Periodic Reporting for period 1 - HSQG (Higher Spin Quantum Gravity: Lagrangian Formulations for Higher Spin Gravity and Their Applications)
Reporting period: 2020-12-01 to 2022-11-30
The problem
The Action "Higher Spin Quantum Gravity: Lagrangian Formulations for Higher Spin Gravity and Their Applications" is looking into the Lagrangian formulation for higher-spin (HS) gravity, one of the long-standing questions in research on Quantum Gravity.
In a particular setup, known as the holographic duality (aka AdS/CFT duality), the "simplest" possible candidate for quantum gravity is the holographic dual of the free conformal field theory, the simplest CFT. There, Quantum Gravity is described by
a theory that contains an infinite tower of massless HS fields. It is known as HS Gravity or Vasiliev theory. Remarkably, this theory is hard to describe even classically: the main obstacle to understanding this theory at the quantum level is the absence
of the classical Lagrangian. Finding this classical Lagrangian formulation would be an important milestone toward establishing a theory of Quantum Gravity.
Why is it important for society?
The problem under consideration is completely theoretical and has no ambition of a direct impact on general society. However, the research in this direction invites attention for several reasons. Apart from being a problem that interests a large number
of specialists and non-experts, it is also one of the leading directions where new mathematical methods are introduced in physics, guided by only the consistency of the framework, without further need for experimental verifications.
The results reported during the project may potentially lead to applications also in other areas of theoretical and experimental physics, e.g. related to monopoles (hypothetical particles carrying magnetic charge).
What are the overall objectives?
The overall objective of the action is to achieve a Lagrangian formulation for HS Gravity - a long-standing problem in theoretical physics. It also has an objective of professional development of the individual researcher (K.M.).
The Action "Higher Spin Quantum Gravity: Lagrangian Formulations for Higher Spin Gravity and Their Applications" is looking into the Lagrangian formulation for higher-spin (HS) gravity, one of the long-standing questions in research on Quantum Gravity.
In a particular setup, known as the holographic duality (aka AdS/CFT duality), the "simplest" possible candidate for quantum gravity is the holographic dual of the free conformal field theory, the simplest CFT. There, Quantum Gravity is described by
a theory that contains an infinite tower of massless HS fields. It is known as HS Gravity or Vasiliev theory. Remarkably, this theory is hard to describe even classically: the main obstacle to understanding this theory at the quantum level is the absence
of the classical Lagrangian. Finding this classical Lagrangian formulation would be an important milestone toward establishing a theory of Quantum Gravity.
Why is it important for society?
The problem under consideration is completely theoretical and has no ambition of a direct impact on general society. However, the research in this direction invites attention for several reasons. Apart from being a problem that interests a large number
of specialists and non-experts, it is also one of the leading directions where new mathematical methods are introduced in physics, guided by only the consistency of the framework, without further need for experimental verifications.
The results reported during the project may potentially lead to applications also in other areas of theoretical and experimental physics, e.g. related to monopoles (hypothetical particles carrying magnetic charge).
What are the overall objectives?
The overall objective of the action is to achieve a Lagrangian formulation for HS Gravity - a long-standing problem in theoretical physics. It also has an objective of professional development of the individual researcher (K.M.).
The work performed during the Project resulted in seven papers (five published, two submitted) in the highly-ranked scientific journals in the field, and more results are yet to be reported.
Despite the limitations due to the Pandemic, I was invited to present my work at 8 international conferences (two of them remotely) and gave around 10 seminars for different institutions (altogether spanning more than 10 countries).
I also participated in a number of local events in the London area and Cambridge. During the project, I gave special courses of lectures for master's and Ph.D. students at Imperial College, gaining experience in teaching and communicating cutting-edge research.
To summarize the research results already reported in publications, I will pinpoint the most important achievements.
We derived the first examples of consistent theories of multiple gravitational fields, that is an extension of Einstein's gravity, containing the latter as a subsector, and admitting flat Minkowski space as a solution.
We constructed a Lagrangian for general nonlinear electrodynamics that features electric and magnetic potentials on equal footing. This leads to the explicit Lagrangian formulation of theories with continuous electric-magnetic duality symmetry.
We developed the democratic Lagrangian formulation for arbitrary (chiral) p-forms in arbitrary dimensions including arbitrary abelian interactions. This includes arbitrary abelian interactions for chiral p-forms, for which the Lorentz-covariant Lagrangian was a challenge.
We studied solutions in non-linear electrodynamics and established several general results.
We presented a universal democratic Lagrangian for ten-dimensional type II supergravities (low energy limits of corresponding type II string theories), treating electric and magnetic potentials on equal footing.
In a short review submitted to a special issue of the Journal “Differential Geometry and its Applications”, we explained the advantages of our new formulation of p-form dynamics compared to existing alternatives.
A Master Thesis entitled "Generalization of non-linear dual symmetric electromagnetic Lagrangians" by Mantas Svazas was completed under my co-supervision with Prof. Arkady Tseytlin.
These results were reported in several conferences and seminars and were received with high interest. In particular, my work received an honorary mention in the conference "Strings 2022", the biggest annual event in theoretical high-energy physics.
I also gave several interviews for Radio and Internet TV in Armenia and wrote several op-eds related to the organization of science on popular internet portals (in Armenian).
Despite the limitations due to the Pandemic, I was invited to present my work at 8 international conferences (two of them remotely) and gave around 10 seminars for different institutions (altogether spanning more than 10 countries).
