Final Report Summary - QUANTUMSUPERSYMMETRY (Quantum aspects of extended supersymmetric gauge theories)
Project context and objectives
This project aimed at studying topical problems of modern high-energy theoretical physics.
It is well known that our universe consists of a number of elementary particles that interact between each other by virtue of four types of fundamental interactions, namely electromagnetic, weak, strong and gravitational. Each of these interactions is characterised by its own energy scale and by the particles involved in the interaction. One of the most striking achievements of theoretical physics is that the first three types of interactions (electro-magnetic, weak and strong) are described by the so called Standard Model, which is based on the quantum field theory of Yang-Mills (or gauge) fields. This model provides us with a very precise description of all known experimental results in elementary particle physics.
The gravitational force has a completely different origin in comparison with the other fundamental interactions. Though the gravitational interactions between single elementary particles are extremely weak, gravity is responsible for the structure of stars, galaxies and the universe as a whole. Recently, the most striking results in the development of theoretical physics based on string theory show that gravity can be described on an equal footing with the other forces, in particular via gauge/gravity correspondence. An important building block of this theoretical construction is supersymmetry, which requires particles of integer and half integer spins to be treated equally within the unified theory. Theorists assume that supersymmetry played an important role in the very early epochs of the universe when the energy density was incredibly high, while it is spontaneously broken at low energy scales. Experimentalists at the European Laboratory for Particle Physics (CERN) in Geneva are looking for traces of supersymmetry in the Large Hadron Collider.
Studying supersymmetric quantum field theories and supergravity is a topical problem, which aims at understanding the possible implications of supersymmetry, both for the properties of the fundamental theory and the phenomenologically relevant model building.
Work performed
This project has dealt with the fundamental aspects of supersymmetric theories. One of the objectives of this project was to reveal and study quantum properties of three-dimensional N=2,4,6 and 8 supersymmetric gauge models of Chern-Simons type, which effectively describe so-called M2-brane systems of superstring theory, playing an important role in gauge/gravity correspondence. To achieve this goal one had first to develop appropriate superfield methods for the description of these models and then to compute leading terms in their quantum effective action, calculate correlation functions of composite operators and reveal their supergravity interpretation.
Another objective was to carry out a similar study of four-dimensional N=3,4 supersymmetric Young-Mills (SYM) theory, which is a supersymmetric prototype of the gauge field part of the Standard Model of elementary particles. In string theory, the N=4 SYM theory is an effective description of systems of 3-D branes, through which one establishes gauge/gravity correspondence in this sector of the unified theory. To reach this objective the harmonic superspaces with USp(4) and SU(2)xSU(2) harmonic variables have been introduced and used to compute the low-energy effective action of N=4, d=4 SYM theory. The symmetries of the Wess-Zumino term of this action were also studied.
Main results
By applying the background superfield method in N=2 superspace developed within this project, the low-energy effective actions for 3-D N=2 supersymmetric Chern--Simons theories and for N=2,4 and 8 SYM theories were obtained and the corresponding leading quantum corrections were computed. The relationship between these effective actions and D2/M2 brane dynamics have been revealed.
The structure of the quantum effective action of N=4, d=4 SYM theory in the USp(4) and SU(2)xSU(2) harmonic superspaces was derived. New forms of its Wess-Zumino term were found and analysed.
The problem of the low-energy effective action of the N=3 SYM theory was solved. The effective Lagrangian was constructed in terms of superfield strengths in N=3 harmonic superspace. The effective action was proved to be superconformally invariant; the component structure of this action was analysed. This provided the basis for comparing the results of quantum computations, which can be carried out in the harmonic superspace with those done using other methods.
The quantum effective action in d=3, N=2 supersymmetric Wess-Zumino model was studied. Leading quantum corrections to the Kaehler and chiral superpotentials were computed and the effective scalar potentials derived.
The novel superfield methods developed in this project and the results obtained should be useful for theoretical groups studying fundamental aspects of supersymmetric gauge theories, in particular their quantum properties, as well as for studies aimed at establishing, via holographic duality, the correspondence of these theories with gravity and the theory of strings and branes.
Socio-economic impact of the project
The research has been in collaboration with theorists in Russia, the United States of America (USA) and Italy, resulting in the important transfer of knowledge to Europe and, in particular, to the Italian host institution in the form of innovative methods, approaches and techniques in which the Russian and American collaborators are well-renowned experts. The established scientific links and the results obtained have laid the foundation for further development on research topics initiated within this project.
The results have been disseminated in five papers that were published in leading international peer-reviewed journals and in one online preprint archive. They have been reported on at six international conferences and six scientific seminars in Europe, Russia and the USA, thus promoting the role of the Marie Curie Actions in the support and development of science.
