%0 Report %D 2018 %T Observables in the equivariant A-model %A Bonechi, F. %A Cattaneo, A.S. %A Riccardo Iraso %A Maxim Zabzine %G eng %U https://arxiv.org/abs/1807.08659 %0 Journal Article %J Phys. Lett. B 672 (2009) 390-395 %D 2009 %T Topological branes, p-algebras and generalized Nahm equations %A Giulio Bonelli %A Alessandro Tanzini %A Maxim Zabzine %X Inspired by the recent advances in multiple M2-brane theory, we consider the generalizations of Nahm equations for arbitrary p-algebras. We construct the topological p-algebra quantum mechanics associated to them and we show that this can be obtained as a truncation of the topological p-brane theory previously studied by the authors. The resulting topological p-algebra quantum mechanics is discussed in detail and the relation with the M2-M5 system is pointed out in the p=3 case, providing a geometrical argument for the emergence of the 3-algebra structure in the Bagger-Lambert-Gustavsson theory %B Phys. Lett. B 672 (2009) 390-395 %G en_US %U http://hdl.handle.net/1963/2702 %1 1398 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-08T15:57:12Z\\nNo. of bitstreams: 1\\n0807.5113v1.pdf: 246583 bytes, checksum: 0013b3623fd81d20db0fb541bd4b9dd4 (MD5) %R 10.1016/j.physletb.2009.01.051 %0 Report %D 2007 %T Computing Amplitudes in topological M-theory %A Giulio Bonelli %A Alessandro Tanzini %A Maxim Zabzine %X We define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is $CY_3\\\\times S^1$ quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. \\nIn particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the $CY_3$, we find that the amplitudes of our model are related to Joyce invariants. %B JHEP 03 (2007) 023 %G en_US %U http://hdl.handle.net/1963/1901 %1 2335 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-12-07T16:26:28Z\\nNo. of bitstreams: 1\\nhep-th0611327.pdf: 307312 bytes, checksum: 9a3a9891aca40624a44c7a531765695b (MD5) %R 10.1088/1126-6708/2007/03/023 %0 Report %D 2006 %T On topological M-theory %A Giulio Bonelli %A Alessandro Tanzini %A Maxim Zabzine %X We construct a gauge fixed action for topological membranes on G2-manifolds such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds. %B Adv. Theor. Math. Phys. 10 (2006) 239-260 %G en_US %U http://hdl.handle.net/1963/1765 %1 2779 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-23T14:41:22Z\\nNo. of bitstreams: 1\\n64FM.pdf: 240192 bytes, checksum: 3c2a8717b7a8a0d235cc7a6ef9e76369 (MD5)