Periodic Reporting for period 1 - CeleBH (The Celestial Road to a Holographic Description of Black Holes)
Reporting period: 2023-10-01 to 2026-03-31
Black holes are at the root of the most striking puzzles in theoretical physics as they lie at the crossroads of two fundamental theories: general relativity, which describes gravitation, and quantum mechanics, the theory which governs physics at very small scales. Black holes are therefore thought to be key to a formulation of a theory of quantum gravity. One of the most promising ideas to access the elusive quantum nature of black holes is the idea of holography, which establishes a correspondence between quantum gravity in a given spacetime and a (non-gravitational) quantum field theory that lives at the boundary of spacetime. The holographic principle has proved extremely successful when applied for idealized models of spacetimes and constitutes a major advance in string theory and quantum gravity.
The challenge now, which lies at the core of this project, is to go away from idealized scenarios and to develop a holographic description of quantum gravity for realistic spacetimes. This would allow us to understand the deep quantum nature of realistic black holes, such as the ones we observe in the sky.
The goal of this project is to make major steps toward a holographic description of quantum gravity in asymptotically flat spacetimes which include black hole geometries ("flat holography"). To achieve this, the project exploits a rich and novel interplay between two complementary frameworks for flat holography. In the first framework, the holographic theory is described in terms of a two-dimensional conformal field theory (CFT) living on the celestial sphere, known as celestial CFT. The second framework leverages the intrinsic geometric structure of the conformal boundary of flat spacetimes, aiming at a formulation in terms of a “conformal Carrollian theory” defined at timelike and null infinity. Both approaches are highly constrained by the infinite-dimensional nature of the boundary symmetries (the so-called BMS symmetries and their extensions). Remarkably, very similar symmetries appear in the vicinity of black hole horizons, and the near-horizon geometry and physics share striking resemblance with the ones at infinity. This project aims to uncover the physical implications of these infinite-dimensional symmetries for black hole spacetimes, combining diverse methodology and insights coming from scattering amplitudes, conformal geometry and conformal field theory, twistor theory, representation theory, gravitational wave observation and string theory, in order to target the ambitious goal of a holographic description of realistic black holes.
The challenge now, which lies at the core of this project, is to go away from idealized scenarios and to develop a holographic description of quantum gravity for realistic spacetimes. This would allow us to understand the deep quantum nature of realistic black holes, such as the ones we observe in the sky.
The goal of this project is to make major steps toward a holographic description of quantum gravity in asymptotically flat spacetimes which include black hole geometries ("flat holography"). To achieve this, the project exploits a rich and novel interplay between two complementary frameworks for flat holography. In the first framework, the holographic theory is described in terms of a two-dimensional conformal field theory (CFT) living on the celestial sphere, known as celestial CFT. The second framework leverages the intrinsic geometric structure of the conformal boundary of flat spacetimes, aiming at a formulation in terms of a “conformal Carrollian theory” defined at timelike and null infinity. Both approaches are highly constrained by the infinite-dimensional nature of the boundary symmetries (the so-called BMS symmetries and their extensions). Remarkably, very similar symmetries appear in the vicinity of black hole horizons, and the near-horizon geometry and physics share striking resemblance with the ones at infinity. This project aims to uncover the physical implications of these infinite-dimensional symmetries for black hole spacetimes, combining diverse methodology and insights coming from scattering amplitudes, conformal geometry and conformal field theory, twistor theory, representation theory, gravitational wave observation and string theory, in order to target the ambitious goal of a holographic description of realistic black holes.
My research team and I have derived powerful new constraints for the sought-after holographic theory of flat spacetimes.
On the celestial side, one of the most pressing questions is to understand to what extent celestial CFTs differ from conventional 2D CFTs. A particularly intriguing feature of celestial CFTs is that the celestial stress tensor exhibits a vanishing central charge. This led us to investigate the framework of logarithmic CFTs. The latter are non-unitary theories characterized by the presence of a scale, while still preserving conformal invariance. We revealed that certain currents in celestial CFT, which capture essential features of the infrared structure of amplitudes, display the same patterns as those found in logarithmic CFTs. We also addressed a second outstanding goal: proving an explicit example of a pair of dual theories. We obtained new top-down results for celestial holography which provide a dual celestial CFT realization for maximally-helicity-violating gluon amplitudes.
On the Carrollian side, we obtained the explicit realization of the newly discovered w-infinity algebra on the asymptotic data at null infinity. Our derivation is the first to provide twistor methods for Carrollian holography. These results bridge together Carrollian theories with the w-symmetries originally discovered by Penrose in twistor theory, as well as with the recently uncovered role these symmetries play for celestial amplitudes. My team and I also showed how an extension of the w-symmetry algebra is encoded, in a hidden way, in the equations of motion in Einstein-Yang-Mills theory.
