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Supersymmetry, Supergravity, and Superstring Phenomenology Advances in High Energy Physics Supersymmetry, Supergravity, and Superstring Phenomenology Guest Editors: Shaaban Khalil, Gordon Kane, Ignatios Antoniadis, and Stefano Moretti Supersymmetry, Supergravity, and Superstring Phenomenology Advances in High Energy Physics Supersymmetry, Supergravity, and Superstring Phenomenology Guest Editors: Shaaban Khalil, Gordon Kane, Ignatios Antoniadis, and Stefano Moretti Copyright © 2016 Hindawi Publishing Corporation. All rights reserved. This is a special issue published in “Advances in High Energy Physics.” All articles are open access articles distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Editorial Board Luis A. Anchordoqui, USA Frank Filthaut, Netherlands Anastasios Petkou, Greece T. Asselmeyer-Maluga, Germany Chao-Qiang Geng, Taiwan Alexey A. Petrov, USA Marco Battaglia, Switzerland Philippe Gras, France Thomas Rössler, Sweden Botio Betev, Switzerland Xiaochun He, USA Juan José Sanz-Cillero, Spain Lorenzo Bianchini, Switzerland Filipe R. Joaquim, Portugal Edward Sarkisyan-Grinbaum, USA Burak Bilki, USA KyungK.Joo,RepublicofKorea Sally Seidel, USA Adrian Buzatu, UK Aurelio Juste, Spain George Siopsis, USA Rong-Gen Cai, China Michal Kreps, UK Luca Stanco, Italy Duncan L. Carlsmith, USA Ming Liu, USA Satyendra Thoudam, Netherlands Ashot Chilingarian, Armenia Enrico Lunghi, USA Smarajit Triambak, South Africa Anna Cimmino, Belgium Piero Nicolini, Germany Elias C. Vagenas, Kuwait Andrea Coccaro, Switzerland Seog H. Oh, USA Nikos Varelas, USA Shi-Hai Dong, Mexico Sergio Palomares-Ruiz, Spain YauW.Wah,USA Edmond C. Dukes, USA Giovanni Pauletta, Italy Amir H. Fatollahi, Iran Yvonne Peters, UK Contents Supersymmetry, Supergravity, and Superstring Phenomenology Shaaban Khalil, Gordon Kane, Ignatios Antoniadis, and Stefano Moretti Volume 2016, Article ID 3595120, 1 page Geometric Algebra Techniques in Flux Compactifications Calin Iuliu Lazaroiu, Elena Mirela Babalic, and Ioana Alexandra Coman Volume 2016, Article ID 7292534, 42 pages Structural Theory and Classification of 2D Adinkras Kevin Iga and Yan X. Zhang Volume 2016, Article ID 3980613, 12 pages Aspects of Moduli Stabilization in Type IIB String Theory Shaaban Khalil, Ahmad Moursy, and Ali Nassar Volume 2016, Article ID 4303752, 17 pages A -Continuum of Off-Shell Supermultiplets Tristan Hübsch and Gregory A. Katona Volume 2016, Article ID 7350892, 11 pages MSSM Dark Matter in Light of Higgs and LUX Results W. Abdallah and S. Khalil Volume 2016, Article ID 5687463, 10 pages Helical Phase Inflation and Monodromy in Supergravity Theory Tianjun Li, Zhijin Li, and Dimitri V. Nanopoulos Volume 2015, Article ID 397410, 12 pages Reciprocity and Self-Tuning Relations without Wrapping Davide Fioravanti, Gabriele Infusino, and Marco Rossi Volume 2015, Article ID 762481, 21 pages Exploring New Models in All Detail with ËÊÀ Florian Staub Volume2015,ArticleID840780,126pages Vacuum Condensates as a Mechanism of Spontaneous Supersymmetry Breaking Antonio Capolupo and Marco Di Mauro Volume 2015, Article ID 929362, 6 pages A Chargeless Complex Vector Matter Field in Supersymmetric Scenario L. P. Colatto and A. L. A. Penna Volume 2015, Article ID 986570, 8 pages Hindawi Publishing Corporation Advances in High Energy Physics Volume 2016, Article ID 3595120, 1 page http://dx.doi.org/10.1155/2016/3595120 Editorial Supersymmetry, Supergravity, and Superstring Phenomenology Shaaban Khalil,1 Gordon Kane,2 Ignatios Antoniadis,3,4 and Stefano Moretti5 1 Center for Fundamental Physics, Zewail City of Science and Technology, Giza, Egypt 2Department of Physics, University of Michigan, Ann Arbor, MI, USA 3Department of Physics, LPTHE, Sorbonne Universite,UPMC,Paris,France´ 4University of Bern, Bern, Switzerland 5Department of Physics, University of Southampton, Southampton, UK Correspondence should be addressed to Shaaban Khalil; [email protected] Received 14 December 2016; Accepted 14 December 2016 Copyright © 2016 Shaaban Khalil et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3. Supersymmetry, supergravity, and superstring are amongst stabilization in type IIB string theory compactification with the most popular research topics in particle physics. Super- fluxes. Another paper in this special issue describes super- symmetry is a generalization of the space-time symmetries of multiplets wherein a continuously variable “tuning parame- quantum field theory that links the matter particles with