125 research outputs found
Infinite coupling duals of N=2 gauge theories and new rank 1 superconformal field theories
We show that a proposed duality [arXiv:0711.0054] between infinitely coupled
gauge theories and superconformal field theories (SCFTs) with weakly gauged
flavor groups predicts the existence of new rank 1 SCFTs. These superconformal
fixed point theories have the same Coulomb branch singularities as the rank 1
E_6, E_7, and E_8 SCFTs, but have smaller flavor symmetry algebras and
different central charges. Gauging various subalgebras of the flavor algebras
of these rank 1 SCFTs provides many examples of infinite-coupling dualities,
satisfying an intricate set of consistency checks. They also provide examples
of N=2 conformal theories with marginal couplings but no weak-coupling limits.Comment: 12 page
Tree scattering amplitudes of the spin-4/3 fractional superstring I: the untwisted sectors
Scattering amplitudes of the spin-4/3 fractional superstring are shown to
satisfy spurious state decoupling and cyclic symmetry (duality) at tree-level
in the string perturbation expansion. This fractional superstring is
characterized by the spin-4/3 fractional superconformal algebra---a
parafermionic algebra studied by Zamolodchikov and Fateev involving chiral
spin-4/3 currents on the world-sheet in addition to the stress-energy tensor.
Examples of tree scattering amplitudes are calculated in an explicit c=5
representation of this fractional superconformal algebra realized in terms of
free bosons on the string world-sheet. The target space of this model is
three-dimensional flat Minkowski space-time with a level-2 Kac-Moody so(2,1)
internal symmetry, and has bosons and fermions in its spectrum. Its closed
string version contains a graviton in its spectrum. Tree-level unitarity (i.e.,
the no-ghost theorem for space-time bosonic physical states) can be shown for
this model. Since the critical central charge of the spin-4/3 fractional
superstring theory is 10, this c=5 representation cannot be consistent at the
string loop level. The existence of a critical fractional superstring
containing a four-dimensional space-time remains an open question.Comment: 42 pages, 4 figures, latex, IASSNS-HEP-93/57, CLNS-92/117
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
N=2 SU Quiver with USP Ends or SU Ends with Antisymmetric Matter
We consider the four dimensional scale invariant N=2 SU quiver gauge theories
with USp(2N) ends or SU(2N) ends with antisymmetric matter representations. We
argue that these theories are realized as six dimensional A_{2N-1} (0,2)
theories compactified on spheres with punctures. With this realization, we can
study various strongly coupled cusps in moduli space and find the S-dual
theories. We find a class of isolated superconformal field theories with only
odd dimensional operators and superconformal field theories with
only even dimensional operators .Comment: Minor changes are made; refrences are added; 21 pages, 18 figure
Kac and New Determinants for Fractional Superconformal Algebras
We derive the Kac and new determinant formulae for an arbitrary (integer)
level fractional superconformal algebra using the BRST cohomology
techniques developed in conformal field theory. In particular, we reproduce the
Kac determinants for the Virasoro () and superconformal () algebras.
For there always exist modules where the Kac determinant factorizes
into a product of more fundamental new determinants. Using our results for
general , we sketch the non-unitarity proof for the minimal series;
as expected, the only unitary models are those already known from the coset
construction. We apply the Kac determinant formulae for the spin-4/3
parafermion current algebra ({\em i.e.}, the fractional superconformal
algebra) to the recently constructed three-dimensional flat Minkowski
space-time representation of the spin-4/3 fractional superstring. We prove the
no-ghost theorem for the space-time bosonic sector of this theory; that is, its
physical spectrum is free of negative-norm states.Comment: 33 pages, Revtex 3.0, Cornell preprint CLNS 93/124
Argyres-Seiberg duality and the Higgs branch
We demonstrate the agreement between the Higgs branches of two N=2 theories
proposed by Argyres and Seiberg to be S-dual, namely the SU(3) gauge theory
with six quarks, and the SU(2) gauge theory with one pair of quarks coupled to
the superconformal theory with E_6 flavor symmetry. In mathematical terms, we
demonstrate the equivalence between a hyperkaehler quotient of a linear space
and another hyperkaehler quotient involving the minimal nilpotent orbit of E_6,
modulo the identification of the twistor lines.Comment: 27 pages; v2: published versio
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
Central Charge Reduction and Spacetime Statistics in the Fractional Superstring
Fractional superstrings in the tensor-product formulation experience
``internal projections'' which reduce their effective central charges. Simple
expressions for the characters of the resulting effective worldsheet theory are
found. All states in the effective theory can be consistently assigned definite
spacetime statistics. The projection to the effective theory is shown to be
described by the action of a dimension-three current in the original
tensor-product theory.Comment: 11 pages (LaTeX), CLNS 92/1168, McGill/92-41 (minor typos corrected
The Omega deformed B-model for rigid N=2 theories
We give an interpretation of the Omega deformed B-model that leads naturally
to the generalized holomorphic anomaly equations. Direct integration of the
latter calculates topological amplitudes of four dimensional rigid N=2 theories
explicitly in general Omega-backgrounds in terms of modular forms. These
amplitudes encode the refined BPS spectrum as well as new gravitational
couplings in the effective action of N=2 supersymmetric theories. The rigid N=2
field theories we focus on are the conformal rank one N=2 Seiberg-Witten
theories. The failure of holomorphicity is milder in the conformal cases, but
fixing the holomorphic ambiguity is only possible upon mass deformation. Our
formalism applies irrespectively of whether a Lagrangian formulation exists. In
the class of rigid N=2 theories arising from compactifications on local
Calabi-Yau manifolds, we consider the theory of local P2. We calculate motivic
Donaldson-Thomas invariants for this geometry and make predictions for
generalized Gromov-Witten invariants at the orbifold point.Comment: 73 pages, no figures, references added and typos correcte
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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