Periodic Reporting for period 2 - HiSS (Higher Spin Symmetry in Quantum Gravity, Condensed Matter and Mathematics)
Berichtszeitraum: 2023-03-01 bis 2024-08-31
The workflow and results of HiSS during the first period can be roughly divided into (but are not limited to) the following areas:
1) Development of Chiral higher spin gravity (HiSGRA)
The main result of the first stage is the explicit construction of covariant, gauge-invariant equations of motion of Chiral HiSGRA in the form of the sigma-model.
The underlying strong homotopy algebra was found to be a pre-Calabi-Yau algebra and all structure maps are explicitly given in the form of certain configuration space integrals reminiscent of (Shoikhet-Tsygan-)Kontsevich formality. Following the formality theorems, the consistency of the theory has been proven via Stokes’ theorem. Since the first two levels of the strong homotopy algebra are directly related to (Shoikhet-Tsygan-)Kontsevich formality the result indicates the existence of a vast extension of these formality theorems.
Based on the existence of a well-defined, local Chiral HiSGRA in anti-de Sitter space it was pointed out that there have to exist two closed subsectors in Chern-Simons vector models. It was also shown the 3d bosonization duality is a simple consequence of existence of Chiral HiSGRA at least up to the level of four-point functions. On the CFT side the construction of invariants of the slightly-broken higher spin symmetry has been completed and combined with the already proven uniqueness of those implies the 3d bosonization duality in the large-N limit.
A close connection to twistor theory has begun to emerge. It was shown that the higher spin extensions of self-dual Yang-Mills and self-dual gravity, which are contractions of Chiral HiSGRA, can naturally be formulated on twistor space. Analogs of Penrose and Ward theorems have also been proved. It was shown that the action of Chiral HiSGRA on twistor space is captured by Chern-Simons theory.
2) Black hole scattering from massive higher spins.
Everything compact and rotating (with microscopic or macroscopic angular momentum), from hadrons and nuclei to black holes and stars, can, in principle, be modelled by effective field theories of massive particles with spin. Since Dirac, Fierz, Pauli and many others, it has been a notoriously complicated problem to construct interacting theories of massive fields with spin. Positive solutions are limited to spontaneously broken Yang-Mills theory and to, recently, massive (bi)-gravity.
During the first stage of the project, a new efficient approach — chiral approach — to constructing interactions of massive fields with spin has been proposed. This immediately gave a couple of examples of complete, but parity violating, theories of a single massive arbitrary spin field interacting with electromagnetism and gravity. The main result is the construction of a consistent parity preserving theory of this type up to the quartic order that is supposed to describe the dynamics of black holes.
3) Quantum corrections in AdS/CFT correspondence.
Despite the recent 25 years of AdS/CFT correspondence it still remains a great challenge to compute quantum corrections in the bulk, which is, of course, also relevant for HiSGRA. New techniques to compute the loop diagrams in (anti-)de Sitter space have been developed and applied to compute anomalous dimensions of all double-trace operators at one loop.
4) Asymptotic symmetries and S-matrix.
The famous Weinberg low energy theorem was shown to have a loophole allowing for low-derivative interactions of massless higher spin fields, which are indeed present in Chiral HiSGRA and a number of closely related examples. A deep relation between Celestial and Carrollian holographic points of view on flat space holography has been established.
1) Development of Chiral higher spin gravity (HiSGRA)
The main result of the first stage is the explicit construction of covariant, gauge-invariant equations of motion of Chiral HiSGRA in the form of the sigma-model.
The underlying strong homotopy algebra was found to be a pre-Calabi-Yau algebra and all structure maps are explicitly given in the form of certain configuration space integrals reminiscent of (Shoikhet-Tsygan-)Kontsevich formality. Following the formality theorems, the consistency of the theory has been proven via Stokes’ theorem. Since the first two levels of the strong homotopy algebra are directly related to (Shoikhet-Tsygan-)Kontsevich formality the result indicates the existence of a vast extension of these formality theorems.
Based on the existence of a well-defined, local Chiral HiSGRA in anti-de Sitter space it was pointed out that there have to exist two closed subsectors in Chern-Simons vector models. It was also shown the 3d bosonization duality is a simple consequence of existence of Chiral HiSGRA at least up to the level of four-point functions. On the CFT side the construction of invariants of the slightly-broken higher spin symmetry has been completed and combined with the already proven uniqueness of those implies the 3d bosonization duality in the large-N limit.
A close connection to twistor theory has begun to emerge. It was shown that the higher spin extensions of self-dual Yang-Mills and self-dual gravity, which are contractions of Chiral HiSGRA, can naturally be formulated on twistor space. Analogs of Penrose and Ward theorems have also been proved. It was shown that the action of Chiral HiSGRA on twistor space is captured by Chern-Simons theory.
2) Black hole scattering from massive higher spins.