One of the most significant results of the project is the construction of wavefunctions for unitary irreducible representations (UIRs) of the BMS group, namely BMS particles. This work extends the usual notion of Poincaré particles to account for the infinite-dimensional nature of the asymptotic symmetry group of gravity.
My team and I also made substantial progress in understanding the connection between black hole horizons and null infinity. We developed a unified framework for treating both regions based on a geometric duality that relates null infinity to an extremal horizon, and this correspondence led us to uncover a novel infinite tower of gravitational charges near black holes.
Finally, in an interdisciplinary collaboration with astrophysics for gravitational wave detection, we investigated current and future experimental efforts to detect and measure gravitational wave memory effects, including both displacement and spin memory.
On the celestial side, one of the most pressing questions is to understand to what extent celestial CFTs differ from conventional 2D CFTs. A particularly intriguing feature of celestial CFTs is that the celestial stress tensor exhibits a vanishing central charge. This led us to investigate the framework of logarithmic CFTs. The latter are non-unitary theories characterized by the presence of a scale, while still preserving conformal invariance. We revealed that certain currents in celestial CFT, which capture essential features of the infrared structure of amplitudes, display the same patterns as those found in logarithmic CFTs. We also addressed a second outstanding goal: proving an explicit example of a pair of dual theories. We obtained new top-down results for celestial holography which provide a dual celestial CFT realization for maximally-helicity-violating gluon amplitudes.
On the Carrollian side, we obtained the explicit realization of the newly discovered w-infinity algebra on the asymptotic data at null infinity. Our derivation is the first to provide twistor methods for Carrollian holography. These results bridge together Carrollian theories with the w-symmetries originally discovered by Penrose in twistor theory, as well as with the recently uncovered role these symmetries play for celestial amplitudes. My team and I also showed how an extension of the w-symmetry algebra is encoded, in a hidden way, in the equations of motion in Einstein-Yang-Mills theory.
One of the most significant results of the project is the construction of wavefunctions for unitary irreducible representations (UIRs) of the BMS group, namely BMS particles. This work extends the usual notion of Poincaré particles to account for the infinite-dimensional nature of the asymptotic symmetry group of gravity.
My team and I also made substantial progress in understanding the connection between black hole horizons and null infinity. We developed a unified framework for treating both regions based on a geometric duality that relates null infinity to an extremal horizon, and this correspondence led us to uncover a novel infinite tower of gravitational charges near black holes.
Finally, in an interdisciplinary collaboration with astrophysics for gravitational wave detection, we investigated current and future experimental efforts to detect and measure gravitational wave memory effects, including both displacement and spin memory.
The identification of BMS particles, defined as unitary irreducible representations (UIRs) of the BMS group, has important implications for the flat space holography program. Any consistent formulation of a holographic correspondence between bulk and boundary states must rely on the equivalence of UIRs of the boundary symmetry group. Before our work, very few attempts had been made to understand the physics encoded in BMS UIRs, and, more broadly, tools from representation theory remained largely underdeveloped in the context of flat space holography. The core innovation of our construction is a complete reconsideration of the classification of BMS UIRs, informed by the hard/soft decomposition of supermomenta, as suggested by recent advancements in scattering amplitudes, soft theorems, and infrared dressings. Our results demonstrate that BMS particles naturally describe quantum superpositions of Poincaré particles propagating on inequivalent gravitational vacua. This demonstrates that representation theory offers a powerful and rigid mathematical framework for both celestial and Carrollian holography.
The formalism of BMS scattering states (and their analogues in quantum electrodynamics) that we introduced also has the potential to provide novel foundations for quantum field theory (QFT) with massless particles. Indeed, since infrared divergences arise, for conventional QFT states, as a necessity to respect BMS conservation laws, we expect BMS S-matrix elements to define genuine, IR-finite, amplitudes when massless particles are involved. A major achievement in this direction would thus be the explicit construction of S-matrix elements for BMS scattering states. As an initial step towards this ambitious program, one should identify the equivalent of Mandelstam variables in this setting. Additionally, appropriate limiting procedures must be developed to establish connections with the conventional S-matrix and observable cross-sections.
The formalism of BMS scattering states (and their analogues in quantum electrodynamics) that we introduced also has the potential to provide novel foundations for quantum field theory (QFT) with massless particles. Indeed, since infrared divergences arise, for conventional QFT states, as a necessity to respect BMS conservation laws, we expect BMS S-matrix elements to define genuine, IR-finite, amplitudes when massless particles are involved. A major achievement in this direction would thus be the explicit construction of S-matrix elements for BMS scattering states. As an initial step towards this ambitious program, one should identify the equivalent of Mandelstam variables in this setting. Additionally, appropriate limiting procedures must be developed to establish connections with the conventional S-matrix and observable cross-sections.