45 research outputs found
The First Thirty Years of Large-N Gauge Theory
I review some developments in the large-N gauge theory since 1974. The main
attention is payed to: multicolor QCD, matrix models, loop equations, reduced
models, 2D quantum gravity, free random variables, noncommutative theories,
AdS/CFT correspondence.Comment: 13.1pp., Latex, 2 figs; v2: 2 refs added. Talk at Large Nc QCD 200
Scaling behavior of regularized bosonic strings
We implement a proper-time UV regularisation of the Nambu-Goto string,
introducing an independent metric tensor and the corresponding Lagrange
multiplier, and treating them in the mean-field approximation justified for
long strings and/or when the dimensions of space-time is large. We compute the
regularised determinant of the 2d Laplacian for the closed string winding
around a compact dimension, obtaining in this way the effective action, whose
minimisation determines the energy of the string ground state in the mean-field
approximation. We discuss the existence of two scaling limits when the cutoff
is taken to infinity. One scaling limit reproduces the results obtained by the
hypercubic regularisation of the Nambu-Goto string as well as by the use of the
dynamical triangulation regularisation of the Polyakov string. The other
scaling limit reproduces the results obtained by canonical quantisation of the
Nambu-Goto string.Comment: 35 page
Semiclassical Regge trajectories of noncritical string and large-N QCD
By properly treating the path integral over the boundary value of the
Liouville field (associated with reparametrizations of the boundary contour) in
open string theory, we derive consistent off-shell scattering amplitudes in
d=26 dimensions. In d<26 we consider a recently proposed boundary ansatz which
reproduces a semiclassical correction to the classical string (known as the
Luscher term) and obtain in the semiclassical approximation a linear Regge
trajectory with the intercept (d-2)/24. We associate it with the
quark-antiquark Regge trajectory in large-N QCD and explain why it dominates
over perturbative QCD when t > -few GeV^2.Comment: 20pp., 2 figures; v2: minor changes, to appear in JHE
String theory as a Lilliputian world
Lattice regularizations of the bosonic string allow no tachyons. This has
often been viewed as the reason why these theories have never managed to make
any contact to standard continuum string theories when the dimension of
spacetime is larger than two. We study the continuum string theory in large
spacetime dimensions where simple mean field theory is reliable. By keeping
carefully the cutoff we show that precisely the existence of a tachyon makes it
possible to take a scaling limit which reproduces the lattice-string results.
We compare this scaling limit with another scaling limit which reproduces
standard continuum-string results. If the people working with lattice
regularizations of string theories are akin to Gulliver they will view the
standard string-world as a Lilliputian world no larger than a few lattice
spacings.Comment: 11 pages, 1 figur
What Quantum Strings can tell us about Quantum Gravity
I describe the recent progress in resolving two problems of nonperturbative
bosonic string inherited from 1980's. Both the lattice and KPZ-DDK no-go
theorems can be bypassed thanks to specific features of the theory with
diffeomorphism invariance.Comment: 12 pages, 2 figures. Talk at the International Conference on Quantum
Field Theory, High-Energy Physics and Cosmology, Dubna July 18--21, 2022; v2:
reduced to 8 page
Exact solution of higher-derivative conformal theory and minimal models
I investigate the two-dimensional four-derivative conformal theory that
emerges from the Nambu-Goto string after the path-integration over all fields
but the metric tensor. Using the method of singular products which accounts for
tremendous cancellations in perturbation theory, I show the (intelligent)
one-loop approximation to give an exact solution. It is conveniently described
through the minimal models where the central charge in the Kac spectrum
depends on the parameters of the four-derivative action. The relation is
nonlinear so the domain of physical parameters is mapped onto thus
bypassing the KPZ barrier of the Liouville action.Comment: 11 pages. arXiv admin note: text overlap with arXiv:2307.06295; v2:
polishe