143 research outputs found
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
Six-dimensional Supergravity and Projective Superfields
We propose a superspace formulation of N=(1,0) conformal supergravity in six
dimensions. The corresponding superspace constraints are invariant under
super-Weyl transformations generated by a real scalar parameter. The known
variant Weyl super-multiplet is recovered by coupling the geometry to a
super-3-form tensor multiplet. Isotwistor variables are introduced and used to
define projective superfields. We formulate a locally supersymmetric and
super-Weyl invariant action principle in projective superspace. Some families
of dynamical supergravity-matter systems are presented.Comment: 39 pages; v3: some modifications in section 2; equations (2.3),
(2.14b), (2.16) and (2.17) correcte
The linear multiplet and ectoplasm
In the framework of the superconformal tensor calculus for 4D N=2
supergravity, locally supersymmetric actions are often constructed using the
linear multiplet. We provide a superform formulation for the linear multiplet
and derive the corresponding action functional using the ectoplasm method (also
known as the superform approach to the construction of supersymmetric
invariants). We propose a new locally supersymmetric action which makes use of
a deformed linear multiplet. The novel feature of this multiplet is that it
corresponds to the case of a gauged central charge using a one-form potential
not annihilated by the central charge (unlike the standard N=2 vector
multiplet). Such a gauge one-form can be chosen to describe a variant nonlinear
vector-tensor multiplet. As a byproduct of our construction, we also find a
variant realization of the tensor multiplet in supergravity where one of the
auxiliaries is replaced by the field strength of a gauge three-form.Comment: 31 pages; v3: minor corrections and typos fixed, version to appear in
JHE
From correlation functions to scattering amplitudes
We study the correlators of half-BPS protected operators in N=4
super-Yang-Mills theory, in the limit where the positions of the adjacent
operators become light-like separated. We compute the loop corrections by means
of Lagrangian insertions. The divergences resulting from the light-cone limit
are regularized by changing the dimension of the integration measure over the
insertion points. Switching from coordinates to dual momenta, we show that the
logarithm of the correlator is identical with twice the logarithm of the
matching MHV gluon scattering amplitude. We present a number of examples of
this new relation, at one and two loops.Comment: typos corrected, references adde
On duality symmetries of supergravity invariants
The role of duality symmetries in the construction of counterterms for
maximal supergravity theories is discussed in a field-theoretic context from
different points of view. These are: dimensional reduction, the question of
whether appropriate superspace measures exist and information about non-linear
invariants that can be gleaned from linearised ones. The former allows us to
prove that F-term counterterms cannot be E7(7)-invariant in D=4, N=8
supergravity or E6(6)-invariant in D=5 maximal supergravity. This is confirmed
by the two other methods which can also be applied to D=4 theories with fewer
supersymmetries and allow us to prove that N=6 supergravity is finite at three
and four loops and that N=5 supergravity is three-loop finite.Comment: Clarification of arguments and their consistency with higher
dimensional divergences added, e.g. we prove the 5D 4L non-renormalisation
theorem. The 4L N=6 divergence is also ruled out. References adde
N = 2 supersymmetric sigma-models and duality
For two families of four-dimensional off-shell N = 2 supersymmetric nonlinear
sigma-models constructed originally in projective superspace, we develop their
formulation in terms of N = 1 chiral superfields. Specifically, these theories
are: (i) sigma-models on cotangent bundles T*M of arbitrary real analytic
Kaehler manifolds M; (ii) general superconformal sigma-models described by
weight-one polar supermultiplets. Using superspace techniques, we obtain a
universal expression for the holomorphic symplectic two-form \omega^{(2,0)}
which determines the second supersymmetry transformation and is associated with
the two complex structures of the hyperkaehler space T*M that are complimentary
to the one induced from M. This two-form is shown to coincide with the
canonical holomorphic symplectic structure. In the case (ii), we demonstrate
that \omega^{(2,0)} and the homothetic conformal Killing vector determine the
explicit form of the superconformal transformations. At the heart of our
construction is the duality (generalized Legendre transform) between off-shell
N = 2 supersymmetric nonlinear sigma-models and their on-shell N = 1 chiral
realizations. We finally present the most general N = 2 superconformal
nonlinear sigma-model formulated in terms of N = 1 chiral superfields. The
approach developed can naturally be generalized in order to describe 5D and 6D
superconformal nonlinear sigma-models in 4D N = 1 superspace.Comment: 31 pages, no figures; V2: reference and comments added, typos
corrected; V3: more typos corrected, published versio
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
Bi-harmonic superspace for N=4 d=4 super Yang-Mills
We develop N=4 d=4 bi-harmonic superspace and use it to derive a novel form
for the low-energy effective action in N=4 super Yang-Mills theory. We solve
the N=4 supergauge constraints in this superspace in terms of analytic
superfields. Using these superfields, we construct a simple functional that
respects N=4 supersymmetry and scale invariance. In components, it reproduces
all on-shell terms in the four-derivative part of the N=4 SYM effective action;
in particular, the F^4/X^4 and Wess-Zumino terms. The latter comes out in a
novel SO(3) x SO(3)-invariant form.Comment: 1+19 pages; minor corrections, references adde
N=2 Conformal Superspace in Four Dimensions
We develop the geometry of four dimensional N=2 superspace where the entire
conformal algebra of SU(2,2|2) is realized linearly in the structure group
rather than just the SL(2,C) x U(2)_R subgroup of Lorentz and R-symmetries,
extending to N=2 our prior result for N=1 superspace. This formulation
explicitly lifts to superspace the existing methods of the N=2 superconformal
tensor calculus; at the same time the geometry, when degauged to SL(2,C) x
U(2)_R, reproduces the existing formulation of N=2 conformal supergravity
constructed by Howe.Comment: 43 pages; v2 references added, acknowledgments update
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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