On the partial breaking of $\mathcal{N}=2$ rigid supersymmetry with complex hypermultiplet

Abstract

We study partial supersymmetry breaking in effective $\mathcal{N}=2$ U${\left(1\right)}^n$ gauge theory coupled to complex hypermultiplets by using the method of \textrm{"{\small arXiv:1501.07842}" to which we refer to as ADFT method}. We derive the generalisation of the symplectic invariant ADFT formula ${\zeta }_a=\frac{1}{2}{\epsilon }_{abc}\left({\mathcal{P}}^{bM}{\mathcal{C}}_{MN}{\mathcal{P}}^{cN}\right)$ capturing information on partial breaking. Our extension of this anomaly is expressed like $d_a=\frac{1}{2}{\epsilon }_{abc}{\mathbb{P}}^{bM}{\mathcal{C}}_{MN}{\mathbb{P}}^{cN}+{\mathcal{J}}_a$; the generalized moment maps ${\mathbb{P}}^{aM}$ contain ${\mathcal{P}}^{aM}$ and depend as well on electric/magnetic coupling charges $G^M=\left({\eta }^i,g_i\right)$, the ${\mathcal{J}}_a$ is an extra contribution \textrm{\ induced by Killing isometries in complex hypermatter sector}. Using SP$\left(2n,\mathbb{R}\right)$ symplectic symmetry, we also give the $\mathcal{N}=2$ partial breaking condition and derive the model of "{\small arXiv: 1204.2141}" by a particular realisation of $d_a$ anomaly.

arXiv comment21 pages, Accepted for publication in Progress of Theoretical and Experimental Physics

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