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1. Counting operators in N = 1 supersymmetric gauge theories

   https://doi.org/10.1007/JHEP07(2023)081  

   Delgado, Antonio; Martin, Adam; Wang, Runqing (July 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> Following a recent publication, in this paper we count the number of independent operators at arbitrary mass dimension inN= 1 supersymmetric gauge theories and derive their field and derivative content. This work uses Hilbert series machinery and extends a technique from our previous work on handling integration by parts redundancies to vector superfields. The method proposed here can be applied to both abelian and non-abelian gauge theories and for any set of (chiral/antichiral) matter fields. We work through detailed steps for the abelian case with single flavor chiral superfield at mass dimension eight, and provide other examples in the appendices. 

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2. Basis for non-factorizable superamplitudes in $$ \mathcal{N} $$ = 1 supersymmetry

   https://doi.org/10.1007/JHEP09(2024)051  

   Delgado, Antonio; Martin, Adam; Wang, Runqing (September 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In this paper we develop a semi-standard Young tableau (SSYT) approach to construct a basis of non-factorizable superamplitudes in$$ \mathcal{N} $$ $N$= 1 massless supersymmetry. This amplitude basis can be directly translated to a basis for higher dimensional supersymmetric operators, yielding both the number of independent operators and their form. We deal with distinguishable (massless) chiral/vector superfields at first, then generalize the result to the indistinguishable case. Finally, we discuss the advantages and disadvantages of this method compared to the previously studied Hilbert series approach. 

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3. Goldstino condensation?

   https://doi.org/10.1007/JHEP08(2022)166  

   Kallosh, Renata; Linde, Andrei; Wrase, Timm; Yamada, Yusuke (August 2022, Journal of High Energy Physics)

   A bstract It was argued in [1] that the Volkov-Akulov (VA) model as well as similar models in supergravity and the related KKLT model in string theory, suffer from tachyonic instabilities due to goldstino condensation. The authors of [1] constructed a specific model with two unconstrained interacting chiral superfields with linearly realized supersymmetry which has an unstable vacuum. They claimed that this model becomes equivalent to the VA model in the UV limit. We show that the UV limit of their model is discontinuous, and the vacuum instability of the model proposed in [1] is not relevant to the VA model, to related models in supergravity, and to the KKLT construction. 

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4. A ν supersymmetric anomaly-free atlas

   https://doi.org/10.1007/JHEP02(2022)144  

   Allanach, B. C.; Madigan, Maeve; Tooby-Smith, Joseph (February 2022, Journal of High Energy Physics)

   A bstract Extensions of the minimal supersymmetric standard model (MSSM) gauge group abound in the literature. Several of these include an additional U(1) X gauge group. Chiral fermions’ charge assignments under U(1) X are constrained to cancel local anomalies in the extension and they determine the structure and phenomenology of it. We provide all anomaly-free charge assignments up to a maximum absolute charge of Q max = 10, assuming that the chiral superfield content of the model is that of the MSSM plus up to three Standard Model (SM) singlet superfields. The fermionic components of these SM singlets may play the rôle of right-handed neutrinos, whereas one of the scalar components may play the rôle of the flavon, spontaneously breaking U(1) X . Easily scanned lists of the charge assignments are made publicly available on Zenodo. For the case where no restriction is placed upon Q max , we also provide an analytic parameterisation of the general solution using simple techniques from algebraic geometry. 

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5. Twisted characters and holomorphic symmetries

   https://doi.org/10.1007/s11005-020-01319-4  

   Saberi, Ingmar; Williams, Brian R. (October 2020, Letters in Mathematical Physics)

   null (Ed.)

   Abstract We consider holomorphic twists of arbitrary supersymmetric theories in four dimensions. Working in the BV formalism, we rederive classical results characterizing the holomorphic twist of chiral and vector supermultiplets, computing the twist explicitly as a family over the space of nilpotent supercharges in minimal supersymmetry. The BV formalism allows one to work with or without auxiliary fields, according to preference; for chiral superfields, we show that the result of the twist is an identical BV theory, the holomorphic $$\beta \gamma $$ β γ system with superpotential, independent of whether or not auxiliary fields are included. We compute the character of local operators in this holomorphic theory, demonstrating agreement of the free local operators with the usual index of free fields. The local operators with superpotential are computed via a spectral sequence and are shown to agree with functions on a formal mapping space into the derived critical locus of the superpotential. We consider the holomorphic theory on various geometries, including Hopf manifolds and products of arbitrary pairs of Riemann surfaces, and offer some general remarks on dimensional reductions of holomorphic theories along the $$(n-1)$$ ( n - 1 ) -sphere to topological quantum mechanics. We also study an infinite-dimensional enhancement of the flavor symmetry in this example, to a recently studied central extension of the derived holomorphic functions with values in the original Lie algebra, that generalizes the familiar Kac–Moody enhancement in two-dimensional chiral theories. 

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