标题： AdS$_4$中的类希格斯（伪）标量，CFT_3 中的边缘和无关变形以及 S^3 上的瞬子 显示英文标题

标题： Higgs-like (pseudo)Scalars in AdS$_4$, Marginal and Irrelevant Deformations in CFT_3 and Instantons on S^3

摘要： 在非动态AdS$_4 \times S^7/Z_k$背景上的11维超引力的4形式假设下，内部空间为CP$^3$上的$S^1$丛，我们得到一个一致截断。 在欧几里得AdS_4 空间中得到的标量方程中的（伪）标量，可以看作是从（反）M膜环绕（Wick旋转）斜转M2膜背景中的内部方向产生的（如所得理论是针对反M2膜的），因此实现了在交换SO(8)的三个基本表示$8_s, 8_c, 8_v$后的模式。 考虑对外部和内部空间的反作用，我们得到了无质量与有质量模式，分别对应边界CFT$_3$上的精确边缘和边缘无关变形，并为体方程写出闭合解并计算其对背景作用量的修正。 接下来，考虑类似Higgs的（呼吸）模式$m^2=18$，该模式具有所有超对称性、宇称和尺度不变性被破坏，通过数学方法特别是Adomian分解方法求解相关体方程，并分析解在边界附近的行为，我们在ABJM模型的SU(4) x U(1)单态部分中实现了边界对偶。 然后，引入由双基础标量、费米子和U(1)规范场组成的新的双变形算符$\Delta_+$ = 3, 6，我们得到了SO(4)不变解，这些解是在无穷远处半径为三球面上的小瞬子，实际上对应于导致大挤压奇点的体泡坍缩。 显示英文摘要

摘要： With a 4-form ansatz of 11-dimensional supergravity over non-dynamical AdS$_4 \times S^7/Z_k$ background, with the internal space as a $S^1$ Hopf fibration on CP$^3$, we get a consistent truncation. The (pseudo)scalars, in the resulting scalar equations in Euclidean AdS_4 space, may be viewed as arising from (anti)M-branes wrapping around internal directions in the (Wick-rotated) skew-whiffed M2-branes background (as the resulting theory is for anti-M2-branes) and so, realizing the modes after swapping the three fundamental representations $8_s, 8_c, 8_v$ of SO(8). Taking the backreaction on the external and internal spaces, we get massless and massive modes, corresponding to exactly marginal and marginally irrelevant deformations on the boundary CFT$_3$, and write a closed solution for the bulk equation and compute its correction to the background action. Next, considering the Higgs-like (breathing) mode $m^2=18$, having all supersymmetries, parity and scale-invariance broken, by solving the associated bulk equation with mathematical methods, especially the Adomian decomposition method, and analyzing the behavior near the boundary of the solutions, we realize the boundary duals in SU(4) x U(1)-singlet sectors of the ABJM model. Then, introducing new dual deformation $\Delta_+$ = 3, 6 operators made of bi-fundamental scalars, fermions and U(1) gauge fields, we obtain SO(4)-invariant solutions as small instantons on a three-sphere with radius at infinity, which actually correspond to collapsing bulk bubbles leading to big-crunch singularities.