370 research outputs found
Comments on N = 2 supersymmetric sigma models in projective superspace
For the most general off-shell N = 2 supersymmetric sigma model in projective
superspace, we elaborate on its formulation in terms of N = 1 chiral
superfields. A universal (model-independent) expression is obtained for the
holomorphic symplectic two-form, which determines the second supersymmetry
transformation. This two-form is associated with the two complex structures of
the hyperkahler target space, which are complimentary to the one used to
realize the target space as a Kahler manifold.Comment: 7 pages; V2: reference [18] correcte
Self-dual effective action of N = 4 SYM revisited
More evidence is provided for the conjectured correspondence between the
D3-brane action in AdS_5 x S^5 and the low-energy effective action for N = 4
SU(N) SYM on its Coulomb branch, where the gauge group SU(N) is spontaneously
broken to SU(N-1) x U(1) and the dynamics is described by a single N = 2 vector
multiplet corresponding to the U(1) factor of the unbroken group. Using an
off-shell formulation for N = 4 SYM in N = 2 harmonic superspace, within the
background-field quantization scheme we compute the two-loop quantum correction
to a holomorphic sector of the effective action, which is a supersymmetric
completion of interactions of the form \Omega ((F^+)^2 |Y|^{-4}) (F^+)^2(F^-)^2
|Y|^{-4}, with F^\pm the (anti) self-dual components of the U(1) gauge field
strength, and Y the complex scalar belonging to the vector multiplet. In the
one-loop approximation, \Omega was shown in hep-th/9911221 to be constant. It
is demonstrated in the present paper that \Omega \propto (F^+)^2 |Y|^{-4} at
the two-loop order. The corresponding coefficient proves to agree with the F^6
coefficient in the D3-brane action, after implementing the nonlinear field
redefinition which was sketched in hep-th/9810152 and which relates the N = 2
vector multiplet component fields with those living on the D3-brane. In the
approximation considered, our results are consistent with the conjecture of
hep-th/9810152 that the N = 4 SYM effective action is self-dual under N = 2
superfield Legendre transformation, and also with the stronger conjecture of
hep-th/0001068 that it is self-dual under supersymmetric U(1) duality
rotations.Comment: 0+37 pages, 1 figure, latex; V2: references, comments added; V3:
comments, references adde
The Real Anatomy of Complex Linear Superfields
Recent work on classicication of off-shell representations of N-extended
worldline supersymmetry without central charges has uncovered an unexpectedly
vast number--trillions of even just (chromo)topology types--of so called
adinkraic supermultiplets. Herein, we show by explicit analysis that a
long-known but rarely used representation, the complex linear supermultiplet,
is not adinkraic, cannot be decomposed locally, but may be reduced by means of
a Wess-Zumino type gauge. This then indicates that the already unexpectedly
vast number of adinkraic off-shell supersymmetry representations is but the
proverbial tip of the iceberg.Comment: 21 pages, 4 figure
On 2D N=(4,4) superspace supergravity
We review some recent results obtained in studying superspace formulations of
2D N=(4,4) matter-coupled supergravity. For a superspace geometry described by
the minimal supergravity multiplet, we first describe how to reduce to
components the chiral integral by using ``ectoplasm'' superform techniques as
in arXiv:0907.5264 and then we review the bi-projective superspace formalism
introduced in arXiv:0911.2546. After that, we elaborate on the curved
bi-projective formalism providing a new result: the solution of the covariant
type-I twisted multiplet constraints in terms of a weight-(-1,-1) bi-projective
superfield.Comment: 18 pages, LaTeX, Contribution to the proceedings of the International
Workshop "Supersymmetries and Quantum Symmetries" (SQS'09), Dubna, July
29-August 3 200
Conformal Invariance, N-extended Supersymmetry and Massless Spinning Particles in Anti-de Sitter Space
Starting with a manifestly conformal ( invariant) mechanics model in
space and 2 time dimensions, we derive the action for a massless spinning
particle in -dimensional anti-de Sitter space. The action obtained possesses
both gauge -extended worldline supersymmetry and local invarince.
