论文标题
BVW字符串的免费字段实现
The free field realisation of the BVW string
论文作者
论文摘要
$ \ mathbb {t}^4 $的对称的Orbifold最近被证明是$ {\ rm ADS} _3 \ times {\ rm s}^3 \ times \ times \ times \ mathbb {t}^4 $的符合字符串理论的偶性。最好根据Berkovits，Vafa＆Witten（BVW）的杂交形式主义提出的世界表格理论，就$ {\ rm ads} _3 \ times {\ rm s}^3 $而言，由$ \ \ mathfrak {psu {psu}（psu}（psu}（1,1,1,1,1，2）_k Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz Wz WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WZ WAM WONEL。在级别$ k = 1 $，$ \ mathfrak {psu}（1,1 | 2）_1 $具有免费的字段实现，该实现是从$ \ mathfrak {u}（1,1 | 2）_1 $的$ \ mathfrak {u \ mathfrak {u}（1）_1 $中获得的，通常称为$ z $，通常称为$ z $。我们表明，$ {\ cal n} = 2 $ BVW的发电机（其同时定义物理状态）的免费现场版本不会产生$ {\ cal n} = 2 $代数，但相当污染与$ z $ field的术语。我们还通过引入实现商$ z $的其他幽灵字段来展示如何克服这个问题。
The symmetric orbifold of $\mathbb{T}^4$ was recently shown to be exactly dual to string theory on ${\rm AdS}_3\times {\rm S}^3 \times \mathbb{T}^4$ with minimal ($k=1$) NS-NS flux. The worldsheet theory is best formulated in terms of the hybrid formalism of Berkovits, Vafa & Witten (BVW), in terms of which the ${\rm AdS}_3\times {\rm S}^3$ factor is described by a $\mathfrak{psu}(1,1|2)_k$ WZW model. At level $k=1$, $\mathfrak{psu}(1,1|2)_1$ has a free field realisation that is obtained from that of $\mathfrak{u}(1,1|2)_1$ upon setting a $\mathfrak{u}(1)$ field, often called $Z$, to zero. We show that the free field version of the ${\cal N}=2$ generators of BVW (whose cohomology defines the physical states) does not give rise to an ${\cal N}=2$ algebra, but is rather contaminated by terms proportional to the $Z$-field. We also show how to overcome this problem by introducing additional ghost fields that implement the quotienting by $Z$.
