34 research outputs found
On supersymmetry breaking and the Dijkgraaf-Vafa conjecture
We investigate the Dijkgraaf-Vafa proposal when supersymmetry is broken. We
consider U(N) SYM with chiral adjoint matter where the coupling constants in
the tree-level superpotential are promoted to chiral spurions. The holomorphic
part of the low-energy glueball superpotential can still be analyzed. We
compute the holomorphic supersymmetry breaking contributions using methods of
the geometry underlying the N=1 effective gauge theory viewed as a Whitham
system. We also study the change in the effective glueball superpotential using
perturbative supergraph techniques in the presence of spurions.Comment: 24 pages, LaTeX; minor changes, one reference added, version to
appear in JHE
Chiral supergravity actions and superforms
The superform construction of supergravity actions, christened the "ectoplasm
method," is based on the use of a closed super d-form in the case of d
space-time dimensions. In known examples, such superforms are obtained by
iteratively solving nontrivial cohomological problems. The latter usually makes
this scheme no less laborious than the normal coordinate method for deriving
component actions for matter-coupled supergravity. In this note we present an
alternative procedure to generate required superforms in four space-time
dimensions, which makes use of self-dual vector multiplets. It provides the
shortest derivation of chiral actions in two different theories: (i) N = 1 old
minimal supergravity; and (ii) N = 2 conformal supergravity. The N = 2
superform construction is developed here for the first time. Although our
consideration is restricted to the case of four dimensions, a generalization to
higher dimensions is plausible.Comment: 14 pages; V2: minor correction
Covariant superspace approaches to supergravity
We provide a unified description of the three covariant superspace approaches
to conformal supergravity in four dimensions: (i) conformal
superspace; (ii) superspace; and (iii)
superspace. Each of them can be used to formulate general supergravity-matter
systems, although conformal superspace has the largest structure group and is
intimately related to the superconformal tensor calculus. We review the
structure of covariant projective multiplets and demonstrate how they are used
to describe pure and matter-coupled supergravity, including locally
superconformal off-shell sigma models. Higher-derivative invariants,
topological invariants and super-Weyl anomalies are also briefly discussed.Comment: 58 pages. Invited chapter for the "Handbook of Quantum Gravity" (Eds.
C. Bambi, L. Modesto and I.L. Shapiro, Springer, expected in 2023
4D N = 2 Supergravity and Projective Superspace
This paper presents a projective superspace formulation for 4D N = 2
matter-coupled supergravity. We first describe a variant superspace realization
for the N = 2 Weyl multiplet. It differs from that proposed by Howe in 1982 by
the choice of the structure group (SO(3,1) x SU(2) versus SO(3,1) x U(2)),
which implies that the super-Weyl transformations are generated by a
covariantly chiral parameter instead of a real unconstrained one. We introduce
various off-shell supermultiplets which are curved superspace analogues of the
superconformal projective multiplets in global supersymmetry and which describe
matter fields coupled to supergravity. A manifestly locally supersymmetric and
super-Weyl invariant action principle is given. Off-shell locally
supersymmetric nonlinear sigma models are presented in this new superspace.Comment: 26 pages, LaTeX, no figures; V2: comments and references added,
version published in JHEP; V3: typo in eq. (2.7e) correcte
Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
Using N=2 superspace techniques we compute the four-loop spectrum of single
trace operators in the SU(2) x SU(2) sector of ABJM and ABJ supersymmetric
Chern-Simons theories. Our computation yields a four-loop contribution to the
function h^2(\lambda) (and its ABJ generalization) in the magnon dispersion
relation which has fixed maximum transcendentality and coincides with the
findings in components given in the revised versions of arXiv:0908.2463 and
arXiv:0912.3460. We also discuss possible scenarios for an all-loop function
h^2(\lambda) that interpolates between weak and strong couplings.Comment: LaTeX, feynmp, 34 pages; v2: typos corrected, formulations improved,
references adde
Ectoplasm & Superspace Integration Measure for 2D Supergravity with Four Spinorial Supercurrents
Building on a previous derivation of the local chiral projector for a two
dimensional superspace with eight real supercharges, we provide the complete
density projection formula required for locally supersymmetrical theories in
this context. The derivation of this result is shown to be very efficient using
techniques based on the Ectoplasmic construction of local measures in
superspace.Comment: 18 pages, LaTeX; V2: minor changes, typos corrected, references
added; V3: version to appear in J. Phys. A: Math. Theor., some comments and
references added to address a referee reques
A Derivation of an Off-Shell N = (2,2) Supergravity Chiral Projection Operator
Utilizing the known off-shell formulation of 2D, N = (2,2) supergravity,
containing a finite number of auxiliary fields, there is shown to exist a
simple form for a 'chiral projection operator' and an explicit expression for
it is given.Comment: 10 pages, no figures, one new reference adde
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
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
On conformal supergravity and projective superspace
The projective superspace formulation for four-dimensional N = 2
matter-coupled supergravity presented in arXiv:0805.4683 makes use of the
variant superspace realization for the N = 2 Weyl multiplet in which the
structure group is SL(2,C) x SU(2) and the super-Weyl transformations are
generated by a covariantly chiral parameter. An extension to Howe's realization
of N = 2 conformal supergravity in which the tangent space group is SL(2,C) x
U(2) and the super-Weyl transformations are generated by a real unconstrained
parameter was briefly sketched. Here we give the explicit details of the
extension.Comment: 17 pages, no figure; V2: comments and references added, published
versio