Nonabelian orbifolds and the boson-fermion correspondence
Nonabelian orbifolds and the boson-fermion correspondence
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非阿贝尔轨道折叠和玻色子-费米子对应
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
G. Mason
中科院分区：
文献类型：
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作者：
C. Dong;G. Mason
摘要对于可被 8 整除的正整数，存在一个（玻色子）全纯顶点算子代数 (VOA)
$$V_{伽玛_l}$$
与自旋晶格 Γl 相关。对于一类广泛的有限群 G 的自同构
$$V_{伽玛_l}$$
我们证明了不可约g-扭曲的存在性和唯一性
$$V_{伽玛_l}$$
-modules 并建立 G 中交换元素的配分函数 Z(g, h, τ) 的模不变性。特别是，对于任何有限群，存在无限多个承认 G 且这些性质成立的全纯 VOA。玻色子-费米子对应关系促进了证明，该对应关系给出了之间的 VOA 同构
$$V_{伽玛_l}$$
以及某种费米子结构，它扩展了弗兰克尔等人的工作。
AbstractFor a positive integerl divisible by 8 there is a (bosonic) holomorphic vertex operator algebra (VOA)
$$V_{Gamma _l }$$
associated to the spin lattice Γl. For a broad class of finite groupsG of automorphisms of
$$V_{Gamma _l }$$
we prove the existence and uniqueness of irreducibleg-twisted
$$V_{Gamma _l }$$
-modules and establish the modular-invariance of the partition functionsZ(g, h, τ) for commuting elements inG. In particular, for any finite group there are infinitely many holomorphic VOAs admittingG for which these properties hold. The proof is facilitated by a boson-fermion correspondence which gives a VOA isomorphism between
$$V_{Gamma _l }$$
and a certain fermionic construction, and which extends work of Frenkel and others.