5,427 research outputs found

### On the Quantum Moduli Space of Vacua of $N=2$ Supersymmetric $SU(N_c)$ Gauge Theories

We construct families of hyper-elliptic curves which describe the quantum
moduli spaces of vacua of $N=2$ supersymmetric $SU(N_c)$ gauge theories coupled
to $N_f$ flavors of quarks in the fundamental representation. The quantum
moduli spaces for $N_f < N_c$ are determined completely by imposing
$R$-symmetry, instanton corrections and the proper classical singularity
structure. These curves are verified by residue and weak coupling monodromy
calculations. The quantum moduli spaces for $N_f\geq N_c$ theories are
parameterized and their general structure is worked out using residue
calculations. Global symmetry considerations suggest a complete description of
them. The results are supported by weak coupling monodromy calculations. The
exact metrics on the quantum moduli spaces as well as the exact spectrum of
stable massive states are derived. We find an example of a novel symmetry of a
quantum moduli space: Invariance under the exchange of a moduli parameter and
the bare mass. We apply our method for the construction of the quantum moduli
spaces of vacua of $N=1$ supersymmetric theories in the coulomb phase.Comment: 35 pages, late

### On the Quantum Moduli Space of N=2 Supersymmetric Gauge Theories

Families of hyper-elliptic curves which describe the quantum moduli spaces of
vacua of $N=2$ supersymmetric $SO(N_c)$ gauge theories coupled to $N_f$ flavors
of quarks in the vector representation are constructed. The quantum moduli
spaces for $2N_f < N_c-1$ are determined completely by imposing $R$-symmetry,
instanton corrections and the proper classical singularity structure. These
curves are verified by residue calculations. The quantum moduli spaces for
$2N_f\geq N_c-1$ theories are parameterized and their general structure is
worked out using residue calculations. The exact metrics on the quantum moduli
spaces as well as the exact spectrum of stable massive states are derived. The
results presented here together with recent results of Martinec and Warner
provide a natural conjecture for the form of the curves for the other gauge
groups.Comment: 19 page

### Duality of Sp(2N) and SO(N) Supersymmetric Gauge Theories with Adjoint Matter

We discuss electric-magnetic duality in two new classes of supersymmetric
Yang-Mills theories. The models have gauge group Sp(2\nc) or SO(\nc) with
matter in both the adjoint and defining representations. By perturbing these
theories with various superpotentials, we find a variety of new infrared fixed
points with dual descriptions. This work is complementary to that of Kutasov
and Schwimmer on SU(\nc) and of Intriligator on other models involving
Sp(2\nc) and SO(\nc).Comment: 14 pages, no figures, uses harvma

### 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

### Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics

We study (non-renormalizable) five dimensional supersymmetric field theories.
The theories are parametrized by quark masses and a gauge coupling. We derive
the metric on the Coulomb branch exactly. We use stringy considerations to
learn about new non-trivial interacting field theories with exceptional global
symmetry $E_n$ ($E_8$, $E_7$, $E_6$, $E_5=Spin(10)$, $E_4=SU(5)$,
$E_3=SU(3)\times SU(2)$, $E_2=SU(2)\times U(1)$ and $E_1=SU(2)$). Their Coulomb
branch is ${\bf R}^+$ and their Higgs branch is isomorphic to the moduli space
of $E_n$ instantons. One of the relevant operators of these theories leads to a
flow to $SU(2)$ gauge theories with $N_f=n-1$ flavors. In terms of these
$SU(2)$ IR theories this relevant parameter is the inverse gauge coupling
constant. Other relevant operators (which become quark masses after flowing to
the $SU(2)$ theories) lead to flows between them. Upon further
compactifications to four and three dimensions we find new fixed points with
exceptional symmetries.Comment: 13 pages, uses harvmac, one reference adde

### Duality and the Legendre Transform

We define a weak-strong coupling transformation based on the Legendre
transformation of the effective action. In the case of N\es 2 supersymmetric
Yang-Mills theory, this coincides with the duality transform on the low energy
effective action considered by Seiberg and Witten. This Legendre transform
interpretation of duality generalizes directly to the full effective action,
and in principle to other theories.Comment: 6 pages, LaTe

### Toroidal Compactification of Heterotic 6D Non-Critical Strings Down to Four Dimensions

The low-energy limit of the 6D non-critical string theory with $N=1$ SUSY and
$E_8$ chiral current algebra compactified on $T^2$ is generically an $N=2$
$U(1)$ vector multiplet. We study the analog of the Seiberg-Witten solution for
the low-energy effective action as a function of $E_8$ Wilson lines on the
compactified torus and the complex modulus of that torus. The moduli space
includes regions where the Seiberg-Witten curves for $SU(2)$ QCD are recovered
as well as regions where the newly discovered 4D theories with enhanced
$E_{6,7,8}$ global symmetries appear.Comment: 15pp LaTe

### A Comment on Duality in N=1 Supersymmetric Non -- Abelian Gauge Theories

Recently N. Seiberg has shown that certain N=1 supersymmetric Yang -- Mills
theories have the property that their infrared physics can be equivalently
described by {\it two different} gauge theories, with the strong coupling
region of one corresponding to the weak coupling region of the other. This
duality leads to interesting results about the infrared dynamics of these
theories. We generalize Seiberg's ideas to a new class of models for which a
similar duality allows one to obtain rather detailed dynamical information
about the long distance physics.Comment: 9 pages, harvma

### Non-trivial Fixed Points of The Renormalization Group in Six Dimensions

We start a systematic analysis of supersymmetric field theories in six
dimensions. We find necessary conditions for the existence of non-trivial
interacting fixed points. String theory provides us with examples of such
theories. We conjecture that there are many other examples.Comment: 6 pages, uses harvma

### Remarks on Non-Abelian Duality in N=1 Supersymmetric Gauge Theories

Recently Seiberg has conjectured a duality symmetry connecting different
theories of the supersymmetric QCD type. We provide support for this conjecture
by analyzing a flat direction of the theory along which the two dual theories
go over to the same theory in the IR.Comment: 17 pages, harvma

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