强直ISO（7）度量N=8超重力的超对称Janus解探析
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"这篇学术文章探讨了强直性ISO（7）度量的N $$ \mathcal{N} $$ = 8超重力中的超对称Janus解。Janus解是一种在空间或时空中具有对称性变化的特殊解，这种变化通常发生在二维界面或者边界上。本文主要研究了这些解如何流动到3维N $$ \mathcal{N} $$ = 8超 Yang-Mills (SYM) 相，这个相与D2-brane的世界体积理论相关，并且是非共形的。此外，作者还发现了从临界点出发流向3维超共形场论（SCFT）的解决方案，这些临界点源自D2-brane理论的变形。"
在AdS/CFT对应（Anti-de Sitter/Conformal Field Theory correspondence）的背景下，这类研究具有重要意义，因为它连接了引力理论与量子场论。N $$ \mathcal{N} $$ = 8超重力是具有最高超对称性的理论之一，其在超弦理论和膜理论中扮演着核心角色。ISO（7）是对称性群的一种，表示在特定情况下保持不变的对称性。在这篇文章中，dyonic ISO（7）-gauged N $$ \mathcal{N} $$ = 8超重力是指带有电荷和磁荷的ISO（7）对称的超重力理论。
文章结构如下：
1. 引言：简要介绍了Janus解的研究背景和重要性，以及文章将要探讨的主要内容。
2. Dyonic ISO（7）-gauged N $$ \mathcal{N} $$ = 8 supergravity：这部分详细阐述了所使用的理论框架，即带电荷和磁荷的ISO（7）对称的超重力模型。
3. SU(3)-invariant Janus solutions：这部分专注于研究具有SU(3)对称性的Janus解，可能涉及特定的几何结构和对称性质。
4. G2-invariant Janus solutions：接着，作者讨论了G2对称性的Janus解，G2是一个在某些维度下的Lie群，它的作用可能是提供一种更特殊的对称性结构。
5. 结论：总结了研究的主要发现和它们在理论物理中的意义。
6. 附录：包括了运动方程的详细信息和一个SO(4)-对称性截断的分析，这些都是进行计算和求解问题的关键工具。
文章的开放访问特性意味着任何感兴趣的读者都可以免费获取和阅读，这有助于促进学术交流和知识传播。文章由Springer出版，并被SCOAP3资助，表明了它在高能物理领域的专业性和影响力。通过DOI链接（https://doi.org/10.1007/JHEP04(2018)109），可以方便地找到原始文献，以便进一步深入研究。
JHEP04(2018)109
point with N = 2, U(1)
R
×SU(3) symmetry [21, 22]. Otherwise, by adding a mass term
to one of the chiral scalars, it flows to another conformal fixed point with N = 3, SO(4)
symmetry [23]. Recently, gravity duals of these 3d SCFTs from D2-branes were discovered
in dyonic ISO(7)-gauged N = 8 supergravity [24].
Dyonic ISO(7)-gauged N = 8 supergravity is a consistent truncation of massive type
IIA supergravity on six-sphere [25–27]. The Romans mass corresponds to the magnetic
gauge coupling of dyonic ISO(7)-gauged N = 8 supergravity. The scalar potential of the
theory has four known superymmetric critical points, and they are N = 2 SU(3)×U(1),
N = 1 SU(3), N = 1 G
2
, and N = 3 SO(4) critical points. The N = 2 SU(3)×U(1) and
N = 3 SO(4) critical points are dual to the 3d SCFTs from the deformations of D2-brane
theory discussed in the previous paragraph. The fixed point AdS solutions were uplifted to
massive type IIA supergravity [26], and holographic RG flows between critical points were
studied [28]. The gravitational free energies [25, 29, 30] and spin-2 spectrum [31, 32] were
calculated and matched with the field theory results.
In the usual supergravity theories, most of the RG flows and Janus solutions are
attracted to critical points which are dual to conformal field theories e.g. N = 4 super
Yang-Mills theory, ABJM theory, and 6d (2,0) theory. On the other hand, in dyonic ISO(7)-
gauged N = 8 supergravity, most of the RG flows and Janus solutions are attracted to a
non-conformal phase which is dual to 3d N = 8 SYM on the worldvolume of D2-branes.
Therefore, as we will see, usual Janus solutions in dyonic ISO(7)-gauged N = 8 supergravity
do not exhibit AdS-behavior. On the other hand, if we fine-tune initial values of the scalar
fields, we obtain Janus solutions staying at a critical point for a while and then moving
away to the non-conformal 3d SYM phase.
In section 2, we review the N = 1, Z
2
×SO(3)-invariant truncation of dyonic ISO(7)-
gauged N = 8 supergravity. In section 3, we study Janus solutions in the N = 2,
SU(3)×U(1)-invariant truncation. In section 4, we study Janus solutions in the N = 1,
G
2
-invariant truncation. We conclude in section 5. In appendix A we present the equa-
tions of motion from the truncations we consider. In appendix B, we present the N = 1,
SO(4)-invariant truncation.
2 Dyonic ISO(7)-gauged N = 8 supergravity
We begin by considering the N = 1, Z
2
×SO(3)-invariant truncation of dyonic ISO(7)-
gauged N = 8 supergravity. This truncation was studied in detail in appendix A of [25],
and we review it in this section. There are three complex scalar fields, Φ
1
, Φ
2
and Φ
3
. In
terms of canonical N = 1 formulation, the scalar action is given by
S =
1
16πG
4
Z
d
4
x
√
−g
R + 6
∂
µ
Φ
1
∂
µ
Φ
1
(Φ
1
− Φ
1
)
2
+ 2
∂
µ
Φ
2
∂
µ
Φ
2
(Φ
2
− Φ
2
)
2
+ 6
∂
µ
Φ
3
∂
µ
Φ
3
(Φ
3
− Φ
3
)
2
− P
. (2.1)
The K¨ahler potential is
K = −3 log
−i(Φ
1
− Φ
1
)
− log
−i(Φ
2
− Φ
2
)
− 3 log
−i(Φ
3
− Φ
3
)
, (2.2)
– 2 –
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