New challenges in unified theories
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ew Challenges in Unified Theories1 G. Zoupanos Theory Group, Physics Department, CERN, Geneva, Switzerland2 email: [email protected] Abstract—Among the research directions that we have presented during the Workshop SQS'2011, we have chosen to discuss here in some detail the derivation of the effective action in four dimensions of the ten dimensional N = 1 heterotic supergravity coupled to N = 1 supersymmetric Yang–Mills resulting from the dimensional reduction over nearlyKähler manifolds. DOI: 10.1134/S1063779612050401 21
1. INTRODUCTION
A large and sustained effort has been done in the recent years aiming to achieve a unified description of all interactions. Out of this endeavor two main direc tions have emerged as the most promising to attack the problem, namely, the superstring theories and non commutative geometry. The two approaches, although at a different stage of development, have common uni fication targets and share similar hopes for exhibiting improved renormalization properties in the ultraviolet (UV) as compared to ordinary field theories. Moreover the two frameworks came closer by the observation that a natural realization of noncommutativity of space appears in the string theory context of Dbranes in the presence of a constant background antisymmet ric field. However, despite the importance of having frameworks to discuss quantum gravity in a selfcon sistent way and possibly to construct there finite theo ries, it is very interesting to search for the minimal realistic framework in which finiteness can take place. In addition, the main goal expected from a unified description of interactions by the particle physics community is to understand the present day large number of free parameters of the Standard Model (SM) in terms of a few fundamental ones. In other words, to achieve reduction of couplings at a more fundamental level. It is a thoroughly fascinating fact that many interesting ideas that have survived various theoretical and phenomenological tests, as well as the solution to the UV divergences problem, find a com mon ground in the framework of N = 1 Finite Unified Theories, which is one of the research directions that we have presented in the Workshop SQS'2011. From the theoretical side they solve the problem of UV divergences in a minimal way. On the phenomenolog ical side, since they are based on the principle of reduction of couplings (expressed via RGI relations 1 The article is published in the original. 2 On leave from Physics Department, National Technical Univer
sity of Athens, Zografou Campus, GR15780 Zografou, Greece.
among couplings and masses), they provide strict selection rules in choosing realistic models which lead to testable predictions [1]. Given the above considerations our group is devel oping activities in the following research directions: 1. Dimensional Reduction of the heterotic string over nearlyKähler Manifolds [2, 4]. 2. Higher dimensional Unification with Fuzzy Extra Dimensions [5–8]. 3. Finite Unification [1]. Due to lack of space we discuss in
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