N=2\mathcal{N}=2 Supersymmetry Partial Breaking and Tadpole Anomaly

We consider the $U(1) ^{n}$ extension of the effective $\mathcal{N}=2$ supersymmetric $U(1) \times U(1)$ model of $arXiv:1204.2141$; and study the explicit relationship between partial breaking of $\mathcal{N}=2$ supersymmetry constraint and D3 brane tadpole anomaly of type IIB string on Calabi-Yau threefolds in presence of H$^{RR}$ and H$^{NS}$ fluxes. We also comment on supersymmetry breaking in the particular $\mathcal{N}=2$ $U(1)$ Maxwell theory; and study its interpretation in connection with the tadpole anomaly with extra localized flux sources.Comment: LaTex 37 page

Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets

We show that the integer quantum Hall effect systems in plane, sphere or disc, can be formulated in terms of an algebraic unified scheme. This can be achieved by making use of a generalized Weyl--Heisenberg algebra and investigating its basic features. We study the electromagnetic excitation and derive the Hamiltonian for droplets of fermions on a two-dimensional Bargmann space (phase space). This excitation is introduced through a deformation (perturbation) of the symplectic structure of the phase space. We show the major role of Moser's lemma in dressing procedure, which allows us to eliminate the fluctuations of the symplectic structure. We discuss the emergence of the Seiberg--Witten map and generation of an abelian noncommutative gauge field in the theory. As illustration of our model, we give the action describing the electromagnetic excitation of a quantum Hall droplet in two-dimensional manifold.Comment: 23 page

Shape invariant potential formalism for photon-added coherent state construction

An algebro-operator approach, called shape invariant potential method, of constructing generalized coherent states for photon-added particle system is presented. Illustration is given on Poschl-Teller potential