论文标题
手性$λ$ - $ \ MATHFRAK {BMS} _4 $ AD的对称性$ _4 $重力
A Chiral $Λ$-$\mathfrak{bms}_4$ Symmetry of AdS$_4$ Gravity
论文作者
论文摘要
Generalising the chiral boundary conditions of $\mathbb{R}^{1,3}$ gravity for AdS$_4$ gravity, we derive chiral locally AdS$_4$ solutions in the Newman-Unti gauge consistent with a variational principle whose asymptotic symmetry algebra we show, to be an infinite-dimensional chiral extension of $ \ mathfrak {so}（2,3）$。此对称代数与手性$ \ mathfrak {bms} _4 $代数在平面空间限制中。我们将此对称代数视为最近发现的$λ$ - $ \ mathfrak {bms} _4 $代数的手性版本。我们假定与此对应于此手性对称代数相对应的大量广告的线积分费用，并表明指控遵守$ \ Mathcal {w} $的半古典限制，其中包括一个级别$κ$ kac-moody $ \ kac-moody $ \ nmathfrak $ \ nmaterbra $ allbra $ allbra（2，2，2，2，2，2，2，2，2，2，2，2，2 ,，此外，使用$ 2D $ CFT的标准工具，我们得出了此$ \ MATHCAL {W} $ - 代数的量子版本，该代数可以用$ \ Mathcal {W}（2;（3/2）^2,1^3）$表示。
Generalising the chiral boundary conditions of $\mathbb{R}^{1,3}$ gravity for AdS$_4$ gravity, we derive chiral locally AdS$_4$ solutions in the Newman-Unti gauge consistent with a variational principle whose asymptotic symmetry algebra we show, to be an infinite-dimensional chiral extension of $\mathfrak{so}(2,3)$. This symmetry algebra coincides with the chiral $\mathfrak{bms}_4$ algebra in the flat space limit. We posit this symmetry algebra as the chiral version of recently discovered $Λ$-$\mathfrak{bms}_4$ algebra. We postulate line integral charges from the bulk AdS$_4$ gravity corresponding to this chiral symmetry algebra and show that the charges obey the semi-classical limit of a $\mathcal{W}$-algebra that includes a level $κ$ Kac-Moody $\mathfrak{sl}(2,\mathbb{R})$ current algebra. Furthermore, using the standard tools of $2d$ CFT, we derive the quantum version of this $\mathcal{W}$-algebra which may be denoted by $\mathcal{W}(2;(3/2)^2,1^3)$.
