Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe N=1 Supersymmetric Landau Problem and its Supersymmetric Landau Level Projections: the N=1 Supersymmetric Moyal-Voros Superplane
223
0
0.0
(
0
)
Authors
Joseph Ben Geloun
Ask ChatGPT about the research
No Arabic abstract
The N=1 supersymmetric invariant Landau problem is constructed and solved. By considering Landau level projections remaining non trivial under N=1 supersymmetry transformations, the algebraic structures of the N=1 supersymmetric covariant non(anti)commutative superplane analogue of the ordinary N=0 noncommutative Moyal-Voros plane are identified.
rate research
Read More
We analyze the component structure of models for 4D N = 1 supersymmetric nonlinear electrodynamics that enjoy invariance under continuous duality rotations. The N = 1 supersymmetric Born-Infeld action is a member of this family. Such dynamical systems have a more complicated structure, especially in the presence of supergravity, as compared with well-studied effective supersymmetric theories containing at most two derivatives (including nonlinear Kahler sigma-models). As a result, when deriving their canonically normalized component actions, it becomes impractical and cumbersome to follow the traditional approach of (i) reducing to components; and then (ii) applying a field-dependent Weyl and local chiral transformation. It proves to be more efficient to follow the Kugo-Uehara scheme which consists of (i) extending the superfield theory to a super-Weyl invariant system; and then (ii) applying a plain component reduction along with imposing a suitable super-Weyl gauge condition. Here we implement this scheme to derive the bosonic action of self-dual supersymmetric electrodynamics coupled to the dilaton-axion chiral multiplet and a Kahler sigma-model. In the fermionic sector, the action contains higher derivative terms. In the globally supersymmetric case, a nonlinear field redefinition is explicitly constructed which eliminates all the higher derivative terms and brings the fermionic action to a one-parameter deformation of the Akulov-Volkov action for the Goldstino. The Akulov-Volkov action emerges, in particular, in the case of the N = 1 supersymmetric Born-Infeld action.
We compute the supersymmetric partition function of $mathcal{N}{=}1$ supersymmetric gauge theories with an $R$-symmetry on $mathcal{M}_4 cong mathcal{M}_{g,p}times S^1$, a principal elliptic fiber bundle of degree $p$ over a genus-$g$ Riemann surface, $Sigma_g$. Equivalently, we compute the generalized supersymmetric index $I_{mathcal{M}_{g,p}}$, with the supersymmetric three-manifold ${mathcal{M}_{g,p}}$ as the spatial slice. The ordinary $mathcal{N}{=}1$ supersymmetric index on the round three-sphere is recovered as a special case. We approach this computation from the point of view of a topological $A$-model for the abelianized gauge fields on the base $Sigma_g$. This $A$-model---or $A$-twisted two-dimensional $mathcal{N}{=}(2,2)$ gauge theory---encodes all the information about the generalized indices, which are viewed as expectations values of some canonically-defined surface defects wrapped on $T^2$ inside $Sigma_g times T^2$. Being defined by compactification on the torus, the $A$-model also enjoys natural modular properties, governed by the four-dimensional t Hooft anomalies. As an application of our results, we provide new tests of Seiberg duality. We also present a new evaluation formula for the three-sphere index as a sum over two-dimensional vacua.
We consider N=1 supersymmetric renormalization group flows of N=4 Yang-Mills theory from the perspective of ten-dimensional IIB supergravity. We explicitly construct the complete ten-dimensional lift of the flow in which exactly one chiral superfield becomes massive (the LS flow). We also examine the ten-dimensional metric and dilaton configurations for the ``super-QCD flow (the GPPZ flow) in which all chiral superfields become massive. We show that the latter flow generically gives rise to a dielectric 7-brane in the infra-red, but the solution contains a singularity that may be interpreted as a ``duality averaged ring distribution of 5-branes wrapped on S^2. At special values of the parameters the singularity simplifies to a pair of S-dual branes with (p,q) charge (1,pm 1).
A formulation of (non-anticommutative) N=1/2 supersymmetric U(N) gauge theory in noncommutative space is studied. We show that at one loop UV/IR mixing occurs. A generalization of Seiberg-Witten map to noncommutative and non-anticommutative superspace is employed to obtain an action in terms of commuting fields at first order in the noncommutativity parameter tetha. This leads to abelian and non-abelian gauge theories whose supersymmetry transformations are local and non-local, respectively.
After recalling different formulations of the definition of supersymmetric quantum mechanics given in the literature, we discuss the relationships between them in order to provide an answer to the question raised in the title.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
