Misra, Aalok MQCD, (“barely”) \(G_2\) manifolds and (orientifold of) a compact Calabi-Yau. (English) Zbl 1067.81109 Int. J. Mod. Phys. A 20, No. 10, 2059-2097 (2005). Summary: We begin with a discussion on two apparently disconnected topics — one related to nonperturbative superpotential generated from wrapping an \(M2\)-brane around a supersymmetric three cycle embedded in a \(G_2\)-manifold evaluated by the path-integral inside a path-integral approach of Ref. 1, and the other centered around the compact Calabi–Yau \(CY_3(3, 243)\) expressed as a blow-up of a degree-24 Fermat hypersurface in \(W\mathbb{C}\mathbb{P}^4[1, 1, 2, 8, 12]\). For the former, we compare the results with the ones of Witten on heterotic worldsheet instantons. The subtopics covered in the latter include an \(\mathcal N=1\) triality between Heterotic, \(M\)- and \(F\)-theories, evaluation of \(\mathbb{R}\mathbb{P}^2\)-instanton superpotential, Picard–Fuchs equation for the mirror Landau–Ginzburg model corresponding to CY\(_3(3, 243)\), \(D = 11\) supergravity corresponding to M-theory compactified on a “barely” \(G_2\) manifold involving CY\(_3(3, 243)\) and a conjecture related to the action of antiholomorphic involution on period integrals. We then shown an indirect connection between the two topics by showing a connection between each one of the two and Witten’s MQCD. As an aside, we show that in the limit of vanishing ”\(\zeta\)”, a complex constant that appears in the Riemann surfaces relevant to defining the boundary conditions for the domain wall in MQCD, the infinite series of Ref. 4 used to represent a suitable embedding of a supersymmetric 3-cycle in a \(G_2\)-mannifold, can be summed. MSC: 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81V05 Strong interaction, including quantum chromodynamics Keywords:Membrane instantons; superpotential; heat-kernel asymptotics; triality; compact Calabi–Yau’s; orientifolds; Picard–Fuchs equation; Meijer basis; supergravity; MQCD PDFBibTeX XMLCite \textit{A. Misra}, Int. J. Mod. Phys. A 20, No. 10, 2059--2097 (2005; Zbl 1067.81109) Full Text: DOI arXiv References: [1] Becker K., Nucl. Phys. 456 pp 130– · Zbl 0925.81161 [2] Witten E., J. High Energy Phys. 0002 pp 030– [3] Witten E., Nucl. Phys. 507 pp 658– · Zbl 0925.81388 [4] Volovich A., Phys. Rev. 59 pp 065005– [5] Misra A., J. High Energy Phys. 0210 pp 056– [6] Misra A., Int. J. Mod. Phys. 19 pp 1441– · Zbl 1080.81580 [7] DOI: 10.1002/prop.200410117 · Zbl 1040.81077 [8] DOI: 10.1002/prop.200310170 · Zbl 1062.83088 [9] DOI: 10.4310/ATMP.1999.v3.n5.a5 · Zbl 0972.81135 [10] Lima E., Nucl. Phys. 614 pp 117– · Zbl 0972.81153 [11] DOI: 10.1007/s000290050016 · Zbl 0908.53027 [12] Deser S., Phys. Rev. 57 pp 7444– [13] Becker K., Nucl. Phys. 480 pp 225– · Zbl 0925.14009 [14] Witten E., Nucl. Phys. 474 pp 343– · Zbl 0925.32012 [15] DOI: 10.1016/0920-5632(96)00025-4 · Zbl 0957.81590 [16] Hull C. M., Nucl. Phys. 438 pp 109– · Zbl 1052.83532 [17] Witten E., Nucl. Phys. 443 pp 85– · Zbl 0990.81663 [18] Kachru S., Nucl. Phys. 450 pp 69– · Zbl 0957.14509 [19] Mohri K., Int. J. Mod. Phys. 14 pp 845– · Zbl 0935.81050 [20] Curio G., Int. J. Mod. Phys. 12 pp 5847– · Zbl 0902.53054 [21] DOI: 10.1007/s002200050154 · Zbl 0919.14010 [22] Andreas B., Phys. Lett. 417 pp 41– [23] Klemm A., Nucl. Phys. 518 pp 515– · Zbl 0920.14016 [24] Witten E., Nucl. Phys. 403 pp 159– · Zbl 0910.14020 [25] DOI: 10.1007/BF02100589 · Zbl 0814.53056 [26] Diaconescu D. E., J. High Energy Phys. 0307 pp 041– [27] Vafa C., Mod. Phys. Lett. 6 pp 337– · Zbl 1020.81886 [28] DOI: 10.1088/0264-9381/8/5/005 · Zbl 0743.32021 [29] Kachru S., J. High Energy Phys. 0310 pp 007– [30] Klemm A., Nucl. Phys. 477 pp 746– · Zbl 0925.81196 [31] Kaplunovsky V. S., Nucl. Phys. 552 pp 209– · Zbl 0958.81184 [32] DOI: 10.1103/PhysRevLett.71.1295 · Zbl 0972.81596 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.