5,257 research outputs found

### Manifest supersymmetry and the ADHM construction of instantons

We present the (0,4) superspace version of Witten's sigma model construction
for ADHM instantons. We use the harmonic superspace formalism, which exploits
the three complex structures common to both (0,4) supersymmetry and self-dual
Yang-Mills theory. A novel feature of the superspace formulation is the
manifest interplay between the ADHM construction and its twistor counterpart.Comment: minor changes in the text; also an Appendix on off-shell structure of
chiral fermion multiplets in (0,4) supersymmetry, and references adde

### N=2 Super-Yang-Mills Theory from a Chern-Simons Action

We present a Chern-Simons action for N=2 Super-Yang-Mills theory (SYM) in
'full' N=2 superspace (hyperspace) augmented by coordinates of the internal
SU(2) group and show that this action can be reduced to the usual SYM action in
the Harmonic hyperspace. We also discover that the 'choice' of Harmonic
hyperspace is not unique and under suitable conditions, further reduction to
the well-known Projective hyperspace is possible.Comment: 1+8+1 pages, 1 figur

### Harmonicity in N=4 supersymmetry and its quantum anomaly

The holomorphicity property of N=1 superpotentials or of N=2 F-terms
involving vector multiplets is generalized to the case of N=4 1/2-BPS effective
operators defined in harmonic superspace. The resulting harmonicity equations
are shown to control the moduli dependence of the couplings of higher
dimensional operators involving powers of the N=4 Weyl superfield, computed by
N=4 topological amplitudes. These equations can also be derived on the string
side, exhibiting an anomaly from world-sheet boundary contributions that leads
to recursion relations for the non-analytic part of the couplings.Comment: 36 page

### Superconformal spaces and implications for superstrings

We clarify some properties of projective superspace by using a manifestly
superconformal notation. In particular, we analyze the N=2 scalar multiplet in
detail, including its action, and the propagator and its super-Schwinger
parameters. The internal symmetry is taken to be noncompact (after Wick
rotation), allowing boundary conditions that preserve it off shell.
Generalization to N=4 suggests the coset superspace PSU(2,2|4)/OSp(4|4) for the
AdS/CFT superstring.Comment: 19 pages, no figures; v2: fixed sign, added note & reference; v3:
added note & references, version to appear in Physical Review

### The effective hyper-K"ahler potential in the N=2 supersymmetric QCD

The effective low-energy hyper-K"ahler potential for a massive N=2 matter in
the N=2 super-QCD is investigated. The N=2 extended supersymmetry severely
restricts that N=2 matter self-couplings so that their exact form can be fixed
by a few parameters, which is apparent in the N=2 harmonic superspace. In the
N=2 QED with a single matter hypermultiplet, the one-loop perturbative
calculations lead to the Taub-NUT hyper-K"ahler metric in the massive case, and
a free metric in the massless case. It is remarkable that the naive
non-renormalization `theorem' does not apply. There exists a manifestly N=2
supersymmetric duality transformation converting the low-energy effective
action for the N=2 QED hypermultiplet into a sum of the quadratic and the
improved (non-polynomial) actions for an N=2 tensor multiplet. The duality
transformation also gives a simple connection between the low-energy effective
action in the N=2 harmonic superspace and the component results.Comment: 12 pages, LaTeX, one figure and macros include

### Scale Invariant Low-Energy Effective Action in N=3 SYM Theory

Using the harmonic superspace approach we study the problem of low-energy
effective action in N=3 SYM theory. The candidate effective action is a scale
and \gamma_5-invariant functional in full N=3 superspace built out of N=3
off-shell superfield strengths. This action is constructed as N=3 superfield
generalization of F^4/\phi^4 component term which is leading in the low-energy
effective action and is simultaneously the first nontrivial term in scale
invariant Born-Infeld action. All higher-order terms in the scale invariant
Born-Infeld action are also shown to admit an off-shell superfield completion
in N=3 harmonic superspace.Comment: 17 pages; v2: typos correcte

### Harmonic Twistor Formalism and Transgression on Hyperk\"ahler manifolds

In this paper we continue our study of the fourth order transgression on
hyper\"ahler manifolds introduced in the previous paper. We give a local
construction for the fourth-order transgression of the Chern character form of
an arbitrary vector bundle supplied with a self-dual connection on a four
dimensional hyperk\"ahler manifold. The construction is based on the harmonic
twistor formalism. Remarkably, the resulted expression for the fourth order
transgression is given in terms of the determinant of the
$\bar{\partial}$-operator defined on fibers of the twistor fibration.Comment: 10pp., Late

### The matreoshka of supersymmetric self-dual theories

Extended super self-dual systems have a structure reminiscent of a
``matreoshka''. For instance, solutions for N=0 are embedded in solutions for
N=1, which are in turn embedded in solutions for N=2, and so on. Consequences
of this phenomenon are explored. In particular, we present an explicit
construction of local solutions of the higher-N super self-duality equations
starting from any N=0 self-dual solution. Our construction uses N=0 solution
data to produce N=1 solution data, which in turn yields N=2 solution data, and
so on; each stage introducing a dependence of the solution on sufficiently many
additional arbitrary functions to yield the most general supersymmetric
solution having the initial N=0 solution as the helicity +1 component. The
problem of finding the general local solution of the $N>0$ super self-duality
equations therefore reduces to finding the general solution of the usual (N=0)
self-duality equations. Another consequence of the matreoshka phenomenon is the
vanishing of many conserved currents, including the supercurrents, for super
self-dual systems.Comment: 19 pages, Bonn-HE-93-2

### Supersymmetric sigma models and the 't Hooft instantons

Witten's linear sigma model for ADHM instantons possesses a natural $(0,4)$
supersymmetry. We study generalizations of the infrared limit of the model that
are invariant under $(4,4)$ supersymmetry. In the case of four space-time
dimensions a background with a conformally flat metric and torsion is required.
The geometry is specified by a single real scalar function satisfying Laplace's
equation. It gives rise to 't Hooft instantons for the gauge group $SU(2)$,
instead of the general ADHM instantons for an $SO(n)$ gauge group in the case
$(0,4)$.Comment: 11 pages, Latex fil

### Covariant Harmonic Supergraphity for N = 2 Super Yang--Mills Theories

We review the background field method for general N = 2 super Yang-Mills
theories formulated in the N = 2 harmonic superspace. The covariant harmonic
supergraph technique is then applied to rigorously prove the N=2
non-renormalization theorem as well as to compute the holomorphic low-energy
action for the N = 2 SU(2) pure super Yang-Mills theory and the leading
non-holomorphic low-energy correction for N = 4 SU(2) super Yang-Mills theory.Comment: 17 pages, LAMUPHYS LaTeX, no figures; based on talks given by I.
Buchbinder and S. Kuzenko at the International Seminar ``Supersymmetries and
Quantum Symmetries'', July 1997, Dubna; to be published in the proceeding

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