标题： 全息RG流和三维规范超引力中的边界条件 显示英文标题

标题： Holographic RG flows and boundary conditions in a 3D gauged supergravity

摘要： 在本工作中，我们关注对共形场论的RG流的研究，这些共形场论在全息对应下与$D=3$、$\mathcal{N}=(2,0)$规范超引力耦合到目标空间为$SU(1, 1)/U(1) = H^2$的sigma模型的庞加莱域墙解相对应。该理论被截断到一个子领域，在该子领域中矢量场和标量场的相位消失，并我们考虑剩余实标量场的不同边界条件。大部分非超对称的RG流通过将超引力场方程视为标量场及其关于尺度因子的导数的动力系统来进行分析。针对参数$a^2$的不同值构建了相图，该参数与标量流形的曲率相关。通过利用边界附近解的行为来确定其类型，基于相应的假超势的展开。通过结合边界条件的信息，使用全息字典来解释获得的RG流。还提供了假超势的数值解和图表。 显示英文摘要

摘要： In this work we focus on the study of RG flows of conformal field theories that are holographically dual to Poincar\'e domain wall solutions in $D=3$, $\mathcal{N}=(2,0)$ gauged supergravity coupled to a sigma model with target space $SU(1, 1)/U(1) = H^2$. This theory is truncated to a subsector where the vector field and phase of the scalar field vanish and we consider different boundary conditions for the remaining real scalar field. The RG flows, which are mostly non-superysymmetric, are analyzed by treating the supergravity field equations as a dynamical system for the scalar field and its derivative with respect to the scale factor. Phase diagrams are constructed for different values of the parameter $a^2$, which is related to the curvature of the scalar manifold. The behavior of solutions near the boundary is used to determine their type based on the expansion of the corresponding fake superpotential. By incorporating information on the boundary conditions, the obtained RG flows are interpreted using the holographic dictionary. Numerical solutions and plots of the fake superpotential are also provided.