Everything compact and rotating (with microscopic or macroscopic angular momentum), from hadrons and nuclei to black holes and stars, can, in principle, be modelled by effective field theories of massive particles with spin. Since Dirac, Fierz, Pauli and many others, it has been a notoriously complicated problem to construct interacting theories of massive fields with spin. Positive solutions are limited to spontaneously broken Yang-Mills theory and to, recently, massive (bi)-gravity.
During the first stage of the project, a new efficient approach — chiral approach — to constructing interactions of massive fields with spin has been proposed. This immediately gave a couple of examples of complete, but parity violating, theories of a single massive arbitrary spin field interacting with electromagnetism and gravity. The main result is the construction of a consistent parity preserving theory of this type up to the quartic order that is supposed to describe the dynamics of black holes.
3) Quantum corrections in AdS/CFT correspondence.
Despite the recent 25 years of AdS/CFT correspondence it still remains a great challenge to compute quantum corrections in the bulk, which is, of course, also relevant for HiSGRA. New techniques to compute the loop diagrams in (anti-)de Sitter space have been developed and applied to compute anomalous dimensions of all double-trace operators at one loop.
4) Asymptotic symmetries and S-matrix.
The famous Weinberg low energy theorem was shown to have a loophole allowing for low-derivative interactions of massless higher spin fields, which are indeed present in Chiral HiSGRA and a number of closely related examples. A deep relation between Celestial and Carrollian holographic points of view on flat space holography has been established.
The workflow and results of HiSS during the first period can be roughly divided into (but are not limited to) the following areas:
1) Development of Chiral higher spin gravity (Chiral HiSGRA)
The main result of the first stage is the explicit construction of covariant, gauge-invariant equations of motion of Chiral HiSGRA in the form of the sigma-model.
The underlying strong homotopy algebra was found to be a pre-Calabi-Yau algebra and all structure maps are explicitly given in the form of certain configuration space integrals reminiscent of (Shoikhet-Tsygan-)Kontsevich formality. Following the formality theorems, the consistency of the theory has been proven via Stokes’ theorem. Since the first two levels of the strong homotopy algebra are directly related to (Shoikhet-Tsygan-)Kontsevich formality the result indicates the existence of a vast extension of these formality theorems.
Based on the existence of a well-defined, local Chiral HiSGRA in anti-de Sitter space it was pointed out that there have to exist two closed subsectors in Chern-Simons vector models. It was also shown the 3d bosonization duality is a simple consequence of existence of Chiral HiSGRA at least up to the level of four-point functions. On the CFT side the construction of invariants of the slightly-broken higher spin symmetry has been completed and combined with the already proven uniqueness of those implies the 3d bosonization duality in the large-N limit.
A close connection to twistor theory has begun to emerge. It was shown that the higher spin extensions of self-dual Yang-Mills and self-dual gravity, which are contractions of Chiral HiSGRA, can naturally be formulated on twistor space. Analogs of Penrose and Ward theorems have also been proved. It was shown that the action of Chiral HiSGRA on twistor space is captured by Chern-Simons theory.
2) Black hole scattering from massive higher spins.
Everything compact and rotating (with microscopic or macroscopic angular momentum), from hadrons and nuclei to black holes and stars, can, in principle, be modelled by effective field theories of massive particles with spin. Since Dirac, Fierz, Pauli and many others, it has been a notoriously complicated problem to construct interacting theories of massive fields with spin. Positive solutions are limited to spontaneously broken Yang-Mills theory and to, recently, massive (bi)-gravity.
During the first stage of the project, a new efficient approach — chiral approach — to constructing interactions of massive fields with spin has been proposed. This immediately gave a couple of examples of complete, but parity violating, theories of a single massive arbitrary spin field interacting with electromagnetism and gravity. The main result is the construction of a consistent parity preserving theory of this type up to the quartic order that is supposed to describe the dynamics of black holes.
3) Quantum corrections in AdS/CFT correspondence.
Despite the recent 25 years of AdS/CFT correspondence it still remains a great challenge to compute quantum corrections in the bulk, which is, of course, also relevant for HiSGRA. New techniques to compute the loop diagrams in (anti-)de Sitter space have been developed and applied to compute anomalous dimensions of all double-trace operators at one loop.
4) Asymptotic symmetries and S-matrix.
The famous Weinberg low energy theorem was shown to have a loophole allowing for low-derivative interactions of massless higher spin fields, which are indeed present in Chiral HiSGRA and a number of closely related examples. A deep relation between Celestial and Carrollian holographic points of view on flat space holography has been established.
1) Development of Chiral higher spin gravity (Chiral HiSGRA)
The main result of the first stage is the explicit construction of covariant, gauge-invariant equations of motion of Chiral HiSGRA in the form of the sigma-model.
