2,298 research outputs found

### 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

### 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

### 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

### 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

### 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

### N=4, 3D Supersymmetric Quantum Mechanics in Non-Abelian Monopole Background

Using the harmonic superspace approach, we construct the three-dimensional
N=4 supersymmetric quantum mechanics of the supermultiplet (3,4,1) coupled to
an external SU(2) gauge field. The off-shell N=4 supersymmetry requires the
gauge field to be a static form of the 't Hooft ansatz for the 4D self-dual
SU(2) gauge fields, that is a particular solution of Bogomolny equations for
BPS monopoles. We present the explicit form of the corresponding superfield and
component actions, as well as of the quantum Hamiltonian and N=4 supercharges.
The latter can be used to describe a more general N=4 mechanics system, with an
arbitrary BPS monopole background and on-shell N=4 supersymmetry. The essential
feature of our construction is the use of semi-dynamical spin (4,4,0) multiplet
with the Wess-Zumino type action.Comment: 16 pages, reference added, published versio

### Relating harmonic and projective descriptions of N=2 nonlinear sigma models

Recent papers have established the relationship between projective superspace
and a complexified version of harmonic superspace. We extend this construction
to the case of general nonlinear sigma models in both frameworks. Using an
analogy with Hamiltonian mechanics, we demonstrate how the Hamiltonian
structure of the harmonic action and the symplectic structure of the projective
action naturally arise from a single unifying action on a complexified version
of harmonic superspace. This links the harmonic and projective descriptions of
hyperkahler target spaces. For the two examples of Taub-NUT and Eguchi-Hanson,
we show how to derive the projective superspace solutions from the harmonic
superspace solutions.Comment: 25 pages; v3: typo fixed in eq (1.36

### On pseudo-hyperk\"ahler prepotentials

An explicit surjection from a set of (locally defined) unconstrained
holomorphic functions on a certain submanifold of (Sp_1(C) \times C^{4n}) onto
the set HK_{p,q} of local isometry classes of real analytic
pseudo-hyperk\"ahler metrics of signature (4p,4q) in dimension 4n is
constructed. The holomorphic functions, called prepotentials, are analogues of
K\"ahler potentials for K\"ahler metrics and provide a complete
parameterisation of HK_{p,q}. In particular, there exists a bijection between
HK_{p,q} and the set of equivalence classes of prepotentials. This affords the
explicit construction of pseudo-hyperk\"ahler metrics from specified
prepotentials. The construction generalises one due to Galperin, Ivanov,
Ogievetsky and Sokatchev. Their work is given a coordinate-free formulation and
complete, self-contained proofs are provided. An appendix provides a vital tool
for this construction: a reformulation of real analytic G-structures in terms
of holomorphic frame fields on complex manifolds.Comment: 53 pages; v2: minor amendments to Def.4.1 and Theorem 4.5; a
paragraph inserted in the proof of the latter; V3: minor changes; V4: minor
changes/ typos corrected for journal versio

### Harmonic space and quaternionic manifolds

We find a principle of harmonic analyticity underlying the quaternionic
(quaternion-K\"ahler) geometry and solve the differential constraints which
define this geometry. To this end the original $4n$-dimensional quaternionic
manifold is extended to a bi-harmonic space. The latter includes additional
harmonic coordinates associated with both the tangent local $Sp(1)$ group and
an extra rigid $SU(2)$ group rotating the complex structures. Then the
constraints can be rewritten as integrability conditions for the existence of
an analytic subspace in the bi-harmonic space and solved in terms of two
unconstrained potentials on the analytic subspace. Geometrically, the
potentials have the meaning of vielbeins associated with the harmonic
coordinates. We also establish a one-to-one correspondence between the
quaternionic spaces and off-shell $N=2$ supersymmetric sigma-models coupled to
$N=2$ supergravity. The general $N=2$ sigma-model Lagrangian when written in
the harmonic superspace is composed of the quaternionic potentials. Coordinates
of the analytic subspace are identified with superfields describing $N=2$
matter hypermultiplets and a compensating hypermultiplet of $N=2$ supergravity.
As an illustration we present the potentials for the symmetric quaternionic
spaces.Comment: 44 pages, LATEX, JHU-TIPAC-920023, ENSLAPP-L-405-92, MPI-Ph/92-8

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