Spin-Bits and N=4 SYM

We briefly review the spin-bit formalism, describing the non-planar dynamics of the $\mathcal{N}=4,d=4$ Super Yang-Mills SU(N) gauge theory. After considering its foundations, we apply such a formalism to the $su(2)$ sector of purely scalar operators. In particular, we report an algorithmic formulation of a deplanarizing procedure for local operators in the planar gauge theory, used to obtain planarly-consistent, testable conjectures for the higher-loop $su(2)$ spin-bit Hamiltonians. Finally, we outlook some possible developments and applications.Comment: 29 pages; contribution to the Proceedings of the 43rd Erice International School of Subnuclear Physics ``Towards New Milestones in our Quest to go Beyond the Standard Model'', Erice, Italy (29 August--7 September 2005); v2: some references adde

Perturbative and Non-Perturbative Aspects of N=8 Supergravity

Some aspects of quantum properties of N=8 supergravity in four dimensions are discussed for non-practitioners. At perturbative level, they include the Weyl trace anomaly as well as composite duality anomalies, the latter being relevant for perturbative finiteness. At non-perturbative level, we briefly review some facts about extremal black holes, their Bekenstein-Hawking entropy and attractor flows for single- and two-centered solutions.Comment: 1+18 pages. Contribution to the Proceedings of the International School of Subnuclear Physics, 48th Course: "What is Known and Unexpected at LHC" Erice, Italy, Aug 29 - Sep 7 201

Majorana Fermions, Supersymmetry Breaking, and Born-Infeld Theory

This review is devoted to highlight some aspects of the relevance of Majorana fermions in rigid supersymmetry breaking in four spacetime dimensions. After introducing some basic facts on spinors, and on their symmetries and reality properties, we consider Goldstino actions describing partial breaking of rigid supersymmetry, then focussing on Born-Infeld non-linear theory, its duality symmetry, and its supersymmetric extensions, also including multi-field generalizations exhibiting doubly self-duality.Comment: 1+27 pages, 1 Table. Contribution to the Proceedings of the Erice International School of Subnuclear Physics, 53rd Course : "The Future of Our Physics Including New Frontiers", and Celebration of the Triumph of Ettore Majorana, Erice, 24 June-3 July 2015. Dedicated to the memory of Guido Altarell