2,863 research outputs found
On Duality in Supersymmetric Yang-Mills Theory
We discuss non-abelian gauge theory coupled to an adjoint chiral
superfield , and a number of fundamental chiral superfields . Using
duality, we show that turning on a superpotential W(X)=\Tr\sum_{l=1}^k g_l
X^{l+1} leads to non-trivial long distance dynamics, a large number of
multicritical IR fixed points and vacua, connected to each other by varying the
coefficients .Comment: 11 pages, harvma
SUSY field theories, integrable systems and their stringy/brane origin -- II
Five and six dimensional SUSY gauge theories, with one or two compactified
directions, are discussed. The 5d theories with the matter hypermultiplets in
the fundamental representation are associated with the twisted spin
chain, while the group product case with the bi-fundamental matter corresponds
to the higher rank spin chains. The Riemann surfaces for theories with
fundamental matter and two compact directions are proposed to correspond to the
spin chain based on the Sklyanin algebra. We also discuss the obtained
results within the brane and geometrical engeneering frameworks and explain the
relation to the toric diagrams.Comment: LaTeX, 21 pages, no figure
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
INSTANTON CALCULATIONS VERSUS EXACT RESULTS IN 4 DIMENSIONAL SUSY GAUGE THEORIES.
We relate the non-perturbative exact results in supersymmetry to perturbation
theory using several different methods: instanton calculations at weak or
strong coupling, a method using gaugino condensation and another method
relating strong and weak coupling. This allows many precise numerical checks of
the consistency of these methods, especially the amplitude of instanton
effects, and of the network of exact solutions in supersymmetry. However, there
remain difficulties with the instanton computations at strong coupling.Comment: 17 pages, uses harvmac
BPS States and Minimal Surfaces
It was observed recently, that the low energy effective action of the
four-dimensional supersymmetric theories may be obtained as a certain limit of
M Theory. From this point of view, the BPS states correspond to the minimal
area membranes ending on the M Theory fivebrane. We prove that for the
configuration, corresponding to the SU(2) Super Yang-Mills theory, the BPS
spectrum is correctly reproduced, and develop techniques for analyzing the BPS
spectrum in more general cases. We show that the type of the supermultiplet is
related to the topology of the membrane: disks correspond to hypermultiplets,
and cylinders to vector multiplets. We explain the relation between minimal
surfaces and geodesic lines, which shows that our description of BPS states is
closely related to one arising in Type II string compactification on Calabi-Yau
threefolds.Comment: 31 pp., LaTeX, 6 PostScript figures. The construction of bosonic and
fermionic zero modes is explained in more invariant terms and generalized to
membranes of arbitrary topology. Mistake in the discussion of membrane
worldsheet theory is corrected. The relation between membranes and geodesic
lines is explaine
Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
We consider general aspects of N=2 gauge theories in three dimensions,
including their multiplet structure, anomalies and non-renormalization
theorems. For U(1) gauge theories, we discuss the quantum corrections to the
moduli space, and their relation to ``mirror symmetries'' of 3d N=4 theories.
Mirror symmetry is given an interpretation in terms of vortices. For SU(N_c)
gauge groups with N_f fundamental flavors, we show that, depending on the
number of flavors, there are quantum moduli spaces of vacua with various
phenomena near the origin.Comment: 40 pages, harvma
Simple Singularities and N=2 Supersymmetric Yang-Mills Theory
We present a first step towards generalizing the work of Seiberg and Witten
on N=2 supersymmetric Yang-Mills theory to arbitrary gauge groups.
Specifically, we propose a particular sequence of hyperelliptic genus
Riemann surfaces to underly the quantum moduli space of N=2
supersymmetric gauge theory. These curves have an obvious generalization to
arbitrary simply laced gauge groups, which involves the A-D-E type simple
singularities. To support our proposal, we argue that the monodromy in the
semiclassical regime is correctly reproduced. We also give some remarks on a
possible relation to string theory.Comment: 13p, harvmac/lanlmac with hyperlinks 1 uuencoded PostScript figure
appended (Some inconsistencies and typos were corrected, we also dropped our
conjectures for the monodromies at strong coupling, of which we know now that
they are different.
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
Hyperelliptic curves for Supersymmetric Yang-Mills
In this paper we discuss the hyperelliptic curve for super
Yang-Mills with six flavors of hypermultiplets. We start with a generic genus
two surface and construct the curve in terms of genus two theta functions. From
this one can construct the curve for . This curve is explicitly dual
under a subgroup of which is not isomorphic to . We then
proceed to construct the curve for the general theory and discuss the
duality properties of the theory. The results given here differ from those
given previously.Comment: 21 pages using phyzzx forma
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