353 research outputs found
Topics in 3D N=2 AdS supergravity in superspace
We review some recent results on the construction in superspace of 3D N=2 AdS
supergravities and on the formulation of rigid supersymmetric theories in (1,1)
and (2,0) AdS superspaces.Comment: 6 pages, Contribution to the proceedings of the "XVII European
Workshop on String Theory 2011", Padova, Italy, 5-9 September 2011; to appear
in Fortschritte der Physi
Field theory in 4D N=2 conformally flat superspace
Building on the superspace formulation for four-dimensional N=2
matter-coupled supergravity developed in arXiv:0805.4683, we elaborate upon a
general setting for field theory in N=2 conformally flat superspaces, and
concentrate specifically on the case of anti-de Sitter (AdS) superspace. We
demonstrate, in particular, that associated with the N=2 AdS supergeometry is a
unique vector multiplet such that the corresponding covariantly chiral field
strength W_0 is constant, W_0=1. This multiplet proves to be intrinsic in the
sense that it encodes all the information about the N=2 AdS supergeometry in a
conformally flat frame. Moreover, it emerges as a building block in the
construction of various supersymmetric actions. Such a vector multiplet, which
can be identified with one of the two compensators of N=2 supergravity, also
naturally occurs for arbitrary conformally flat superspaces. An explicit
superspace reduction N=2 to N=1 is performed for the action principle in
general conformally flat N=2 backgrounds, and examples of such reduction are
given.Comment: 48 pages, LaTex, no figures; V2: typos corrected, eq. (4.50), (4.57)
and (4.63a) modifie
Conformally flat supergeometry in five dimensions
Using the superspace formulation for the 5D N = 1 Weyl supermultiplet
developed in arXiv:0802.3953, we elaborate the concept of conformally flat
superspace in five dimensions. For a large family of supersymmetric theories
(including sigma-models and Yang-Mills theories) in the conformally flat
superspace, we describe an explicit procedure to formulate their dynamics in
terms of rigid 4D N = 1 superfields. The case of 5D N = 1 anti-de Sitter
superspace is discussed as an example.Comment: 16 pages, no figures; V2: typos corrected, comments added; V3: typo
in eq. (79) correcte
N=4 supersymmetric Yang-Mills theories in AdS_3
For all types of N=4 anti-de Sitter (AdS) supersymmetry in three dimensions,
we construct manifestly supersymmetric actions for Abelian vector multiplets
and explain how to extend the construction to the non-Abelian case. Manifestly
N=4 supersymmetric Yang-Mills (SYM) actions are explicitly given in the cases
of (2,2) and critical (4,0) AdS supersymmetries. The N=4 vector multiplets and
the corresponding actions are then reduced to (2,0) AdS superspace, in which
only N=2 supersymmetry is manifest. Using the off-shell structure of the N=4
vector multiplets, we provide complete N=4 SYM actions in (2,0) AdS superspace
for all types of N=4 AdS supersymmetry. In the case of (4,0) AdS supersymmetry,
which admits a Euclidean counterpart, the resulting N=2 action contains a
Chern-Simons term proportional to q/r, where r is the radius of AdS_3 and q is
the R-charge of a chiral scalar superfield. The R-charge is a linear
inhomogeneous function of X, an expectation value of the N=4 Cotton superfield.
Thus our results explain the mysterious structure of N=4 supersymmetric
Yang-Mills theories on S^3 discovered in arXiv:1401.7952. In the case of (3,1)
AdS supersymmetry, which has no Euclidean counterpart, the SYM action contains
both a Chern-Simons term and a chiral mass-like term. In the case of (2,2) AdS
supersymmetry, which admits a Euclidean counterpart, the SYM action has no
Chern-Simons and chiral mass-like terms.Comment: 45 pages; V3: minor corrections, version published in JHE
New nilpotent superfields
We propose new off-shell models for spontaneously broken local
supersymmetry, in which the supergravity multiplet couples to nilpotent
Goldstino superfields that contain either a gauge one-form or a gauge two-form
in addition to spin-1/2 Goldstone fermions and auxiliary fields. In the case of
Poincar\'e supersymmetry, we elaborate on the concept of twisted
chiral superfields and present a nilpotent superfield that
underlies the cubic nilpotency conditions given in arXiv:1707.03414 in terms of
constrained superfields.Comment: 20 pages; V3: typos correcte
Higher derivative couplings and massive supergravity in three dimensions
We develop geometric superspace settings to construct arbitrary higher
derivative couplings (including R^n terms) in three-dimensional supergravity
theories with N=1,2,3 by realising them as conformal supergravity coupled to
certain compensators. For all known off-shell supergravity formulations, we
construct supersymmetric invariants with up to and including four derivatives.
As a warming-up exercise, we first give a new and completely geometric
derivation of such invariants in N=1 supergravity. Upon reduction to
components, they agree with those given in arXiv:0907.4658 and arXiv:1005.3952.
We then carry out a similar construction in the case of N=2 supergravity for
which there exist two minimal formulations that differ by the choice of
compensating multiplet: (i) a chiral scalar multipet; (ii) a vector multiplet.
For these formulations all four derivative invariants are constructed in
completely general and gauge independent form. For a general supergravity model
(in the N=1 and minimal N=2 cases) with curvature-squared and lower order
terms, we derive the superfield equations of motion, linearise them about
maximally supersymmetric backgrounds and obtain restrictions on the parameters
that lead to models for massive supergravity. We use the non-minimal
formulation for N = 2 supergravity (which corresponds to a complex linear
compensator) to construct a novel consistent theory of massive supergravity. In
the case of N = 3 supergravity, we employ the off-shell formulation with a
vector multiplet as compensator to construct for the first time various higher
derivative invariants. These invariants may be used to derive models for N = 3
massive supergravity. As a bi-product of our analysis, we also present
superfield equations for massive higher spin multiplets in (1,0), (1,1) and
(2,0) anti-de Sitter superspaces.Comment: 84 pages; V3: references added, minor modifications, published
versio
deformations with supersymmetry
We investigate the behaviour of two-dimensional quantum field theories with
supersymmetry under a deformation induced by the
`' composite operator. We show that the deforming operator can be
defined by a point-splitting regularisation in such a way as to preserve
supersymmetry. As an example of this construction, we work
out the deformation of a free theory and compare to that
induced by the Noether stress-energy tensor. Finally, we show that the
supersymmetric deformed action actually possesses
symmetry, half of which is non-linearly realised
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