878 research outputs found
The M theory lift of two O6 planes and four D6 branes
We solve for the effective actions on the Coulomb branches of a class of N=2
supersymmetric theories by finding the complex structure of an M5 brane in an
appropriate background hyperkahler geometry corresponding to the lift of two
O6^- orientifolds and four D6 branes to M theory. The resulting Seiberg-Witten
curves are of finite genus, unlike other solutions proposed in the literature.
The simplest theories in this class are the scale invariant Sp(k) theory with
one antisymmetric and four fundamental hypermultiplets and the SU(k) theory
with two antisymmetric and four fundamental hypermultiplets. Infinite classes
of related theories are obtained by adding extra SU(k) factors with
bifundamental matter and by turning on masses to flow down to various
asymptotically free theories. The N=4 supersymmetric SU(k) theory can be
embedded in these asymptotically free theories, allowing a derivation of a
subgroup of its S duality group as an exact equivalence of quantum field
theories.Comment: 45 pages, 3 figures. Reference adde
Singular points in N=2 SQCD
We revisit the study of singular points in N=2 SQCD with classical gauge
groups. Using a technique proposed recently by Gaiotto, Seiberg and Tachikawa
we find that the low-energy physics at the maximally singular point involves
two superconformal sectors coupled to an infrared free SU(2) gauge group. When
one softly breaks extended supersymmetry to N=1 adding a mass term for the
chiral multiplet in the adjoint representation, a finite number of vacua remain
and the theory becomes confining. Our analysis allows to identify the
low-energy physics at these distinguished points in the moduli space. In some
cases, which we will describe in detail, two sectors coupled to an infrared
free SU(2) gauge group emerge as before. For USp and SO gauge groups one of
these sectors is always free, contrary to the SU case.Comment: 22 pages, 2 figure
Comments on scaling limits of 4d N=2 theories
We revisit the study of the maximally singular point in the Coulomb branch of
4d N=2 SU(N) gauge theory with N_f=2n flavors for N_f= 2, we find
that the low-energy physics is described by two non-trivial superconformal
field theories coupled to a magnetic SU(2) gauge group which is infrared free.
(In the special case n=2, one of these theories is a theory of free
hypermultiplets.) This observation removes a possible counter example to a
conjectured a-theorem.Comment: 13 page
Multiscalar production amplitudes beyond threshold
We present exact tree-order amplitudes for , for final states
containing one or two particles with non-zero three-momentum, for various
interaction potentials. We show that there are potentials leading to tree
amplitudes that satisfy unitarity, not only at threshold but also in the above
kinematical configurations and probably beyond. As a by-product, we also
calculate tree amplitudes at threshold and show that for the unbroken
theory they vanish for , for the Standard Model Higgs they
vanish for and for a model potential, respecting tree-order
unitarity, for even and . Finally, we calculate the imaginary part of
the one-loop amplitude in both symmetric and spontaneously broken
theory.Comment: 11 pages, Latex, 3 figures (available on request
On amplitude zeros at threshold
The occurrence of zeros of 2 to n amplitudes at threshold in scalar theories
is studied. We find a differential equation for the scalar potential, which
incorporates all known cases where the 2 to n amplitudes at threshold vanish
for all sufficiently large , in all space-time dimensions, . This
equation is related to the reflectionless potentials of Quantum Mechanics and
to integrable theories in 1+1 dimensions. As an application, we find that the
sine-Gordon potential and its hyperbolic version, the sinh-Gordon potential,
also have amplitude zeros at threshold, , for and
, independently of the mass and the coupling constant.Comment: 6 pages, Latex, CERN-TH.6762/9
Sp(N) higher-derivative F-terms via singular superpotentials
We generalize the higher-derivative F-terms introduced by Beasley and Witten
(hep-th/0409149) for SU(2) superQCD to Sp(N) gauge theories with fundamental
matter. We generate these terms by integrating out massive modes at tree level
from an effective superpotential on the chiral ring of the microscopic theory.
Though this superpotential is singular, its singularities are mild enough to
permit the unambiguous identification of its minima, and gives sensible answers
upon integrating out massive modes near any given minimum.Comment: 15 pages, 6 figure
Renormalization Group and Dynamics of Supersymmetric Gauge Theories
We discuss questions related to renormalization group and to nonperturbative
aspects of non-Abelian gauge theories with N=2 and/or N=1 supersymmetry.
Results on perturbative and nonperturbative functions of these theories
are reviewed, and new mechanisms of confinement and dynamical symmetry breaking
recently found in a class of , and theories are
discussed.Comment: 13 pages, 3 figures, uses ws-p9-75x6-50.cls. Lecture given at the
Second Conference on the ERG, Rome 200
The Coulomb branch of N=1 supersymmetric SU(N_c) x SU(N_c) gauge theories
We analyze the low energy behavior of N=1 supersymmetric gauge theories with
SU(N_c) x SU(N_c) gauge group and a Landau-Ginzburg type superpotential. These
theories contain fundamentals transforming under one of the gauge groups as
well as bifundamental matter which transforms as a fundamentals under each. We
obtain the parametrization of the gauge coupling on the Coulomb branch in terms
of a hyperelliptic curve. The derivation of this curve involves making use of
Seiberg's duality for SQCD as well as the classical constraints for N_f=N_c+1
and the quantum modified constraints for N_f=N_c.Comment: 16 pages, no figures, revtex; typos correcte
A semiclassical realization of infrared renormalons
Perturbation series in quantum field theory are generally divergent
asymptotic series which are also typically not Borel resummable in the sense
that the resummed series is ambiguous. The ambiguity is associated with
singularities in the Borel plane on the positive real axis. In quantum
mechanics there are cases in which the ambiguity that arises in perturbation
theory cancels against a similarly ambiguous contribution from
instanton--anti-instanton events. In asymptotically free gauge theories this
mechanism does not suffice because perturbation theory develops ambiguities
associated with singularities in the Borel plane which are closer to the origin
by a factor of about N (the rank of the gauge group) compared to the
singularities realized by instanton events. These are called IR renormalon
poles, and on R**4 they do not possess any known semiclassical realization. By
using continuity on R**3 x S**1, and by generalizing the works of Bogomolny and
Zinn-Justin to QFT, we identify saddle point field configurations, e.g.,
bion--anti-bion events, corresponding to singularities in the Borel plane which
are of order N times closer to the origin than the 4d BPST
instanton--anti-instanton singularity. We conjecture that these are the leading
singularities in the Borel plane and that they are the incarnation of the
elusive renormalons in the weak coupling regime.Comment: 4 page
Generalized Konishi anomaly, Seiberg duality and singular effective superpotentials
Using the generalized Konishi anomaly (GKA) equations, we derive the
effective superpotential of four-dimensional N=1 supersymmetric SU(n) gauge
theory with n+2 fundamental flavors. We find, however, that the GKA equations
are only integrable in the Seiberg dual description of the theory, but not in
the direct description of the theory. The failure of integrability in the
direct, strongly coupled, description suggests the existence of
non-perturbative corrections to the GKA equations.Comment: 20 pages; v3: corrected the comparison to the SU(2) cas
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