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Freudenthal Gauge Theory

机译：弗洛伊登塔尔规范理论

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摘要

We present a novel gauge field theory, based on the Freudenthal Triple System (FTS), a ternary algebra with mixed symmetry (not completely symmetric) structure constants. The theory, named Freudenthal Gauge Theory (FGT), is invariant under two (off-shell) symmetries: the gauge Lie algebra constructed from the FTS triple product and a novel global non-polynomial symmetry, the so-called Freudenthal duality. Interestingly, a broad class of FGT gauge algebras is provided by the Lie algebras “of type ( {{mathfrak{e}}_7} )” which occur as conformal symmetries of Euclidean Jordan algebras of rank 3, and as U -duality algebras of the corresponding (super)gravity theories in D = 4. We prove a No-Go Theorem, stating the incompatibility of the invariance under Freudenthal duality and the coupling to space-time vector and/or spinor fields, thus forbidding non-trivial supersymmetric extensions of FGT. We also briefly discuss the relation between FTS and the triple systems occurring in BLG-type theories, in particular focusing on superconformal Chern-Simons-matter gauge theories in D = 3.
机译：我们提出了一种新的规范场理论，该理论基于Freudenthal三重系统（FTS），具有混合对称（非完全对称）结构常数的三元代数。该理论名为弗洛伊登塔尔规范理论（FGT），在两个（脱壳）对称性下是不变的：由FTS三乘积构造的规范李代数和新颖的全局非多项式对称性，即所谓的弗洛伊登塔尔对偶性。有趣的是，“类型（{{mathfrak {e}} _ 7}”类型的Lie代数提供了广泛的FGT规范代数，它们作为3级欧几里德Jordan代数的共形对称性出现，并且作为U-duality代数相应的D = 4中的（超）重力理论。我们证明了无定理，指出了在弗洛伊登塔尔对偶下不变性与时空矢量和/或自旋场的耦合，因此禁止了非平凡的超对称扩展。 FGT。我们还简要讨论了FTS与BLG型理论中出现的三元系统之间的关系，尤其关注于D = 3中的超共形Chern-Simons物规理论。

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  • 来源
    《Journal of High Energy Physics》 |2013年第3期|1-38|共38页
  • 作者

    Alessio Marrani; Cong-Xin Qiu; Sheng-Yu Darren Shih; Anthony Tagliaferro; Bruno Zumino;

  • 作者单位

    1.Theory division CERN CH 1211 Geneva 23 Switzerland;

    2.School of Physics and Astronomy University of Minnesota/Twin Cities Minneapolis MN 55455 U.S.A;

    3.Department of Physics and Center for Theoretical Sciences University of California Berkeley CA 94720-7300 U.S.A;

    3.Department of Physics and Center for Theoretical Sciences University of California Berkeley CA 94720-7300 U.S.A;

    3.Department of Physics and Center for Theoretical Sciences University of California Berkeley CA 94720-7300 U.S.A 4.Lawrence Berkeley National Laboratory Theory Group Berkeley CA 94720-8162 U.S.A;

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  • 原文格式 PDF
  • 正文语种 eng
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  • 关键词

    Gauge Symmetry; Global Symmetries; Chern-Simons Theories;

    机译：规范对称;全局对称;Chern-Simons理论;

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