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Register a new userNew nilpotent ${cal N}= 2$ superfields
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Gabriele Tartaglino-Mazzucchelli
Publication date
2017
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English
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We propose new off-shell models for spontaneously broken local ${cal N}=2$ 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 ${cal N}=2$ Poincare supersymmetry, we elaborate on the concept of twisted chiral superfields and present a nilpotent ${cal N}=2$ superfield that underlies the cubic nilpotency conditions given in arXiv:1707.03414 in terms of constrained ${cal N}=1$ superfields.
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We present off-shell N=2 supergravity actions, which exhibit spontaneously broken local supersymmetry and allow for de Sitter vacua for certain values of the parameters. They are obtained by coupling the standard N=2 supergravity-matter systems to the Goldstino superfields introduced in arXiv:1105.3001 and arXiv:1607.01277 in the rigid supersymmetric case. These N=2 Goldstino superfields include nilpotent chiral and linear supermultiplets. We also describe a new reducible N=1 Goldstino supermultiplet.
Considered are ${cal N}=2, SU(N_c)$ or $U(N_c)$ SQCD with $N_F<2N_c-1$ quark flavors with the quark mass term $m{rm Tr},({bar Q} Q)$ in the superpotential. ${cal N}=2$ supersymmetry is softly broken down to ${cal N}=1$ by the mass term $mu_{rm x}{rm Tr},(X^2)$ of colored adjoint scalar partners of gluons, $mu_{rm x}llLambda_2$ ($Lambda_2$ is the scale factor of the $SU(N_c)$ gauge coupling). There is a large number of different types of vacua in these theories with both unbroken and spontaneously broken flavor symmetry, $U(N_F)rightarrow U({rm n}_1)times U({rm n}_2)$. We consider in this paper the large subset of these vacua with the unbroken nontrivial $Z_{2N_c-N_Fgeq 2}$ discrete symmetry, at different hierarchies between the Lagrangian parameters $mgtrlessLambda_2,,, mu_{rm x}gtrless m$. The forms of low energy Lagrangians, quantum numbers of light particles and mass spectra are described in the main text for all these vacua. The calculations of power corrections to the leading terms of the low energy quark and dyon condensates are presented in two important Appendices. These calculations confirm additionally in a non-trivial way a self-consistency of the whole approach. Our results differ essentially from corresponding results in recent related papers arXiv:1304.0822, arXiv:1403.6086, and arXiv:1704.06201 of M.Shifman and A.Yung (and in a number of their numerous previous papers on this subject), and we explain in the text the reasons for these differences (see also the extended critique of a number of results of these authors in section 8 of arXiv:1308.5863).
We study partial supersymmetry breaking from ${cal N}=2$ to ${cal N}=1$ by adding non-linear terms to the ${cal N}=2$ supersymmetry transformations. By exploiting the necessary existence of a deformed supersymmetry algebra for partial breaking to occur, we systematically use ${cal N}=2$ projective superspace with central charges to provide a streamlined setup. For deformed ${cal O}(2)$ and ${cal O}(4)$ hypermultiplets, besides reproducing known results, we describe new models exhibiting partial supersymmetry breaking with and without higher-derivative interactions.
We derive the planar limit of 2- and 3-point functions of single-trace chiral primary operators of ${cal N}=2$ SQCD on $S^4$, to all orders in the t Hooft coupling. In order to do so, we first obtain a combinatorial expression for the planar free energy of a hermitian matrix model with an infinite number of arbitrary single and double trace terms in the potential; this solution might have applications in many other contexts. We then use these results to evaluate the analogous planar correlation functions on ${mathbb R}^4$. Specifically, we compute all the terms with a single value of the $zeta$ function for a few planar 2- and 3-point functions, and conjecture general formulas for these terms for all 2- and 3-point functions on ${mathbb R}^4$.
We introduce two new N = (2, 2) vector multiplets that couple naturally to generalized Kahler geometries. We describe their kinetic actions as well as their matter couplings both in N = (2, 2) and N = (1, 1) superspace.
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