arXiv 2005.003582020-05hep-thmath-phmath.MP

AdS_4中标量方程的Adomian方法和边界CFT_3对偶解

Solutions For Scalar Equations in AdS_4 with Adomian Method and Boundary CFT_3 Duals

M. Naghdi

备注：: 22 pages, than the v2 edition: Added related discussions on hadron spectra in AdS/QCD in section 6 along with relevant references
发表信息：: Eur. Phys. J. Plus 138, 300 (2023)
DOI：: 10.1140/epjp/s13360-023-03905-6

摘要：

对于由AdS_4 × S^7/Z_k上的11维超引力截断产生的Euclidean AdS_4体中的（伪）标量的非线性偏微分方程，我们使用数学工具，特别是Adomian分解方法，从特解或通解的边界行为附近得到初始数据，虽然我们关注于归一化模和Dirichlet边界条件，求出了m ^2 =4，0，-9/4的三种特殊模式的微扰级数解（在探针近似下方程有效）。同时，我们还指出，在斜吹的M2-膜背景下，存在Higgs类（伪）标量使方程齐次，并提供了自发对称性破缺。然后，在所有超对称性和宇称都被破坏的情况下，我们用SO（8）的三个基本表示交换引力子，用各种相应的由费米子，标量和SU（N）规范场组成的SU（4）x U（1）-单线态算符变形ABJM类三维边界作用量，找到新的SO（4）-不变瞬子，最后调整体解和边界解，确定态算符AdS_4/CFT_3对应关系。

英文摘要：

For a nonlinear partial differential equation for (pseudo)scalars in the bulk of Euclidean AdS_4, arising from a truncation of 11-dimensional supergravity over AdS_4 x S^7/Z_k, we use math tools and in particular Adomian Decomposition Method, with initial data from near the boundary behavior of a special or general solution, although we focus on normalizable modes and Dirichlet boundary condition, to get perturbative series solutions (of the equation valid in probe approximation) for three special modes of m^2=4, 0, -9/4. Meantime, we remind that for the skew-whiffed M2-branes background, there are Higgs-like (pseudo)scalars that make the equation homogeneous and provide spontaneous symmetry breaking. Then, with the setups and solutions in the bulk, where all supersymmetries and parity are broken, we swap the three fundamental representations of SO(8) for gravitino, deform the ABJM-like three-dimensional boundary actions with various corresponding SU(4) x U(1)-singlet operators made of fermions, scalars and SU(N) gauge fields, find new SO(4)-invariant instantons, and finally adjust the bulk and boundary solutions and confirm state-operator AdS_4/CFT_3 correspondence.

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