21 research outputs found
Generalized N = 2 Super Landau Models
We generalize previous results for the superplane Landau model to exhibit an
explicit worldline N = 2 supersymmetry for an arbitrary magnetic field on any
two-dimensional manifold. Starting from an off-shell N = 2 superfield
formalism, we discuss the quantization procedure in the general case
characterized by two independent potentials on the manifold and show that the
relevant Hamiltonians are factorizable. In the restricted case when both the
Gauss curvature and the magnetic field are constant over the manifold and, as a
consequence, the underlying potentials are related, the Hamiltonians admit
infinite series of factorization chains implying the integrability of the
associated systems. We explicitly determine the spectrum and eigenvectors for
the particular model with CP^1 as the bosonic manifold.Comment: 26 page
Modifying the Sum Over Topological Sectors and Constraints on Supergravity
The standard lore about the sum over topological sectors in quantum field
theory is that locality and cluster decomposition uniquely determine the sum
over such sectors, thus leading to the usual theta-vacua. We show that without
changing the local degrees of freedom, a theory can be modified such that the
sum over instantons should be restricted; e.g. one should include only
instanton numbers which are divisible by some integer p. This conclusion about
the configuration space of quantum field theory allows us to carefully
reconsider the quantization of parameters in supergravity. In particular, we
show that FI-terms and nontrivial Kahler forms are quantized. This analysis
also leads to a new derivation of recent results about linearized supergravity.Comment: 17 pages, minor change
Variant supercurrent multiplets
In N = 1 rigid supersymmetric theories, there exist three standard
realizations of the supercurrent multiplet corresponding to the (i) old
minimal, (ii) new minimal and (iii) non-minimal off-shell formulations for N =
1 supergravity. Recently, Komargodski and Seiberg in arXiv:1002.2228 put
forward a new supercurrent and proved its consistency, although in the past it
was believed not to exist. In this paper, three new variant supercurrent
multiplets are proposed. Implications for supergravity-matter systems are
discussed.Comment: 11 pages; V2: minor changes in sect. 3; V3: published version; V4:
typos in eq. (2.3) corrected; V5: comments and references adde
Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity
We analyze various supersymmetry multiplets containing the supercurrent and
the energy-momentum tensor. The most widely known such multiplet, the
Ferrara-Zumino (FZ) multiplet, is not always well-defined. This can happen once
Fayet-Iliopoulos (FI) terms are present or when the Kahler form of the target
space is not exact. We present a new multiplet S which always exists. This
understanding of the supersymmetry current allows us to obtain new results
about the possible IR behavior of supersymmetric theories. Next, we discuss the
coupling of rigid supersymmetric theories to supergravity. When the theory has
an FZ-multiplet or it has a global R-symmetry the standard formalism can be
used. But when this is not the case such simple gauging is impossible. Then, we
must gauge the current S. The resulting theory has, in addition to the graviton
and the gravitino, another massless chiral superfield Phi which is essential
for the consistency of the theory. Some of the moduli of various string models
play the role of Phi. Our general considerations, which are based on the
consistency of supergravity, show that such moduli cannot be easily lifted thus
leading to constraints on gravity/string models.Comment: 27 pages. v2: references added and minor changes. v3: minor changes.
v4: minor clarification
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
Goldstino superfields for spontaneously broken N=2 supersymmetry
We examine spontaneously broken N=2 supersymmetry in four dimensions and
associate a spinor superfield with each Goldstino via a finite supersymmetry
transformation with parameters that are the Grassmann coordinates of N=2
superspace. Making use of a special choice of coset parametrization allows us
to develop a version of nonlinearly realized N=2 supersymmetry for which the
associated Goldstino superfields are defined on harmonic superspace, thereby
providing a natural mechanism for construction of a Goldstino action. The
corresponding superfield Lagrangian is an O(4) multiplet. This property is used
to reformulate the Goldstino action in projective superspace and in
conventional N=2 superspace. We show how to generate matter couplings of the
Goldstinos to supersymmetric matter using the N=2 harmonic, projective and full
superspaces. As a bi-product of our consideration, we also derive an N=2 chiral
Goldstino action.Comment: 20 pages, typos corrected, comments adde