Aspects of gauge / gravity correspondences
Lead Research Organisation:
University of Southampton
Department Name: Sch of Mathematical Sciences
Abstract
Black hole (BH) thermodynamics and Hawking radiation suggest the existence of a statistical or microscopic description of BHs behind the scenes. This description necessarily requires quantum gravity. BHs have an entropy (a quantity that measures the disorder of the system) proportional not to its volume (as usual in other systems) but instead to its horizon's area. This suggests that the quantum information of the BH is distributed over a surface rather than on a volume and motivates the holographic principle according to which quantum gravity in a given volume should have a dual description in terms of a quantum field theory (QFT) on its boundary surface.
The gravity/gauge theory dualities (correspondences) are a concrete realization of this holographic principle. Take (quantum) gravity on an anti-de Sitter (AdS) universe. An AdS background has a gravitational barrier that reflects back any object: effectively, gravity is confined inside a box. The idea behind the holographic principle is that the information inside the "AdS box", where we have typically a BH, is projected (as a hologram) into the boundary wall. There, the same information is encoded in a QFT (ie, gauge theory). So we can write the same information in two different scientific languages (the gravitational and the QFT). It is fundamental to develop the dictionary between these two languages to understand phenomena in one theory that involves hard computations by reformulating it on the dual language where computations can be easier. This proposal will develop this dictionary to understand properties of BHs, QFTs (of the kind that describe the strong nuclear interactions being studied at the Large Hadron Collider at CERN), superconductors and fluids.
In these dualities BHs play an essential role. On the gravity side of the duality, BHs are the most extreme gravitational objects. On the other hand, because they have Hawking temperature, on the QFT side they are the heating source that excites the system up to the point where energetic phenomena appears. I will discover new BH solutions, study BH instabilities, and find what they correspond to in the dual language. One is the ultraspinning instability that makes fastly spinning BHs pinch into black rings ("doughnut-like" BHs). Another is the superradiant instability whereby radiation reflected by the AdS box amplifies its energy when it scatters a BH up to the point where it is so energetic that we have a BH bomb system. Yet another one is the gravitational turbulent instability that might teach us about one of the most mysterious processes in fluids and aerodynamics: turbulence.
Unconventional high-temperature superconductors have been discovered in the lab but no theory can describe their properties satisfactorily. The gravity / condensed matter correspondence proposes that with holographic superconductors one can use gravity to model the experimental superconductors. This project will develop more realistic models of holographic superconductors to get novel insights into strongly coupled physics.
Remarkably the gravity/gauge dualities can have a hydrodynamic description. The tantalising similarities between BH physics, and the properties of soap bubbles and fluid lumps, have been observed from old: A BH has a horizon with surface gravity, like a fluid droplet has a surface tension; Hawking evaporation of a BH bears a resemblance to the fluid droplet's evaporation; Black strings ("tubes") pinch-off into spherical BHs much like a water jet dripping from a faucet breaks into droplets. But, albeit these analogies, only recently was a formal scientific correspondence found between gravity and hydrodynamics: hydrodynamic equations encode in a certain regime Einstein's equations! Phenomena in gravity can be studied using a dual fluid dynamic language. A goal of this project is to develop the dictionary between these scientific languages and use it to study open problems in gravity, QFT and hydrodynamics.
The gravity/gauge theory dualities (correspondences) are a concrete realization of this holographic principle. Take (quantum) gravity on an anti-de Sitter (AdS) universe. An AdS background has a gravitational barrier that reflects back any object: effectively, gravity is confined inside a box. The idea behind the holographic principle is that the information inside the "AdS box", where we have typically a BH, is projected (as a hologram) into the boundary wall. There, the same information is encoded in a QFT (ie, gauge theory). So we can write the same information in two different scientific languages (the gravitational and the QFT). It is fundamental to develop the dictionary between these two languages to understand phenomena in one theory that involves hard computations by reformulating it on the dual language where computations can be easier. This proposal will develop this dictionary to understand properties of BHs, QFTs (of the kind that describe the strong nuclear interactions being studied at the Large Hadron Collider at CERN), superconductors and fluids.
