Zero modes and the Atiyah-Singer index in noncommutative instantons
Zero modes and the Atiyah-Singer index in noncommutative instantons
复制标题
非交换瞬子中的零模式和 Atiyah-Singer 指数
DOI：
10.1103/physrevd.66.025034
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发表时间：
2002
影响因子：
5
通讯作者：
Hyun Seok Yang
中科院分区：
文献类型：
--
作者：
Keun;Bum;Hyun Seok Yang
本文基于ADHM构造研究了非交换实例背景下玻色子和费米子的零模。在$U(N)$规范理论中的k个瞬子背景下，我们展示了如何从ADHM构造中显式地构造伴随表示中的$4Nk$ $(2Nk)$玻色子（费米子）零模式和基本表示中的$2k$ $(k)$玻色子（费米子）零模式。在非交换瞬子背景下，费米子零模的数目也被证明正好等于狄拉克算子的Atiyah-Singer指数。我们指出非bogomol 'nyi-Prasad-Sommerfield实例中的（超）共形零模受到非交换性的影响。本文还简要讨论了非交换性对洛伦兹对称性破缺的作用，以求得U(1)$实例的结构。
We study the bosonic and fermionic zero modes in noncommutative instanton backgrounds based on the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction. In the k instanton background in $U(N)$ gauge theory, we show how to explicitly construct $4Nk$ $(2Nk)$ bosonic (fermionic) zero modes in the adjoint representation and $2k$ $(k)$ bosonic (fermionic) zero modes in the fundamental representation from the ADHM construction. The number of fermionic zero modes is also shown to be exactly equal to the Atiyah-Singer index of the Dirac operator in the noncommutative instanton background. We point out that (super)conformal zero modes in non-Bogomol'nyi-Prasad-Sommerfield instantons are affected by the noncommutativity. The role of Lorentz symmetry breaking by the noncommutativity is also briefly discussed to figure out the structure of $U(1)$ instantons.