multicritical one-matrix models
We study perturbations around the generalized Kazakov multicritical
one-matrix model. The multicritical matrix model has a potential where the
coefficients of only fall off as a power . This implies that
the potential and its derivatives have a cut along the real axis, leading to
technical problems when one performs perturbations away from the generalized
Kazakov model. Nevertheless it is possible to relate the perturbed partition
function to the tau-function of a KdV hierarchy and solve the model by a genus
expansion in the double scaling limit.Comment: 2 figure
Light-Cone Wilson Loops and the String/Gauge Correspondence
We investigate a \Pi-shape Wilson loop in N=4 super Yang--Mills theory, which
lies partially at the light-cone, and consider an associated open superstring
in AdS_5 x S^5. We discuss how this Wilson loop determines the anomalous
dimensions of conformal operators with large Lorentz spin and present an
explicit calculation in perturbation theory to order \lambda. We find the
minimal surface in the supergravity approximation, that reproduces the Gubser,
Klebanov and Polyakov prediction for the anomalous dimensions at large
\lambda=g_YM^2 N, and discuss its quantum-mechanical interpretation.Comment: 17pp., Latex, 4 figures; v.2: factors of 2 put righ
Simplicial vs. Continuum String Theory and Loop Equations
We derive loop equations in a scalar matrix field theory. We discuss their
solutions in terms of simplicial string theory -- the theory describing
embeddings of two--dimensional simplicial complexes into the space--time of the
matrix field theory. This relation between the loop equations and the
simplicial string theory gives further arguments that favor one of the
statements of the paper hep-th/0407018. The statement is that there is an
equivalence between the partition function of the simplicial string theory and
the functional integral in a continuum string theory -- the theory describing
embeddings of smooth two--dimensional world--sheets into the space--time of the
matrix field theory in question.Comment: 6 page
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