1,992 research outputs found
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
Holomorphy and dynamical scales in supersymmetric gauge theories
New recent results in supersymmetric gauge theories based on holomorphy and
symmetry considerations are extended to the case where the gauge coupling
constant is given by the real part of a chiral superfield. We assume here that
its dynamics can be described by an effective quantum field theory. Then its
vacuum expectation value is a function of the other coupling constants, viewed
as chiral background superfields. This functional dependence can be determined
exactly and satisfies highly non-trivial consistency checks.Comment: 14 pages, LaTe
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 -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
More Results in Supersymmetric Gauge Theories
We present the exact effective superpotentials in , supersymmetric
gauge theories with triplets and doublets of matter
superfields. For the theories with a single triplet matter superfield we
present the exact gauge couplings for arbitrary bare masses and Yukawa
couplings.Comment: 9 page
Ground Rings and Their Modules in 2D Gravity with Matter
All solvable two-dimensional quantum gravity models have non-trivial BRST
cohomology with vanishing ghost number. These states form a ring and all the
other states in the theory fall into modules of this ring. The relations in the
ring and in the modules have a physical interpretation. The existence of these
rings and modules leads to nontrivial constraints on the correlation functions
and goes a long way toward solving these theories in the continuum approach.Comment: 13 page
Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect
We study a system of electrons moving on a noncommutative plane in the
presence of an external magnetic field which is perpendicular to this plane.
For generality we assume that the coordinates and the momenta are both
noncommutative. We make a transformation from the noncommutative coordinates to
a set of commuting coordinates and then we write the Hamiltonian for this
system. The energy spectrum and the expectation value of the current can then
be calculated and the Hall conductivity can be extracted. We use the same
method to calculate the phase shift for the Aharonov-Bohm effect. Precession
measurements could allow strong upper limits to be imposed on the
noncommutativity coordinate and momentum parameters and .Comment: 9 pages, RevTeX4, references added, small changes in the tex
Systematic Study of Theories with Quantum Modified Moduli
We begin the process of classifying all supersymmetric theories with quantum
modified moduli. We determine all theories based on a single SU or Sp gauge
group with quantum modified moduli. By flowing among theories we have
calculated the precise modifications to the algebraic constraints that
determine the moduli at the quantum level. We find a class of theories, those
with a classical constraint that is covariant but not invariant under global
symmetries, that have a singular modification to the moduli, which consists of
a new branch.Comment: 21 pages, ReVTeX (or Latex, etc), corrected typos and cQMM discusio
On the Twisted (2,0) and Little-String Theories
We study the compactification of the and type-II little-string
theories on , and with an R-symmetry twist that preserves half
the supersymmetry. We argue that it produces the same moduli spaces of vacua as
compactification of the theory with Wilson lines given by a
maximal embedding of SU(2). In certain limits, this reproduces the moduli space
of SU(2) with a massive adjoint hyper-multiplet. In the type-II little-string
theory case, we observe a peculiar phase transition where the strings condense.
We conjecture a generalization to more than two 5-branes which involves
instantons on non-commutative . We conclude with open questions.Comment: 27pp TeX, one eps figur
Dynamical Supersymmetry Breaking
I review the motivation for dynamical supersymmetry breaking, the various
mechanisms which have been discovered, and the prospects for model building.Comment: 5 pages. invited talk given at SUSY97, May27-31, 1997, University of
Pennsylvani
Symplectic SUSY Gauge Theories with Antisymmetric Matter
We investigate the confining phase vacua of supersymmetric Sp(2\NC) gauge
theories that contain matter in both fundamental and antisymmetric
representations. The moduli spaces of such models with \NF=3 quark flavors
and \NA=1 antisymmetric field are analogous to that of SUSY QCD with
\NF=\NC+1 flavors. In particular, the forms of their quantum superpotentials
are fixed by classical constraints. When mass terms are coupled to
W_{(\NF=3,\NA=1)} and heavy fields are integrated out, complete towers of
dynamically generated superpotentials for low energy theories with fewer
numbers of matter fields can be derived. Following this approach, we deduce
exact superpotentials in and theories which cannot be
determined by symmetry considerations or integrating in techniques. Building
upon these simple symplectic group results, we also examine the ground state
structures of several and models. We
emphasize that the top-down approach may be used to methodically find dynamical
superpotentials in many other confining supersymmetric gauge theories.Comment: 21 pages, Revte
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