发表机构
Department of Physics, Indian Institute of Technology Roorkee（印度理工学院鲁尔基分校物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究有限N热M理论的对偶G结构，证明其诱导的SU(3)结构属于辛近半平类，完成MQGP对偶的G结构分类，并给出有限温度弦论中弱磁场产生的全息机制。
AI 中文摘要
如arXiv:2211.13186所示，在arXiv:1306.4339、2004.07259中构造的类热QCD理论的M理论对偶包含一个闭合G₂结构七维流形ℳ₇，该流形支撑接触3结构（C3S），其诱导出一种“横向”SU(3)结构。我们证明该诱导结构属于辛近半平（S(nearly)HF）类：dω_Φ严格为零，而dΩ₊在红外“MQGP极限”中被压低为𝒪(e^{-N^{1/3}/𝒪(1)})，仅留下W_Φ^{SU(3)}=W₂⁻作为唯一非零的Chiossi-Salamon挠率类，完成了arXiv:1507.02692、2004.07259、2211.13186中启动的MQGP对偶的G结构分类。作为物理应用，通过G₂/S(nearly)HF挠率数据组织的、ℳ₇上G₂结构正三形式微分的十一维霍奇对偶的卡鲁扎-克莱因约化，产生一个径向“磁场”𝒷_{KK}(r)，其模平方可精确分解为外部因子与内部因子。𝒷_{KK}(r)满足一个在视界处具有正则奇点的贝塞尔型常微分方程；归一化条件与红外正则性选取J₂，且上述内部因子的调和性可从大N压低中恢复。𝒷_{KK}通过非线性幂律与IIA味D6膜的磁场相关联，为有限温度弦论中弱磁场的产生提供了自上而下的全息机制。
英文摘要
The ${\cal M}$-theory dual of thermal QCD-like theories constructed in arXiv:1306.4339, 2004.07259 involves, as shown in arXiv:2211.13186, a closed $G_2$-structure seven-fold $\mathcal{M}_7$ supporting Contact 3-Structures (C3S) that induce a ``transverse'' $SU(3)$-structure. We prove that this induced structure belongs to the symplectic nearly half-flat (S(nearly)HF) class: $dω_Φ=0$ exactly, while $dΩ_+$ is suppressed as $\mathcal{O}(e^{-N^{1/3}/\mathcal{O}(1)})$ in the infrared "MQGP limit", leaving $W_Φ^{SU(3)}=W_2^-$ as the sole non-vanishing Chiossi--Salamon torsion class and completing the $G$-structure classification of the MQGP dual initiated in arXiv:1507.02692,2004.07259, 2211.13186. As a physical application, Kaluza--Klein reduction of the eleven-dimensional Hodge dual of the differential of the $G_2$-structure positive three-form on $\mathcal{M}_7$, organised through the $G_2$/S(nearly)HF torsion data, yields a radial ``magnetic field'' $\mathcal{B}_{\rm KK}(r)$ whose squared norm factorises exactly into external and internal factors. $\mathcal{B}_{\rm KK}(r)$ satisfies a Bessel-type ODE with a regular singular point at the horizon; normalisability and infrared regularity select $J_2$, with harmonicity of the aforementioned internal factor recovered from the large-$N$ suppression. $\mathcal{B}_{\rm KK}$ is related to the magnetic field of the type~IIA flavour $D6$-branes via a non-linear power law, furnishing a top-down holographic mechanism for generating weak magnetic fields in finite-temperature string theory.
Commentsv2:1+51 pages, LaTeX; 1 figure; Mathematics subject classification (2020) corrected