The underlying strong homotopy algebra was found to be a pre-Calabi-Yau algebra and all structure maps are explicitly given in the form of certain configuration space integrals reminiscent of (Shoikhet-Tsygan-)Kontsevich formality. Following the formality theorems, the consistency of the theory has been proven via Stokes’ theorem. Since the first two levels of the strong homotopy algebra are directly related to (Shoikhet-Tsygan-)Kontsevich formality the result indicates the existence of a vast extension of these formality theorems.
Based on the existence of a well-defined, local Chiral HiSGRA in anti-de Sitter space it was pointed out that there have to exist two closed subsectors in Chern-Simons vector models. It was also shown the 3d bosonization duality is a simple consequence of existence of Chiral HiSGRA at least up to the level of four-point functions. On the CFT side the construction of invariants of the slightly-broken higher spin symmetry has been completed and combined with the already proven uniqueness of those implies the 3d bosonization duality in the large-N limit.
A close connection to twistor theory has begun to emerge. It was shown that the higher spin extensions of self-dual Yang-Mills and self-dual gravity, which are contractions of Chiral HiSGRA, can naturally be formulated on twistor space. Analogs of Penrose and Ward theorems have also been proved. It was shown that the action of Chiral HiSGRA on twistor space is captured by Chern-Simons theory.
2) Black hole scattering from massive higher spins.
Everything compact and rotating (with microscopic or macroscopic angular momentum), from hadrons and nuclei to black holes and stars, can, in principle, be modelled by effective field theories of massive particles with spin. Since Dirac, Fierz, Pauli and many others, it has been a notoriously complicated problem to construct interacting theories of massive fields with spin. Positive solutions are limited to spontaneously broken Yang-Mills theory and to, recently, massive (bi)-gravity.
During the first stage of the project, a new efficient approach — chiral approach — to constructing interactions of massive fields with spin has been proposed. This immediately gave a couple of examples of complete, but parity violating, theories of a single massive arbitrary spin field interacting with electromagnetism and gravity. The main result is the construction of a consistent parity preserving theory of this type up to the quartic order that is supposed to describe the dynamics of black holes.
3) Quantum corrections in AdS/CFT correspondence.
Despite the recent 25 years of AdS/CFT correspondence it still remains a great challenge to compute quantum corrections in the bulk, which is, of course, also relevant for HiSGRA. New techniques to compute the loop diagrams in (anti-)de Sitter space have been developed and applied to compute anomalous dimensions of all double-trace operators at one loop.
4) Asymptotic symmetries and S-matrix.
The famous Weinberg low energy theorem was shown to have a loophole allowing for low-derivative interactions of massless higher spin fields, which are indeed present in Chiral HiSGRA and a number of closely related examples. A deep relation between Celestial and Carrollian holographic points of view on flat space holography has been established.
The explicit construction of Chiral HiSGRA’s equations of motion gives the first example of a local covariant higher spin gravity with propagating massless fields, which significantly advances the state of the art. This opens up many new research directions as it makes it possible to apply the standard field theory techniques to a higher spin theory.
In particular, it is planned to compute the holographic correlation functions and compare them with the CFT predictions. The latter are to be obtained after identifying the closed hidden subsectors of Chern-Simons matter theories directly on the CFT side. It is also expected to find the uplift of Chiral theory to twistor space and to describe the space of solution, i.e. the space of higher spin instantons. The twistor action for Chiral theory should also help to prove the absence of UV divergences to all orders. Altogether, these developments should establish Chiral HiSGRA as a useful model of quantum gravity that is AdS/CFT dual to an exactly solvable conformal field theory.
The main mathematical results on the structure of the correlation functions in large-N Chern-Simons matter theories have already been obtained and the development along this line of the research will be in getting the explicit form of the correlation functions.
It is important to continue constructing new higher spin gravities in various dimensions, including the toy models in three and two dimensions, which would significantly enrich the space of such theories.
It is natural to apply the newly developed chiral approach to massive higher spin fields to other problems, e.g. to complete the construction of the theory that describes the dynamics of black holes. Some extensions of these ideas to other dimensions are possible as well.
In particular, it is planned to compute the holographic correlation functions and compare them with the CFT predictions. The latter are to be obtained after identifying the closed hidden subsectors of Chern-Simons matter theories directly on the CFT side. It is also expected to find the uplift of Chiral theory to twistor space and to describe the space of solution, i.e. the space of higher spin instantons. The twistor action for Chiral theory should also help to prove the absence of UV divergences to all orders. Altogether, these developments should establish Chiral HiSGRA as a useful model of quantum gravity that is AdS/CFT dual to an exactly solvable conformal field theory.
The main mathematical results on the structure of the correlation functions in large-N Chern-Simons matter theories have already been obtained and the development along this line of the research will be in getting the explicit form of the correlation functions.
It is important to continue constructing new higher spin gravities in various dimensions, including the toy models in three and two dimensions, which would significantly enrich the space of such theories.
It is natural to apply the newly developed chiral approach to massive higher spin fields to other problems, e.g. to complete the construction of the theory that describes the dynamics of black holes. Some extensions of these ideas to other dimensions are possible as well.