Contact Structure-induced Symplectic Nearly Half-Flat SU(3) Structure in Finite-N Thermal cal M-Theory
Abstract
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 G2-structure seven-fold ℳ7 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: dωΦ=0 exactly, while dΩ+ is suppressed as 𝒪(e−N1/3/𝒪(1)) in the infrared "MQGP limit", leaving WΦSU(3)=W2- 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 G2-structure positive three-form on ℳ7, organised through the G2/S(nearly)HF torsion data, yields a radial ``magnetic field'' ℬKK(r) whose squared norm factorises exactly into external and internal factors. ℬKK(r) satisfies a Bessel-type ODE with a regular singular point at the horizon; normalisability and infrared regularity select J2, with harmonicity of the aforementioned internal factor recovered from the large-N suppression. ℬKK 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.
Related
- Infinitesimmaly homogeneous manifolds with symplectic and almost contact structure groups
- Shifted Contact Structures on Exact Symplectic Fibrations
- Elastic knots: compactness, contact, and variational structure
- A numerical benchmark for fluid–structure–contact interaction
- Structure-preserving discretisations for the quasi-incompressible, thermal Maxwell-Stefan equations
BibTeX
@misc{misra2026contact,
title = {{Contact Structure-induced Symplectic Nearly Half-Flat $SU(3)$ Structure in Finite-$N$ Thermal $\cal M$-Theory}},
author = {Aalok Misra},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.26267},
eprint = {2608.26267},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26267},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Contact Structure-induced Symplectic Nearly Half-Flat SU(3) Structure in Finite-N Thermal cal M-Theory
AU - Aalok Misra
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2608.26267
UR - https://arxiv.org/abs/2608.26267
AB - 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 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 𝒪(e^−N^1/3/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 ℳ_7, organised through the G_2/S(nearly)HF torsion data, yields a radial ``magnetic field'' ℬ_KK(r) whose squared norm factorises exactly into external and internal factors. ℬ_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. ℬ_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.
ER -