1,547 research outputs found
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
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
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
Supersymmetric sigma models and the 't Hooft instantons
Witten's linear sigma model for ADHM instantons possesses a natural
supersymmetry. We study generalizations of the infrared limit of the model that
are invariant under 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 ,
instead of the general ADHM instantons for an gauge group in the case
.Comment: 11 pages, Latex fil
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
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
SU(2) reduction in N=4 supersymmetric mechanics
We perform an su(2) Hamiltonian reduction of the general su(2)-invariant
action for a self-coupled (4,4,0) supermultiplet. As a result, we elegantly
recover the N=4 supersymmetric mechanics with spin degrees of freedom which was
recently constructed in arXiv:0812.4276. This observation underscores the
exceptional role played by the ``root'' supermultiplet in N=4 supersymmetric
mechanics.Comment: 1+3 page
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 Projective Hoops: Loops in Hyperspace
We (re)derive the propagators and Feynman rules for the massless scalar and
vector multiplets in N=2 Projective Superspace ('Projective Hyperspace'). With
these, we are able to calculate both the divergent and finite parts of 2, 3 &
4-point functions at 1-loop for N=2 Super-Yang-Mills theory (SYM) explicitly in
Projective Hyperspace itself. We find that effectively only the coupling
constant needs to be renormalized unlike in the N=1 case where an independent
wavefunction renormalization is also required. This feature is similar to that
of the background field gauge, even though we are using ordinary Fermi-Feynman
gauge. The computation of 1-hoop beta-function is then straightforward and
matches with the known result. We also show that it receives no 2-hoops
contributions. All these calculations provide an alternative proof of the
finiteness of N=4 SYM.Comment: 29 pages, 12 figures; Added a reference & modified introduction in v
Worldline Superfield Actions for N=2 Superparticles
We propose doubly supersymmetric actions in terms of n=2(D-2) worldline
superfields for N=2 superparticles in D=3,4 and Type IIA D=6 superspaces. These
actions are obtained by dimensional reduction of superfield actions for N=1
superparticles in D=4,6 and 10, respectively. We show that in all these models
geometrodynamical constraints on target superspace coordinates do not put the
theory on the mass shell, so the actions constructed consistently describe the
dynamics of the corresponding N=2 superparticles. We also find that in contrast
to the IIA D=6 superparticle a chiral IIB D=6 superparticle, which is not
obtainable by dimensional reduction from N=1, D=10, is described by superfield
constraints which produce dynamical equations. This implies that for the IIB
D=6 superparticle the doubly supersymmetric action does not exist in the
conventional form.Comment: Latex, 20 pp. Minor corrections, acknowledgements adde
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