I also participated in a number of local events in the London area and Cambridge. During the project, I gave special courses of lectures for master's and Ph.D. students at Imperial College, gaining experience in teaching and communicating cutting-edge research.
To summarize the research results already reported in publications, I will pinpoint the most important achievements.
We derived the first examples of consistent theories of multiple gravitational fields, that is an extension of Einstein's gravity, containing the latter as a subsector, and admitting flat Minkowski space as a solution.
We constructed a Lagrangian for general nonlinear electrodynamics that features electric and magnetic potentials on equal footing. This leads to the explicit Lagrangian formulation of theories with continuous electric-magnetic duality symmetry.
We developed the democratic Lagrangian formulation for arbitrary (chiral) p-forms in arbitrary dimensions including arbitrary abelian interactions. This includes arbitrary abelian interactions for chiral p-forms, for which the Lorentz-covariant Lagrangian was a challenge.
We studied solutions in non-linear electrodynamics and established several general results.
We presented a universal democratic Lagrangian for ten-dimensional type II supergravities (low energy limits of corresponding type II string theories), treating electric and magnetic potentials on equal footing.
In a short review submitted to a special issue of the Journal “Differential Geometry and its Applications”, we explained the advantages of our new formulation of p-form dynamics compared to existing alternatives.
A Master Thesis entitled "Generalization of non-linear dual symmetric electromagnetic Lagrangians" by Mantas Svazas was completed under my co-supervision with Prof. Arkady Tseytlin.
These results were reported in several conferences and seminars and were received with high interest. In particular, my work received an honorary mention in the conference "Strings 2022", the biggest annual event in theoretical high-energy physics.
I also gave several interviews for Radio and Internet TV in Armenia and wrote several op-eds related to the organization of science on popular internet portals (in Armenian).
The progress beyond the state of the art has been reported so far in two directions: towards the Lagrangian formulation of HS Gravity in d=3 and d=4.
For d=3, the full classification of the interactions involving massless HS fields was completed in 2019. Building on these results, the construction of Lagrangian theories for HS Gravity with a matter in d=3 is a work in progress currently.
In d=4, the macroscopic spacetime dimension of our real world, the standard formulation of massless fields of any spin, the so-called Fronsdal formulation, is not able to capture all the interactions of massless HS fields. Therefore, one needs a new formulation of massless dynamics. In 2019, I started a program of deriving a new
formulation of massless dynamics, treating electric and magnetic degrees of freedom on an equal footing. We already developed such a formulation for spin one making remarkable progress in this century-old subject. We managed to develop a new formulation where the Lorentz invariant Lagrangian is given for the democratic
description of arbitrary non-linear electrodynamics theory and further extend these results to higher-dimensional p-form generalizations. The results of our research were published in highly-ranked scientific journals. In particular, we published a paper in Phys. Rev. Lett., in 2021 with Zhirayr Avetisyan and Oleg Evnin. The development
of this democratic approach to spin two and higher spins is a work in progress. Such a formulation will define a new description with more symmetries for arbitrary massless degrees of freedom in 3+1 dimensions, thus allowing us to address the problem of the nonlinear Lagrangian for Vasiliev's theory from a new perspective.
The results of this project comprise several important steps toward our goal: constructing the simplest complete example of Quantum Gravity. Reaching this goal can spark excitement in the high-energy physics community and lead to the fast development of many new methods relevant to address different issues in particle
physics, gravitational waves, and related areas, finally leading to experiments probing quantum properties of gravity in the real world. The research program started during the project will lead to further high-impact publications over several years to come in addition to the reported publications during the project period.
To conclude, this project has served its purpose making drastic progress toward its final research goals and supporting the professional development of the individual researcher.
For d=3, the full classification of the interactions involving massless HS fields was completed in 2019. Building on these results, the construction of Lagrangian theories for HS Gravity with a matter in d=3 is a work in progress currently.
In d=4, the macroscopic spacetime dimension of our real world, the standard formulation of massless fields of any spin, the so-called Fronsdal formulation, is not able to capture all the interactions of massless HS fields. Therefore, one needs a new formulation of massless dynamics. In 2019, I started a program of deriving a new
formulation of massless dynamics, treating electric and magnetic degrees of freedom on an equal footing. We already developed such a formulation for spin one making remarkable progress in this century-old subject. We managed to develop a new formulation where the Lorentz invariant Lagrangian is given for the democratic
description of arbitrary non-linear electrodynamics theory and further extend these results to higher-dimensional p-form generalizations. The results of our research were published in highly-ranked scientific journals. In particular, we published a paper in Phys. Rev. Lett., in 2021 with Zhirayr Avetisyan and Oleg Evnin. The development
of this democratic approach to spin two and higher spins is a work in progress. Such a formulation will define a new description with more symmetries for arbitrary massless degrees of freedom in 3+1 dimensions, thus allowing us to address the problem of the nonlinear Lagrangian for Vasiliev's theory from a new perspective.
The results of this project comprise several important steps toward our goal: constructing the simplest complete example of Quantum Gravity. Reaching this goal can spark excitement in the high-energy physics community and lead to the fast development of many new methods relevant to address different issues in particle
physics, gravitational waves, and related areas, finally leading to experiments probing quantum properties of gravity in the real world. The research program started during the project will lead to further high-impact publications over several years to come in addition to the reported publications during the project period.
To conclude, this project has served its purpose making drastic progress toward its final research goals and supporting the professional development of the individual researcher.