3,052 research outputs found

### Mirror Symmetry in Three Dimensional Gauge Theories

We discuss non-trivial fixed points of the renormalization group with dual
descriptions in $N=4$ gauge theories in three dimensions. This new duality acts
as mirror symmetry, exchanging the Higgs and Coulomb branches of the theories.
Quantum effects on the Coulomb branch arise classically on the Higgs branch of
the dual theory. We present examples of dual theories whose Higgs/Coulomb
branch are the ALE spaces and whose Coulomb/Higgs branches are the moduli space
of instantons of the corresponding $ADE$ gauge group. In particular, we show
that in three dimensions small $E_8$ instantons in string theory are described
by a local quantum field theory.Comment: 13 pages, harvma

### A Note on Noncommutative String theory and its low energy limit

The noncommutative string theory is described by embedding open string theory
in a constant second rank antisymmetric $B_{\mu\nu}$ field and the
noncommutative gauge theory is defined by a deformed $\star$ product. As a
check, study of various scattering amplitudes in both noncommutative string and
noncommutative gauge theory confirm that in the $\alpha^{'}\to 0$ limit, the
noncommutative string theoretic amplitude goes over to the noncommutative gauge
theoretic amplitude, and the couplings are related as
$g_{YM}=G_0\sqrt{\frac{1}{2\alpha^{'}}}$. Furthermore we show that in this
limit there will not be any correction to the gauge theoretic action because of
absence of massive modes. We get sin/cos factors in the scattering amplitudes
depending on the odd/even number of external photons.Comment: 14 pages including 2 figure

### The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory

We present an exact description of the metric on the moduli space of vacua
and the spectrum of massive states for four dimensional N=2 supersymmetric
SU(n) gauge theories. The moduli space of quantum vacua is identified with the
moduli space of a special set of genus n-1 hyperelliptic Riemann surfaces.Comment: 11 pages, Revtex, 2 figures. Reference adde

### Varieties of vacua in classical supersymmetric gauge theories

We give a simple description of the classical moduli space of vacua for
supersymmetric gauge theories with or without a superpotential. The key
ingredient in our analysis is the observation that the lagrangian is invariant
under the action of the complexified gauge group \Gc. From this point of view
the usual $D$-flatness conditions are an artifact of Wess--Zumino gauge. By
using a gauge that preserves \Gc invariance we show that every constant
matter field configuration that extremizes the superpotential is \Gc
gauge-equivalent (in a sense that we make precise) to a unique classical
vacuum. This result is used to prove that in the absence of a superpotential
the classical moduli space is the algebraic variety described by the set of all
holomorphic gauge-invariant polynomials. When a superpotential is present, we
show that the classical moduli space is a variety defined by imposing
additional relations on the holomorphic polynomials. Many of these points are
already contained in the existing literature. The main contribution of the
present work is that we give a careful and self-contained treatment of limit
points and singularities.Comment: 14 pages, LaTeX (uses revtex.sty

### Two Phases of Supersymmetric Gluodynamics

We argue that supersymmetric gluodynamics has two phases with equivalent
infrared behavior, one of which is asymptotically free and another one is
superstrongly coupled in the ultraviolet domain.Comment: Plain LaTeX, 6 pages, 2 figures in a uuencoded file Final version
which appeared in Phys. Rev. Let.75;2085-2087,1995 Corrected references and
some Comments with no effect on conclusion

### More Comments on String Theory on AdS_3

We clarify a number of issues regarding the worldsheet and spacetime
descriptions of string propagation on AdS_3. We construct the vertex operators
of spacetime current algebra and spacetime (super) Virasoro generators in the
full interacting SL(2) WZW theory and study their Ward identities. We also
explain the relation between the analysis in this note and some recent work on
this subject.Comment: 42 pages, harvmac; references adde

### What do Topologists want from Seiberg--Witten theory? (A review of four-dimensional topology for physicists)

In 1983, Donaldson shocked the topology world by using instantons from
physics to prove new theorems about four-dimensional manifolds, and he
developed new topological invariants. In 1988, Witten showed how these
invariants could be obtained by correlation functions for a twisted N=2 SUSY
gauge theory. In 1994, Seiberg and Witten discovered dualities for such
theories, and in particular, developed a new way of looking at four-dimensional
manifolds that turns out to be easier, and is conjectured to be equivalent to,
Donaldson theory.
This review describes the development of this mathematical subject, and shows
how the physics played a pivotal role in the current understanding of this area
of topology.Comment: 51 pages, 10 figures, 8 postscript files. Submitted to International
Journal of Modern Physics A, July 2002 Uses Latex 2e with class file
ws-ijmpa.cls (included in tar file

### Proposal for a Simple Model of Dynamical SUSY Breaking

We discuss supersymmetric $SU(2)$ gauge theory with a single matter field in
the $I=3/2$ representation. This theory has a moduli space of exactly
degenerate vacua. Classically it is the complex plane with an orbifold
singularity at the origin. There seem to be two possible candidates for the
quantum theory at the origin. In both the global chiral symmetry is unbroken.
The first is interacting quarks and gluons at a non-trivial infrared fixed
point -- a non-Abelian Coulomb phase. The second, which we consider more
likely, is a confining phase where the singularity is simply smoothed out. If
this second, more likely, possibility is realized, supersymmetry will
dynamically break when a tree level superpotential is added. This would be the
simplest known gauge theory which dynamically breaks supersymmetry.Comment: 6 page

### Noncommutativity of the Moving D2-brane Worldvolume

In this paper we study the noncommutativity of a moving membrane with
background fields. The open string variables are analyzed. Some scaling limits
are studied. The equivalence of the magnetic and electric noncommutativities is
investigated. The conditions for equivalence of noncommutativity of the T-dual
theory in the rest frame and noncommutativity of the original theory in the
moving frame are obtained.Comment: 12 pages, Latex, no figure. The equivalence of noncommutativities and
also some scaling limits are adde

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