The 1.5 Order Formalism does not Generate a Valid BRS Transformation for Supergravity
The 1.5 Order Formalism does not Generate a Valid BRS Transformation for Supergravity
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1.5 阶形式主义不能生成有效的超引力 BRS 变换
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发表时间：
2021
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通讯作者：
J. Dixon
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作者：
J. Dixon
1.5阶的形式主义（有时被称为“把戏”）是现代超引力的基石。本文将自由质量Wess Zumino理论作为一个简单的玩具模型来研究一阶、二阶和1.5阶形式的BRS对称性。这很容易表明1.5阶形式主义对所有理论都是有缺陷的。1.5代数看起来很接近。然而，当对其进行详细分析时，在一个简单的模型中，在易于计算的情况下，1.5的形式总是产生一个无效的BRS算子，甚至不是幂零的。这显然也是超重力的情况。由此可见，要正确理解3+1维超引力，需要一个修正的完备的一阶幂零超引力变换集。这样的集合似乎很容易写下来，只需再添加两个辅助场，使自旋连接成为超级ym多路的一部分。
The 1.5 order formalism (sometimes called a ‘trick’) is the cornerstone of modern supergravity. In this paper, the free massive Wess Zumino theory is used as a simple toy model to look at the BRS symmetry of the first, second and 1.5 order formalisms. This easily shows that the 1.5 order formalism is flawed for all theories. The 1.5 algebra naively appears to close. However, when it is analyzed in detail, in a simple model, where easy calculations are available, the 1.5 formalism always generates an invalid BRS operator, which is not even nilpotent. This clearly is also the case for supergravity. It follows that a revised and completed set of nilpotent first order supergravity transformations is needed to properly understand 3+1 dimensional supergravity. Such a set seems easy to write down, by simply adding two more auxiliary fields so that the spin connection becomes part of a super–YM multiplet.