392 research outputs found
On Topologically Massive Spin-2 Gauge Theories beyond Three Dimensions
We investigate in which sense, at the linearized level, one can extend the 3D
topologically massive gravity theory beyond three dimensions. We show that, for
each k=1,2,3... a free topologically massive gauge theory in 4k-1 dimensions
can be defined describing a massive "spin-2" particle provided one uses a
non-standard representation of the massive "spin-2" state which makes use of a
two-column Young tableau where each column is of height 2k-1. We work out the
case of k=2, i.e. 7D, and show, by canonical analysis, that the model
describes, unitarily, 35 massive "spin-2" degrees of freedom. The issue of
interactions is discussed and compared with the three-dimensional situation.Comment: 14 pages. v2: minor changes - published versio
The general gaugings of maximal d=9 supergravity
We use the embedding tensor method to construct the most general maximal
gauged/massive supergravity in d=9 dimensions and to determine its extended
field content. Only the 8 independent deformation parameters (embedding tensor
components, mass parameters etc.) identified by Bergshoeff \textit{et al.} (an
SL(2,R) triplet, two doublets and a singlet can be consistently introduced in
the theory, but their simultaneous use is subject to a number of quadratic
constraints. These constraints have to be kept and enforced because they cannot
be used to solve some deformation parameters in terms of the rest. The
deformation parameters are associated to the possible 8-forms of the theory,
and the constraints are associated to the 9-forms, all of them transforming in
the conjugate representations. We also give the field strengths and the gauge
and supersymmetry transformations for the electric fields in the most general
case. We compare these results with the predictions of the E11 approach,
finding that the latter predicts one additional doublet of 9-forms, analogously
to what happens in N=2, d=4,5,6 theories.Comment: Latex file, 43 pages, reference adde
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
Sigma models with off-shell N=(4,4) supersymmetry and noncommuting complex structures
We describe the conditions for extra supersymmetry in N=(2,2) supersymmetric
nonlinear sigma models written in terms of semichiral superfields. We find that
some of these models have additional off-shell supersymmetry. The (4,4)
supersymmetry introduces geometrical structures on the target-space which are
conveniently described in terms of Yano f-structures and Magri-Morosi
concomitants. On-shell, we relate the new structures to the known
bi-hypercomplex structures.Comment: 20 pages; v2: significant corrections, clarifications, and
reorganization; v3: discussion of supersymmetry vs twisted supersymmetry
added, relevant signs corrected
N=2 supergravity and supercurrents
We address the problem of classifying all N=2 supercurrent multiplets in four
space-time dimensions. For this purpose we consider the minimal formulation of
N=2 Poincare supergravity with a tensor compensator, and derive its linearized
action in terms of three N=2 off-shell multiplets: an unconstrained scalar
superfield, a vector multiplet, and a tensor multiplet. Such an action was
ruled out to exist in the past. Using the action constructed, one can derive
other models for linearized N=2 supergravity by applying N=2 superfield duality
transformations. The action depends parametrically on a constant non-vanishing
real isotriplet g^{ij}=g^{ji} which originates as an expectation value of the
tensor compensator. Upon reduction to N=1 superfields, we show that the model
describes two dually equivalent formulations for the massless multiplet
(1,3/2)+(3/2,2) depending on a choice of g^{ij}. In the case g^{11}=g^{22}=0,
the action describes (i) new minimal N=1 supergravity; and (ii) the
Fradkin-Vasiliev-de Wit-van Holten gravitino multiplet. In the case g^{12}=0,
on the other hand, the action describes (i) old minimal N=1 supergravity; and
(ii) the Ogievetsky-Sokatchev gravitino multiplet.Comment: 40 pages; v2: added references, some comments, new appendi
Rigid Supersymmetric Theories in Curved Superspace
We present a uniform treatment of rigid supersymmetric field theories in a
curved spacetime , focusing on four-dimensional theories with four
supercharges. Our discussion is significantly simpler than earlier treatments,
because we use classical background values of the auxiliary fields in the
supergravity multiplet. We demonstrate our procedure using several examples.
For we reproduce the known results in the literature. A
supersymmetric Lagrangian for exists, but unless the
field theory is conformal, it is not reflection positive. We derive the
Lagrangian for and note that the
time direction can be rotated to Euclidean signature and be
compactified to only when the theory has a continuous R-symmetry. The
partition function on is independent of
the parameters of the flat space theory and depends holomorphically on some
complex background gauge fields. We also consider R-invariant
theories on and clarify a few points about them.Comment: 26 pages, uses harvmac; v2 with added reference
Off-shell superconformal nonlinear sigma-models in three dimensions
We develop superspace techniques to construct general off-shell N=1,2,3,4
superconformal sigma-models in three space-time dimensions. The most general
N=3 and N=4 superconformal sigma-models are constructed in terms of N=2 chiral
superfields. Several superspace proofs of the folklore statement that N=3
supersymmetry implies N=4 are presented both in the on-shell and off-shell
settings. We also elaborate on (super)twistor realisations for (super)manifolds
on which the three-dimensional N-extended superconformal groups act
transitively and which include Minkowski space as a subspace.Comment: 67 pages; V2: typos corrected, one reference added, version to appear
on JHE
N=8 Superspace Constraints for Three-dimensional Gauge Theories
We present a systematic analysis of the N=8 superspace constraints in three
space-time dimensions. The general coupling between vector and scalar
supermultiplets is encoded in an SO(8) tensor W_{AB} which is a function of the
matter fields and subject to a set of algebraic and super-differential
relations. We show how the conformal BLG model as well as three-dimensional
super Yang-Mills theory provide solutions to these constraints and can both be
formulated in this universal framework.Comment: 34 + 10 pages; added references, minor correction
Effective action of three-dimensional extended supersymmetric matter on gauge superfield background
We study the low-energy effective actions for gauge superfields induced by
quantum N=2 and N=4 supersymmetric matter fields in three-dimensional Minkowski
space. Analyzing the superconformal invariants in the N=2 superspace we propose
a general form of the N=2 gauge invariant and superconformal effective action.
The leading terms in this action are fixed by the symmetry up to the
coefficients while the higher order terms with respect to the Maxwell field
strength are found up to one arbitrary function of quasi-primary N=2
superfields constructed from the superfield strength and its covariant spinor
derivatives. Then we find this function and the coefficients by direct quantum
computations in the N=2 superspace. The effective action of N=4 gauge multiplet
is obtained by generalizing the N=2 effective action.Comment: 1+27 pages; v2: minor corrections, references adde
Off-shell supergravity-matter couplings in three dimensions
We develop the superspace geometry of N-extended conformal supergravity in
three space-time dimensions. General off-shell supergravity-matter couplings
are constructed in the cases N=1,2,3,4.Comment: 73 pages; V5: typos in eqs. (3.4b), (3.17) and (4.24) correcte
- âŠ