论文标题
带有任意赤字参数的真实经典几何形状（s）$α（_ {i}）$在变形的jackiw-teitelboim重力中
Real Classical Geometry with arbitrary deficit parameter(s) $α(_{I})$ in Deformed Jackiw-Teitelboim Gravity
论文作者
论文摘要
Witten提出了对Jackiw-teitelboim（JT）重力的有趣变形，它通过添加潜在的项$ u（ϕ）$作为标量Dilaton场的自我耦合。在计算字段上的路径积分时，约束来自$ r（x）+2 =2αδ（\ vec {x} - \ vec {x}'）$。由此产生的欧几里得公制在$ \ vec {x} = \ vec {x}'$上遭受圆锥形奇异性。 $ ds^2 = dr^2+r^2dφ^2，φ\congφ+2π-α$以极性坐标$（r，φ）$在本地建模的可能几何形状。在这封信中，我们表明还有另一个“精确”几何族，用于$α$的任意值。对于$α= 0 $的情况，发现了一对精确的解决方案。一个代表广告的静态贴片，另一个代表广告指标的非静态贴片。这些解决方案用于用$α\ neq 0 $构建不均匀模型的绿色函数。我们解决了理论上不同广告不同斑块之间的一种相变，因为在$ x = x'$的第一个衍生物中的不连续性中的不连续性。我们将研究逐渐归纳为满足约束$ r（x）+2 = 2 \ sum_ {i = 1}^{k}α_iδ^{（2）}（x-x'_i）$作为modulo diffeeMorphisms $（x-x'_i）$的确切空间。该空间是$ g $ riemann表面的模量空间，$ k $ conical奇异性位于$ x'_k $，由$ \ mathcal {m} _ {g，k} $表示。
An interesting deformation of the Jackiw-Teitelboim (JT) gravity has been proposed by Witten by adding a potential term $U(ϕ)$ as a self-coupling of the scalar dilaton field. During calculating the path integral over fields, a constraint comes from integration over $ϕ$ as $R(x)+2=2αδ(\vec{x}-\vec{x}')$. The resulting Euclidean metric suffered from a conical singularity at $\vec{x}=\vec{x}'$. A possible geometry modeled locally in polar coordinates $(r,φ)$ by $ds^2=dr^2+r^2dφ^2,φ\cong φ+2π-α$. In this letter we showed that there exists another family of "exact" geometries for arbitrary values of the $α$. A pair of exact solutions are found for the case of $α=0$. One represents the static patch of the AdS and the other one is the non static patch of the AdS metric. These solutions were used to construct the Green function for the inhomogeneous model with $α\neq 0$. We address a type of the phase transition between different patches of the AdS in theory because of the discontinuity in the first derivative of the metric at $x=x'$. We extended the study to the exact space of metrics satisfying the constraint $R(x)+2=2\sum_{i=1}^{k}α_iδ^{(2)}(x-x'_i)$ as a modulo diffeomorphisms for an arbitrary set of the deficit parameters $(α_1,α_2,..,α_k)$. The space is the moduli space of Riemann surfaces of genus $g$ with $k$ conical singularities located at $x'_k$ denoted by $\mathcal{M}_{g,k}$.