Thus we improve the old statement by Howe et al. that the spinning particle
model with extended worldline supersymmetry admits only flat space-time
background for (spin greater one). The original -dimensional
model is characterized by rather unusual property that the corresponding
supersymmetry transformations do not commute with the conformal ones, in spite
of the explicit invariance of the action.Comment: 13 pages, LaTe
Self-dual supersymmetric nonlinear sigma models
In four-dimensional N=1 Minkowski superspace, general nonlinear sigma models
with four-dimensional target spaces may be realised in term of CCL (chiral and
complex linear) dynamical variables which consist of a chiral scalar, a complex
linear scalar and their conjugate superfields. Here we introduce CCL sigma
models that are invariant under U(1) "duality rotations" exchanging the
dynamical variables and their equations of motion. The Lagrangians of such
sigma models prove to obey a partial differential equation that is analogous to
the self-duality equation obeyed by U(1) duality invariant models for nonlinear
electrodynamics. These sigma models are self-dual under a Legendre
transformation that simultaneously dualises (i) the chiral multiplet into a
complex linear one; and (ii) the complex linear multiplet into a chiral one.
Any CCL sigma model possesses a dual formulation given in terms of two chiral
multiplets. The U(1) duality invariance of the CCL sigma model proves to be
equivalent, in the dual chiral formulation, to a manifest U(1) invariance
rotating the two chiral scalars. Since the target space has a holomorphic
Killing vector, the sigma model possesses a third formulation realised in terms
of a chiral multiplet and a tensor multiplet.
The family of U(1) duality invariant CCL sigma models includes a subset of
N=2 supersymmetric theories. Their target spaces are hyper Kahler manifolds
with a non-zero Killing vector field. In the case that the Killing vector field
is triholomorphic, the sigma model admits a dual formulation in terms of a
self-interacting off-shell N=2 tensor multiplet.
We also identify a subset of CCL sigma models which are in a one-to-one
correspondence with the U(1) duality invariant models for nonlinear
electrodynamics. The target space isometry group for these sigma models
contains a subgroup U(1) x U(1).Comment: 22 page
Three-dimensional (p,q) AdS superspaces and matter couplings
We introduce N-extended (p,q) AdS superspaces in three space-time dimensions,
with p+q=N and p>=q, and analyse their geometry. We show that all (p,q) AdS
superspaces with X^{IJKL}=0 are conformally flat. Nonlinear sigma-models with
(p,q) AdS supersymmetry exist for p+q4 the target space geometries
are highly restricted). Here we concentrate on studying off-shell N=3
supersymmetric sigma-models in AdS_3. For each of the cases (3,0) and (2,1), we
give three different realisations of the supersymmetric action. We show that
(3,0) AdS supersymmetry requires the sigma-model to be superconformal, and
hence the corresponding target space is a hyperkahler cone. In the case of
(2,1) AdS supersymmetry, the sigma-model target space must be a non-compact
hyperkahler manifold endowed with a Killing vector field which generates an
SO(2) group of rotations of the two-sphere of complex structures.Comment: 52 pages; V3: minor corrections, version published in JHE
Extended supersymmetric sigma models in AdS_4 from projective superspace
There exist two superspace approaches to describe N=2 supersymmetric
nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in
terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and
arXiv:1108.5290; and (ii) in terms of N=2 polar supermultiplets using the AdS
projective-superspace techniques developed in arXiv:0807.3368. The virtue of
the approach (i) is that it makes manifest the geometric properties of the N=2
supersymmetric sigma-models in AdS_4. The target space must be a non-compact
hyperkahler manifold endowed with a Killing vector field which generates an
SO(2) group of rotations on the two-sphere of complex structures. The power of
the approach (ii) is that it allows us, in principle, to generate hyperkahler
metrics as well as to address the problem of deformations of such metrics.
Here we show how to relate the formulation (ii) to (i) by integrating out an
infinite number of N=1 AdS auxiliary superfields and performing a superfield
duality transformation. We also develop a novel description of the most general
N=2 supersymmetric nonlinear sigma-model in AdS_4 in terms of chiral
superfields on three-dimensional N=2 flat superspace without central charge.
This superspace naturally originates from a conformally flat realization for
the four-dimensional N=2 AdS superspace that makes use of Poincare coordinates
for AdS_4. This novel formulation allows us to uncover several interesting
geometric results.Comment: 88 pages; v3: typos corrected, version published in JHE
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