In these dualities BHs play an essential role. On the gravity side of the duality, BHs are the most extreme gravitational objects. On the other hand, because they have Hawking temperature, on the QFT side they are the heating source that excites the system up to the point where energetic phenomena appears. I will discover new BH solutions, study BH instabilities, and find what they correspond to in the dual language. One is the ultraspinning instability that makes fastly spinning BHs pinch into black rings ("doughnut-like" BHs). Another is the superradiant instability whereby radiation reflected by the AdS box amplifies its energy when it scatters a BH up to the point where it is so energetic that we have a BH bomb system. Yet another one is the gravitational turbulent instability that might teach us about one of the most mysterious processes in fluids and aerodynamics: turbulence.
Unconventional high-temperature superconductors have been discovered in the lab but no theory can describe their properties satisfactorily. The gravity / condensed matter correspondence proposes that with holographic superconductors one can use gravity to model the experimental superconductors. This project will develop more realistic models of holographic superconductors to get novel insights into strongly coupled physics.
Remarkably the gravity/gauge dualities can have a hydrodynamic description. The tantalising similarities between BH physics, and the properties of soap bubbles and fluid lumps, have been observed from old: A BH has a horizon with surface gravity, like a fluid droplet has a surface tension; Hawking evaporation of a BH bears a resemblance to the fluid droplet's evaporation; Black strings ("tubes") pinch-off into spherical BHs much like a water jet dripping from a faucet breaks into droplets. But, albeit these analogies, only recently was a formal scientific correspondence found between gravity and hydrodynamics: hydrodynamic equations encode in a certain regime Einstein's equations! Phenomena in gravity can be studied using a dual fluid dynamic language. A goal of this project is to develop the dictionary between these scientific languages and use it to study open problems in gravity, QFT and hydrodynamics.
People |
ORCID iD |
| Oscar Joao Campos Dias (Principal Investigator / Fellow) |
Publications
Bea Y
(2021)
Crossing a large-N phase transition at finite volume
in Journal of High Energy Physics
Bea Y
(2021)
Crossing a large-N phase transition at finite volume
Bena I
(2019)
Holographic dual of hot Polchinski-Strassler quark-gluon plasma
in Journal of High Energy Physics
Betzios P
(2019)
Euclidean wormholes and holography
in Journal of High Energy Physics
Betzios P
(2017)
FZZT branes and non-singlets of Matrix Quantum Mechanics
Betzios P
(2018)
Antipodal correlation on the meron wormhole and a bang-crunch universe
in Physical Review D
Cardoso V
(2018)
Constraining the mass of dark photons and axion-like particles through black-hole superradiance
in Journal of Cosmology and Astroparticle Physics
Cayuso R
(2020)
Massive vector fields in Kerr-Newman and Kerr-Sen black hole spacetimes
in Journal of High Energy Physics
| Description | My scientific research interests can be summarized as follows. Essentially, I am an expert on Einstein's general relativity. My research consists on solving the Einstein equation to find its solutions (specially black holes), study their linear and nonlinear stability and understand physical processes that occur in black hole backgrounds. Often, the outcomes of my research have been opening new research avenues in mathematical physics, in particular in mathematical relativity and numerical relativity. Some of my scientific achievements are being possible because I am involved in a long term program aiming at developing numerical schemes to solve the (non-)linear systems of coupled partial differential equations of Einstein's gravity. As a recognition of this programme, we were invited to write a Topical Review on this subject for Classical and Quantum Gravity. Some of my research can be described in more detail as follows. At the beginning of this century there were 4 statements within general relativity (GR), mathematical physics and black hole (BH) physics that seemed to be solid and widely believed to be correct, namely: 1) Hawking's Rigidity theorem: BHs have two Killing isometries (time and rotational translations). 2) 'No hair' theorems: BHs are fully described by conserved charges. 3) Asymptotically flat BHs are stable. 4) If a gravitational system is linearly stable, it ought to be also non-linearly stable. 