245 research outputs found
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
Goldstino superfields in N=2 supergravity
We present off-shell N=2 supergravity actions, which exhibit spontaneously
broken local supersymmetry and allow for de Sitter vacua for certain values of
the parameters. They are obtained by coupling the standard N=2
supergravity-matter systems to the Goldstino superfields introduced in
arXiv:1105.3001 and arXiv:1607.01277 in the rigid supersymmetric case. These
N=2 Goldstino superfields include nilpotent chiral and linear supermultiplets.
We also describe a new reducible N=1 Goldstino supermultiplet.Comment: 40 pages; V2: minor corrections, references added, published versio
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
Effective action of beta-deformed N = 4 SYM theory: Farewell to two-loop BPS diagrams
Within the background field approach, all two-loop sunset vacuum diagrams,
which occur in the Coulomb branch of N = 2 superconformal theories(including N
= 4 SYM), obey the BPS condition m_3 = m_1 + m_2, where the masses are
generated by the scalars belonging to a background N = 2 vector multiplet.
These diagrams can be evaluated exactly, and prove to be homogeneous quadratic
functions of the one-loop tadpoles J(m_1^2), J(m_2^2) and J(m_3^2), with the
coefficients being rational functions of the squared masses. We demonstrate
that, if one switches on the beta-deformation of the N = 4 SYM theory, the BPS
condition no longer holds, and then generic two-loop sunset vacuum diagrams
with three non-vanishing masses prove to be characterized by the following
property: 2(m_1^2 m_2^2 +m_1^2 m_3^2 +m_2^2 m_3^2) > m_1^4 +m_2^4 +m_3^4. In
the literature, there exist several techniques to compute such diagrams. For
the beta-deformed N = 4 SYM theory, we carry out explicit two-loop calculations
of the Kahler potential and F^4 term. Our considerations are restricted to the
case of beta real.Comment: 42 pages, latex, 1 eps figure; V2: references adde
Superform formulation for vector-tensor multiplets in conformal supergravity
The recent papers arXiv:1110.0971 and arXiv:1201.5431 have provided a
superfield description for vector-tensor multiplets and their Chern-Simons
couplings in 4D N = 2 conformal supergravity. Here we develop a superform
formulation for these theories. Furthermore an alternative means of gauging the
central charge is given, making use of a deformed vector multiplet, which may
be thought of as a variant vector-tensor multiplet. Its Chern-Simons couplings
to additional vector multiplets are also constructed. This multiplet together
with its Chern-Simons couplings are new results not considered by de Wit et al.
in hep-th/9710212.Comment: 28 pages. V2: Typos corrected and references updated; V3: References
updated and typo correcte
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