A new SU(2) anomaly
A new SU(2) anomaly
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DOI：
10.1063/1.5082852
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发表时间：
2018-10
影响因子：
1.3
通讯作者：
Juven C. Wang;X. Wen;E. Witten
中科院分区：
文献类型：
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作者：
Juven C. Wang;X. Wen;E. Witten
一个常见的反常在四个维度上影响SU(2)规范理论：在规范群的自旋1/2表示中，更广泛地说，在自旋2R+1/2表示中具有奇数个费米子多重态的理论是不一致的。本文描述了在费米子在SU(2)下以半整数自旋变换，而玻色子以整数自旋变换的条件下，可以在四维空间影响SU(2)规范理论的更微妙的反常。这样的理论，不需要选择自旋结构，并且在自旋4r+3/2的表示中具有奇数个费米子多重态，是不一致的。如果选择自旋或自旋c结构，这个理论是一致的。在希格辛到U(1)的情况下，新的SU(2)反常退化为已知的“全费米子电动力学”反常。与该理论类似，在自旋为4r+3/2的表象中含有奇数个费米子多重态的SU(2)理论可以为五维有隙理论提供一个边界态，该理论在一个封闭的五流形Y上的配分函数是$(-1)^{int_Yw_2w_3}$。所有的语句都用Sp(2N)代替了SU(2)。在五个维度上也有类似的情况。
A familiar anomaly affects SU(2) gauge theory in four dimensions: a theory with an odd number of fermion multiplets in the spin 1/2 representation of the gauge group, and more generally in representations of spin 2r+1/2, is inconsistent. We describe here a more subtle anomaly that can affect SU(2) gauge theory in four dimensions under the condition that fermions transform with half-integer spin under SU(2) and bosons with integer spin. Such a theory, formulated in a way that requires no choice of spin structure, and with an odd number of fermion multiplets in representations of spin 4r+3/2, is inconsistent. The theory is consistent if one picks a spin or spin_c structure. Under Higgsing to U(1), the new SU(2) anomaly reduces to a known anomaly of "all-fermion electrodynamics." Like that theory, an SU(2) theory with an odd number of fermion multiplets in representations of spin 4r+3/2 can provide a boundary state for a five-dimensional gapped theory whose partition function on a closed five-manifold Y is $(-1)^{\int_Y w_2w_3}$. All statements have analogs with SU(2) replaced by Sp(2N). There is also an analog in five dimensions.