99 research outputs found
Three-dimensional N=4 supersymmetry in harmonic N=3 superspace
We consider the map of three-dimensional N=4 superfields to N=3 harmonic
superspace. The left and right representations of the N=4 superconformal group
are constructed on N=3 analytic superfields. These representations are
convenient for the description of N=4 superconformal couplings of the Abelian
gauge superfields with hypermultiplets. We analyze the N=4 invariance in the
non-Abelian N=3 Yang-Mills theory.Comment: Latex file, 22 pages; v2 two references adde
Constrained superpotentials in harmonic gauge theories with 8 supercharges
We consider D-dimensional supersymmetric gauge theories with 8 supercharges
(D<6,) in the framework of harmonic superspaces. The effective
Abelian low-energy action for D=5 contains the free and Chern-Simons terms.
Effective superfield actions for D<4 can be written in terms of
the superpotentials satisfying the superfield constraints and (6-D)-dimensional
Laplace equations. The role of alternative harmonic structures is discussed.Comment: LATEX file, 9 pages, version published in Teor. Mat. Fi
ABJM models in N=3 harmonic superspace
We construct the classical action of the Aharony-Bergman-Jafferis-Maldacena
(ABJM) model in the N=3, d=3 harmonic superspace. In such a formulation three
out of six supersymmetries are realized off shell while the other three mix the
superfields and close on shell. The superfield action involves two
hypermultiplet superfields in the bifundamental representation of the gauge
group and two Chern-Simons gauge superfields corresponding to the left and
right gauge groups. The N=3 superconformal invariance allows only for a minimal
gauge interaction of the hypermultiplets. Amazingly, the correct sextic scalar
potential of ABJM emerges after the elimination of auxiliary fields. Besides
the original U(N)xU(N) ABJM model, we also construct N=3 superfield
formulations of some generalizations. For the SU(2)xSU(2) case we give a simple
superfield proof of its enhanced N=8 supersymmetry and SO(8) R-symmetry.Comment: 1+35 pages, minor changes, a reference added, published versio
Differential Calculus on -Deformed Light-Cone
We propose the ``short'' version of q-deformed differential calculus on the
light-cone using twistor representation. The commutation relations between
coordinates and momenta are obtained. The quasi-classical limit introduced
gives an exact shape of the off-shell shifting.Comment: 11 pages, Standard LaTeX 2.0
A description of n-ary semigroups polynomial-derived from integral domains
We provide a complete classification of the n-ary semigroup structures
defined by polynomial functions over infinite commutative integral domains with
identity, thus generalizing G{\l}azek and Gleichgewicht's classification of the
corresponding ternary semigroups
Nilpotent deformations of N=2 superspace
We investigate deformations of four-dimensional N=(1,1) euclidean superspace
induced by nonanticommuting fermionic coordinates. We essentially use the
harmonic superspace approach and consider nilpotent bi-differential Poisson
operators only. One variant of such deformations (termed chiral nilpotent)
directly generalizes the recently studied chiral deformation of N=(1/2,1/2)
superspace. It preserves chirality and harmonic analyticity but generically
breaks N=(1,1) to N=(1,0) supersymmetry. Yet, for degenerate choices of the
constant deformation matrix N=(1,1/2) supersymmetry can be retained, i.e. a
fraction of 3/4. An alternative version (termed analytic nilpotent) imposes
minimal nonanticommutativity on the analytic coordinates of harmonic
superspace. It does not affect the analytic subspace and respects all
supersymmetries, at the expense of chirality however. For a chiral nilpotent
deformation, we present non(anti)commutative euclidean analogs of N=2 Maxwell
and hypermultiplet off-shell actions.Comment: 1+16 pages; v2: discussion of (pseudo)conjugations extended, version
to appear in JHE
On the relation between effective supersymmetric actions in different dimensions
We make two remarks: (i) Renormalization of the effective charge in a
4--dimensional (supersymmetric) gauge theory is determined by the same graphs
and is rigidly connected to the renormalization of the metric on the moduli
space of the classical vacua of the corresponding reduced quantum mechanical
system. Supersymmetry provides constraints for possible modifications of the
metric, and this gives us a simple proof of nonrenormalization theorems for the
original 4-dimensional theory. (ii) We establish a nontrivial relationship
between the effective (0+1)-dimensional and (1+1)-dimensional Lagrangia (the
latter represent conventional
Kahlerian sigma models).Comment: 15 pages, 2 figure
The Conformal Manifold of Chern-Simons Matter Theories
We determine perturbatively the conformal manifold of N=2 Chern-Simons matter
theories with the aim of checking in the three dimensional case the general
prescription based on global symmetry breaking, recently introduced. We discuss
in details few remarkable cases like the N=6 ABJM theory and its less
supersymmetric generalizations with/without flavors. In all cases we find
perfect agreement with the predictions of global symmetry breaking
prescription.Comment: 1+17 pages, 1 figure, references adde
M-theory on Spin(7) Manifolds, Fluxes and 3D, N=1 Supergravity
We calculate the most general causal N=1 three-dimensional, gauge invariant
action coupled to matter in superspace and derive its component form using
Ectoplasmic integration theory. One example of such an action can be obtained
by compactifying M-theory on a Spin(7) holonomy manifold taking non-vanishing
fluxes into account. We show that the resulting three-dimensional theory is in
agreement with the more general construction. The scalar potential resulting
from Kaluza-Klein compactification stabilizes all the moduli fields describing
deformations of the metric except for the radial modulus. This potential can be
written in terms of the superpotential previously discussed in the literature.Comment: 37 pages no figures (LaTeX 2e
Minimal deformations of the commutative algebra and the linear group GL(n)
We consider the relations of generalized commutativity in the algebra of
formal series , which conserve a tensor -grading and
depend on parameters . We choose the -preserving version of
differential calculus on . A new construction of the symmetrized tensor
product for -type algebras and the corresponding definition of minimally
deformed linear group and Lie algebra are proposed. We
study the connection of and with the special matrix
algebra \mbox{Mat} (n,Q) containing matrices with noncommutative elements.
A definition of the deformed determinant in the algebra \mbox{Mat} (n,Q) is
given. The exponential parametrization in the algebra \mbox{Mat} (n,Q) is
considered on the basis of Campbell-Hausdorf formula.Comment: 14 page
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