This project aimed at studying topical problems of modern high-energy theoretical physics.
It is well known that our universe consists of a number of elementary particles that interact between each other by virtue of four types of fundamental interactions, namely electromagnetic, weak, strong and gravitational. Each of these interactions is characterised by its own energy scale and by the particles involved in the interaction. One of the most striking achievements of theoretical physics is that the first three types of interactions (electro-magnetic, weak and strong) are described by the so called Standard Model, which is based on the quantum field theory of Yang-Mills (or gauge) fields. This model provides us with a very precise description of all known experimental results in elementary particle physics.
The gravitational force has a completely different origin in comparison with the other fundamental interactions. Though the gravitational interactions between single elementary particles are extremely weak, gravity is responsible for the structure of stars, galaxies and the universe as a whole. Recently, the most striking results in the development of theoretical physics based on string theory show that gravity can be described on an equal footing with the other forces, in particular via gauge/gravity correspondence. An important building block of this theoretical construction is supersymmetry, which requires particles of integer and half integer spins to be treated equally within the unified theory. Theorists assume that supersymmetry played an important role in the very early epochs of the universe when the energy density was incredibly high, while it is spontaneously broken at low energy scales. Experimentalists at the European Laboratory for Particle Physics (CERN) in Geneva are looking for traces of supersymmetry in the Large Hadron Collider.
Studying supersymmetric quantum field theories and supergravity is a topical problem, which aims at understanding the possible implications of supersymmetry, both for the properties of the fundamental theory and the phenomenologically relevant model building.
Work performed
This project has dealt with the fundamental aspects of supersymmetric theories. One of the objectives of this project was to reveal and study quantum properties of three-dimensional N=2,4,6 and 8 supersymmetric gauge models of Chern-Simons type, which effectively describe so-called M2-brane systems of superstring theory, playing an important role in gauge/gravity correspondence. To achieve this goal one had first to develop appropriate superfield methods for the description of these models and then to compute leading terms in their quantum effective action, calculate correlation functions of composite operators and reveal their supergravity interpretation.
Another objective was to carry out a similar study of four-dimensional N=3,4 supersymmetric Young-Mills (SYM) theory, which is a supersymmetric prototype of the gauge field part of the Standard Model of elementary particles. In string theory, the N=4 SYM theory is an effective description of systems of 3-D branes, through which one establishes gauge/gravity correspondence in this sector of the unified theory. To reach this objective the harmonic superspaces with USp(4) and SU(2)xSU(2) harmonic variables have been introduced and used to compute the low-energy effective action of N=4, d=4 SYM theory. The symmetries of the Wess-Zumino term of this action were also studied.
Main results
By applying the background superfield method in N=2 superspace developed within this project, the low-energy effective actions for 3-D N=2 supersymmetric Chern--Simons theories and for N=2,4 and 8 SYM theories were obtained and the corresponding leading quantum corrections were computed. The relationship between these effective actions and D2/M2 brane dynamics have been revealed.
The structure of the quantum effective action of N=4, d=4 SYM theory in the USp(4) and SU(2)xSU(2) harmonic superspaces was derived. New forms of its Wess-Zumino term were found and analysed.
The problem of the low-energy effective action of the N=3 SYM theory was solved. The effective Lagrangian was constructed in terms of superfield strengths in N=3 harmonic superspace. The effective action was proved to be superconformally invariant; the component structure of this action was analysed. This provided the basis for comparing the results of quantum computations, which can be carried out in the harmonic superspace with those done using other methods.
The quantum effective action in d=3, N=2 supersymmetric Wess-Zumino model was studied. Leading quantum corrections to the Kaehler and chiral superpotentials were computed and the effective scalar potentials derived.
The novel superfield methods developed in this project and the results obtained should be useful for theoretical groups studying fundamental aspects of supersymmetric gauge theories, in particular their quantum properties, as well as for studies aimed at establishing, via holographic duality, the correspondence of these theories with gravity and the theory of strings and branes.
Socio-economic impact of the project
The research has been in collaboration with theorists in Russia, the United States of America (USA) and Italy, resulting in the important transfer of knowledge to Europe and, in particular, to the Italian host institution in the form of innovative methods, approaches and techniques in which the Russian and American collaborators are well-renowned experts. The established scientific links and the results obtained have laid the foundation for further development on research topics initiated within this project.
The results have been disseminated in five papers that were published in leading international peer-reviewed journals and in one online preprint archive. They have been reported on at six international conferences and six scientific seminars in Europe, Russia and the USA, thus promoting the role of the Marie Curie Actions in the support and development of science.