1,124 research outputs found
Matrix strings from generalized Yang-Mills theory on arbitrary Riemann surfaces
We quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the
gauge where the field strength is diagonal. Twisted sectors originate, as in
Matrix string theory, from permutations of the eigenvalues around homotopically
non-trivial loops. These sectors, that must be discarded in the usual
quantization due to divergences occurring when two eigenvalues coincide, can be
consistently kept if one modifies the action by introducing a coupling of the
field strength to the space-time curvature. This leads to a generalized
Yang-Mills theory whose action reduces to the usual one in the limit of zero
curvature. After integrating over the non-diagonal components of the gauge
fields, the theory becomes a free string theory (sum over unbranched coverings)
with a U(1) gauge theory on the world-sheet. This is shown to be equivalent to
a lattice theory with a gauge group which is the semi-direct product of S_N and
U(1)^N. By using well known results on the statistics of coverings, the
partition function on arbitrary Riemann surfaces and the kernel functions on
surfaces with boundaries are calculated. Extensions to include branch points
and non-abelian groups on the world-sheet are briefly commented upon.Comment: Latex2e, 29 pages, 2 .eps figure
Large-N limit of the generalized 2D Yang-Mills theory on cylinder
Using the collective field theory approach of large-N generalized
two-dimensional Yang-Mills theory on cylinder, it is shown that the classical
equation of motion of collective field is a generalized Hopf equation. Then,
using the Itzykson-Zuber integral at the large-N limit, it is found that the
classical Young tableau density, which satisfies the saddle-point equation and
determines the large-N limit of free energy, is the inverse of the solution of
this generalized Hopf equation, at a certain point.Comment: 11 pages, add a paragraph after eq.(20) and add one reference,
accepted for publication in: Nucl. Phys. B (2000
Two dimensional QCD and abelian bosonization
A bosonized action, that reproduces the structure of the 't Hooft equation
for in the large- limit, up to regularization dependent terms, is
derived.Comment: paper revised, several signs and coefficients corrected. A comment on
regularization dependence and several references adde
Penrose Limit of N=1 Gauge Theories
We find a Penrose limit of AdS_5 x T^{1,1} which gives the pp-wave geometry
identical to the one that appears in the Penrose limit of AdS_5 x S^5. This
leads us to conjecture that there is a subsector of the corresponding N=1 gauge
theory which has enhanced N=4 supersymmetry. We identify operators in the N=1
gauge theory with stringy excitations in the pp-wave geometry and discuss how
the gauge theory operators fall into N=4 supersymmetry multiplets. We find
similar enhancement of symmetry in some other models, but there are also
examples in which there is no supersymmetry enhancement in the Penrose limit.Comment: 26 pages, harvmac; references added, typos corrected; the charge
assignment clarified; an error in section 4 correcte
Generalized two-dimensional Yang-Mills theory is a matrix string theory
We consider two-dimensional Yang-Mills theories on arbitrary Riemann
surfaces. We introduce a generalized Yang-Mills action, which coincides with
the ordinary one on flat surfaces but differs from it in its coupling to
two-dimensional gravity. The quantization of this theory in the unitary gauge
can be consistently performed taking into account all the topological sectors
arising from the gauge-fixing procedure. The resulting theory is naturally
interpreted as a Matrix String Theory, that is as a theory of covering maps
from a two-dimensional world-sheet to the target Riemann surface.Comment: LaTeX, 10 pages, uses espcrc2.sty. Presented by A. D'adda at the
Third Meeting on Constrained Dynamics and Quantum Gravity, Villasimius
(Sardinia, Italy) September 13-17, 1999; to appear in the proceeding
Matrix string states in pure 2d Yang Mills theories
We quantize pure 2d Yang-Mills theory on a torus in the gauge where the field
strength is diagonal. Because of the topological obstructions to a global
smooth diagonalization, we find string-like states in the spectrum similar to
the ones introduced by various authors in Matrix string theory. We write
explicitly the partition function, which generalizes the one already known in
the literature, and we discuss the role of these states in preserving modular
invariance. Some speculations are presented about the interpretation of 2d
Yang-Mills theory as a Matrix string theory.Comment: Latex file of 38 pages plus 6 eps figures. A note and few references
added, figures improve
PP Wave Limit and Enhanced Supersymmetry in Gauge Theories
We observe that the pp wave limit of compactifications of
type IIB string theory is universal, and maximally supersymmetric, as long as
is smooth and preserves some supersymmetry. We investigate a specific
case, . The dual SCFT, describing D3-branes at a
conifold singularity, has operators that we identify with the oscillators of
the light-cone string in the universal pp-wave background. The correspondence
is remarkable in that it relies on the exact spectrum of anomalous dimensions
in this CFT, along with the existence of certain exceptional series of
operators whose dimensions are protected only in the limit of large `t Hooft
coupling. We also briefly examine the singular case , for which
the pp wave background becomes a orbifold of the maximally supersymmetric
background by reflection of 4 transverse coordinates. We find operators in the
corresponding SCFT with the right properties to describe both the
untwisted and the twisted sectors of the closed string.Comment: 15 pages, LaTeX; v2: added more detail to a derivation, and a
preprint number; v3: minor corrections, some remarks and references adde
On Penrose limit of elliptic branes
We discuss a Penrose limit of an elliptic brane configuration with NS5
and D4 branes. This background is T-dual to D3 branes at a fixed
point of a singularity and the T-duality
survives the Penrose limit. The triple scaling limit of and gives
rise to IIA pp-wave solution with a space-like compact direction. We identify
the quiver gauge theory operators and argue that upon exchange of the momentum
along the compact direction and the winding number these operators coincide
with the operators derived in the dual type IIB description. We also find a new
Penrose limit of the type IIB background and the corresponding limit in the
type IIA picture. In the coordinate system we use there are two manifest
space-like isometries. The quiver gauge theory operator duals of the string
states are built of three bosonic fields.Comment: 25 pages with 1 figur
Phase transitions of Large-N two-dimensional Yang-Mills and generalized Yang-Mills theories in the double scaling limit
The large-N behavior of Yang-Mills and generalized Yang-Mills theories in the
double-scaling limit is investigated. By the double-scaling limit, it is meant
that the area of the manifold on which the theory is defined, is itself a
function of N. It is shown that phase transitions of different orders occur,
depending on the functional dependence of the area on N. The finite-size
scalings of the system are also investigated. Specifically, the dependence of
the dominant representation on A, for large but finite N is determined.Comment: 11 pages, to appear in Eur. Phys. J.
Strings and Two-dimensional QCD for Finite N
Minor corrections made and several references changed.Comment: 19 pp., MIT-CTP-226
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