22 research outputs found
Two-dimensional Born-Infeld gauge theory: spectrum, string picture and large-N phase transition
We analyze U(N) Born-Infeld gauge theory in two spacetime dimensions. We
derive the exact energy spectrum on the circle and show that it reduces to N
relativistic fermions on a dual space. This contrasts to the Yang-Mills case
that reduces to nonrelativistic fermions. The theory admits a string theory
interpretation, analogous to the one for ordinary Yang-Mills, but with higher
order string interactions. We also demonstrate that the partition function on
the sphere exhibits a large-N phase transition in the area and calculate the
critical area. The limit in which the dimensionless coupling of the theory goes
to zero corresponds to massless fermions, admits a perturbatively exact free
string interpretation and exhibits no phase transition.Comment: 19 page
Difficulties in Inducing a Gauge Theory at Large N
It is argued that the recently proposed Kazakov-Migdal model of induced gauge
theory, at large , involves only the zero area Wilson loops that are
effectively trees in the gauge action induced by the scalars. This retains only
a constant part of the gauge action excluding plaquettes or anything like them
and the gauge variables drop out.Comment: 6 pages, Latex, AZPH-TH/93-01, COLO-HEP/30
Character Expansion Methods for Matrix Models of Dually Weighted Graphs
We consider generalized one-matrix models in which external fields allow
control over the coordination numbers on both the original and dual lattices.
We rederive in a simple fashion a character expansion formula for these models
originally due to Itzykson and Di Francesco, and then demonstrate how to take
the large N limit of this expansion. The relationship to the usual matrix model
resolvent is elucidated. Our methods give as a by-product an extremely simple
derivation of the Migdal integral equation describing the large limit of
the Itzykson-Zuber formula. We illustrate and check our methods by analyzing a
number of models solvable by traditional means. We then proceed to solve a new
model: a sum over planar graphs possessing even coordination numbers on both
the original and the dual lattice. We conclude by formulating equations for the
case of arbitrary sets of even, self-dual coupling constants. This opens the
way for studying the deep problem of phase transitions from random to flat
lattices.Comment: 22 pages, harvmac.tex, pictex.tex. All diagrams written directly into
the text in Pictex commands. (Two minor math typos corrected.
Acknowledgements added.
Some New/Old Approaches to QCD
This is a talk delivered at the Meeting on Integrable Quantum Field Theories,
Villa Olmo and at STRINGS 1992, Rome, September 1992. I discuss some recent
attempts to revive two old ideas regarding an analytic approach to QCD-the
development of a string representation of the theory and the large N limit of
QCD.Comment: 20 page
Matrix Models, Complex Geometry and Integrable Systems. I
We consider the simplest gauge theories given by one- and two- matrix
integrals and concentrate on their stringy and geometric properties. We remind
general integrable structure behind the matrix integrals and turn to the
geometric properties of planar matrix models, demonstrating that they are
universally described in terms of integrable systems directly related to the
theory of complex curves. We study the main ingredients of this geometric
picture, suggesting that it can be generalized beyond one complex dimension,
and formulate them in terms of the quasiclassical integrable systems, solved by
construction of tau-functions or prepotentials. The complex curves and
tau-functions of one- and two- matrix models are discussed in detail.Comment: 52 pages, 19 figures, based on several lecture courses and the talks
at "Complex geometry and string theory" and the Polivanov memorial seminar;
misprints corrected, references adde
High Temperature Limit of the Confining Phase
The deconfining transition in non-Abelian gauge theory is known to occur by a
condensation of Wilson lines. By expanding around an appropriate Wilson line
background, it is possible at large to analytically continue the confining
phase to arbitrarily high temperatures, reaching a weak coupling confinement
regime. This is used to study the high temperature partition function of an
electric flux tube. It is found that the partition function corresponds
to that of a string theory with a number of world-sheet fields that diverges at
short distance.Comment: 13 page
Challenges of Matrix Models
Brief review of concepts and unsolved problems in the theory of matrix
models.Comment: Contribution to Proceedings of Cargese 200
Wilson Loops and Minimal Surfaces
The AdS/CFT correspondence suggests that the Wilson loop of the large N gauge
theory with N=4 supersymmetry in 4 dimensions is described by a minimal surface
in AdS_5 x S^5. We examine various aspects of this proposal, comparing gauge
theory expectations with computations of minimal surfaces. There is a
distinguished class of loops, which we call BPS loops, whose expectation values
are free from ultra-violet divergence. We formulate the loop equation for such
loops. To the extent that we have checked, the minimal surface in AdS_5 x S^5
gives a solution of the equation. We also discuss the zig-zag symmetry of the
loop operator. In the N=4 gauge theory, we expect the zig-zag symmetry to hold
when the loop does not couple the scalar fields in the supermultiplet. We will
show how this is realized for the minimal surface.Comment: 51 pages, 7 figure
Comments on operators with large spin
We consider high spin operators. We give a general argument for the
logarithmic scaling of their anomalous dimensions which is based on the
symmetries of the problem. By an analytic continuation we can also see the
origin of the double logarithmic divergence in the Sudakov factor. We show that
the cusp anomalous dimension is the energy density for a flux configuration of
the gauge theory on . We then focus on operators in super Yang Mills which carry large spin and SO(6) charge and show that in
a particular limit their properties are described in terms of a bosonic O(6)
sigma model. This can be used to make certain all loop computations in the
string theory.Comment: 33 pages, 1 figure,v2:reference to more recent work added, minor
correction
Pressure effect on the in-plane magnetic penetration depth in YBa_2Cu_4O_8
We report a study of the pressure effect (PE) on the in-plane magnetic field
penetration depth lambda_{ab} in YBa_2Cu_4O_8 by means of Meissner fraction
measurements. A pronounced PE on lambda_{ab}^{-2}(0) was observed with a
maximum relative shift of \Delta\lambda^{-2}_{ab}/\lambda^{-2}_{ab}= 44(3)% at
a pressure of 10.2 kbar. It arises from the pressure dependence of the
effective in-plane charge carrier mass and pressure induced charge carrier
transfer from the CuO chains to the superconducting CuO_2 planes. The present
results imply that the charge carriers in YBa_2Cu_4O_8 are coupled to the
lattice.Comment: 4pages 3 figure