Morita equivalence and T-duality (or B versus Θ)
Morita equivalence and T-duality (or B versus Θ)
复制标题
森田等价和 T 对偶性（或 B 与 θ）
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
Albert S. Schwarz
中科院分区：
文献类型：
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作者：
B. Pioline;Albert S. Schwarz;Albert S. Schwarz
M（矩阵）理论中的T-对偶在非对易环面上的杨-米尔斯理论（NCSYM）中被证明是Morita等价的。尽管两者具有相同的结构群，但它们的作用不同，因为森田等价在NCSYM一侧使用了一个额外的模量，即恒定的阿贝尔磁背景。本文重新分析和澄清了M（矩阵）理论与NCSYM的对应关系，并给出了解决这一难题的两种方法。第一种方法保留了标准映射，忽略了额外模，但用M（矩阵）理论的“静止项”抵消了反常变换。在第二种方法中，对标准映射进行修改，使对偶变换一致，并发现SO（d）对称性以消除伪模。我们认为，这是一个真正的对称性的超对称玻恩-因菲尔德理论的非对易环面，它允许自由贸易的基础空间的非对易性的恒定的磁背景。我们还得到了这个理论的BPS质量公式，在T-对偶，U-对偶和连续SO（d）对称下不变。
T-duality in M(atrix) theory has been argued to be realized as Morita equivalence in Yang-Mills theory on a non-commutative torus (NCSYM). Even though the two have the same structure group, they differ in their action since Morita equivalence makes crucial use of an additional modulus on the NCSYM side, the constant abelian magnetic background. In this paper, we reanalyze and clarify the correspondence between M(atrix) theory and NCSYM, and provide two resolutions of this puzzle. In the first of them, the standard map is kept and the extra modulus is ignored, but the anomalous transformation is offset by the M(atrix) theory ``rest term'. In the second, the standard map is modified so that the duality transformations agree, and a SO(d) symmetry is found to eliminate the spurious modulus. We argue that this is a true symmetry of supersymmetric Born-Infeld theory on a non-commutative torus, which allows to freely trade a constant magnetic background for non-commutativity of the base-space. We also obtain a BPS mass formula for this theory, invariant under T-duality, U-duality, and continuous SO(d) symmetry.