the ter” modifies the supersymmetry transformations. Another force-carrying particles and implies that there are additional paper studies the constraints imposed on the Minimal Super- superparticles necessary to complete the symmetry. Super- symmetric Standard Model (MSSM) parameter space by the gravity is the theory that combines the principles of super- Large Hadron Collider (LHC) Higgs mass measurements symmetry and general relativity. It naturally includes gravity and gluino mass lower bound. Another paper studies helical along with the other fundamental forces (the electromagnetic phase inflation which realizes “monodromy inflation” in force, the weak nuclear force, in turn already unified in the supergravity theory. Another paper considers scalar Wilson electroweak interactions, and the strong nuclear force). String operators of =4Supersymmetric Yang-Mills (SYM) theo- theory is the leading candidate for a theory that unifies all ries at high spin and generic twist operators in the multicolor fundamentalforcesinnatureinaconsistentscheme.Italso limit. Another paper author gives an overview about the provides a consistent framework for the theory of quantum features that the Mathematica package SARAH provides to gravity. Compactified string/M-theories make testable pre- study new supersymmetric models. Another paper reviews a dictions about our four-dimensional world. possible mechanism for the spontaneous breaking of super- The phenomenology of supersymmetry, supergravity, symmetry, based on the presence of vacuum condensates. and superstring is thus very rich and covers many topics: Another paper constructs and studies a formulation of a flavour physics and CP violation, Higgs and collider physics, chargeless complex vector matter field in a supersymmetric modelbuildingbeyondtheStandardModel,andastroparticle framework. physics and cosmology. Some recent developments in these theories, each with important applications to particle physics Shaaban Khalil and/or cosmology, are the main theme of this special issue. Gordon Kane One of the papers of this special issue discusses the Ignatios Antoniadis constrained generalized Killing spinors, which characterize Stefano Moretti supersymmetric flux compactifications of supergravity the- ories, using geometric algebra techniques. Another paper presents a study on what are called Adinkras, which are com- binatorial objects developed to study (1-dimensional) super- symmetry representations. Another paper reviews moduli Hindawi Publishing Corporation Advances in High Energy Physics Volume 2016, Article ID 7292534, 42 pages http://dx.doi.org/10.1155/2016/7292534 Research Article Geometric Algebra Techniques in Flux Compactifications Calin Iuliu Lazaroiu,1 Elena Mirela Babalic,2 and Ioana Alexandra Coman3 1 Institute for Basic Science, Center for Geometry and Physics, Pohang 790-784, Republic of Korea 2Horia Hulubei National Institute for Physics and Nuclear Engineering, Department of Theoretical Physics, Strada Reactorului No. 30, P.O. BOX MG-6, 077125 Magurele, Romania 3DESY,TheoryGroup,Notkestrasse85,Building2a,22607Hamburg,Germany Correspondence should be addressed to Elena Mirela Babalic; [email protected] Received 12 May 2015; Accepted 10 September 2015 Academic Editor: Shaaban Khalil Copyright © 2016 Calin Iuliu Lazaroiu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3. We study “constrained generalized Killing (s)pinors,” which characterize supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually clear and computationally effective methods for translating supersymmetry conditions into differential and algebraic constraints on collections of differential forms. In particular, we give a synthetic description of Fierz identities, which are an important ingredient of such problems. As an application, we show how our approach can be used to efficiently treat N =1compactification of M-theory on eight manifolds and prove that we recover results previously obtained in the literature. 1. Introduction The purpose of this paper is to draw attention to the fact that many of the issues mentioned above can be resolved A fundamental problem in the study of flux compactifications using ideas inspired by a certain incarnation of the theory of of -theory and string theory is to give efficient geometric Clifford bundles known as “geometric algebra,” which goes descriptions of supersymmetric backgrounds in the pres- backto[8,9](seealso[10–14]foranintroduction)—an ence of fluxes. This leads,
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