5) 'Cosmic censorship' forbids time evolutions that form singularities (unbounded curvature) not hidden The last 10 years witnessed the demonstration that these stamens do not hold in general. In the case of theorems this is because their assumptions can be remarkably evaded. Together with my collaborators, I have made some main contributions to arrive to this conclusion. These contributions are reshaping the state-of-the-art of these fields 100 years after Einstein's formulation of GR: It was widely accepted that 4) should be unquestionable. My papers on the nonlinear instability of the Anti-de Sitter space (AdS; the simplest solution of Einstein's gravity with negative curvature that is linearly stable) proved this expectation wrong. Remarkably, this nonlinear instability further shows that turbulence occurs in a gravitational system. Two of these papers were selected by the Editors of Classical and Quantum Gravity to be among the journal's Highlights. We also proved that GR can have BHs with a helical single Killing field (single isometry). So, they are time periodic but not time symmetric neither asymmetric. Their existence was surprising since it was widely believed that they were ruled-out by the famous Hawking's rigidity theorem 1). However, we have shown that an assumption of this theorem can be evaded. We also have shown that 'No hair' theorems 2) formulated for asymptotically flat cannot be extended to anti-de Sitter (AdS) backgrounds. We found the first gravitational instability of an asymptotically flat vacuum BH of GR - the ultraspinning instability - and associated novel lumpy BHs (with an axisymmetric spherical horizon that is deformed along the polar direction). The instability already appears in two textbooks of the Cambridge Univ. Press. It is further inspiring research on other systems that we are currently undergoing. In a paper published in Physical Review Letters, we established the linear mode stability of the Kerr-Newman BH and computed the associated characteristic oscillation frequencies of the system. This was the major open problem of Einstein-Maxwell gravity since Chandrasekhar's seminal textbook ('The mathematical theory of BHs',1983) identified the challenge. (Uniqueness theorems state that this BH is the unique and most general family of stationary BHs of the theory). LIGO - that recently detected gravitational waves from the merger of two black holes - will need to use our data to characterise the observations. We have also contributed to the long-term program that aims at finding the properties, endpoint and novel BH solutions of the superradiant instability. (Superradiance is wave analogue of the Penrose process whereby energy and angular momentum is extracted from a black hole). In particular, we gave overwhelming evidence to conjecture that Cosmic censorship 5) is violated in the evolution of these systems. My research activity is however not restricted to the original Einstein theory. Supergravities are supersymmetric extensions of general relativity described by the Einstein theory augmented with certain bosonic and fermionic fields. They are higher dimensional theories of gravity that turned out to be the low energy classical limit of string theory (which is a mathematically consistent theory of quantum gravity). Supergravity theories play a fundamental role in holographic dualities (aka gauge/gravity or AdS/CFT correspondences). These holographic dualities provide a formal map between gravitational theories and quantum field theories in the absence of gravity. These dualities are improving our understanding of strongly coupled physics in gauge theories like the one we are observing in heavy ion collisions at the Large Hadron Collider (LHC) at CERN. For these duality dictionaries are allowing to address (hard non-perturbative) strongly coupled questions in quantum field theories using weak coupling computations in the dual supergravity theories. The latter computations are much simpler to perform. This strategy is allowing us to learn valuable lessons and insights about strongly coupled physics that would be otherwise hard to obtain. In the holographic duality context, black hole solutions of supergravities play a fundamental role. For they are thermodynamic objects with temperature dual to thermal states in the holographic quantum field theory. Heating the quantum field theory is dual to black hole formation via gravitational collapse. Black hole quasinormal modes - i.e. the oscillations of a perturbed black hole back to equilibrium - are dual to the quantum field theory thermalisation timescales. In the context of these holographic dualities, I have been constructing novel black hole solutions of supergravities that are fundamental to address some of the relevant questions in the holographic duality programme. For example, in the context of this gauge/gravity correspondence, in a paper published in Physical Review Letters, we have numerically constructed asymptotically global AdS5 × S5 black holes that are localised on the S5. These are solutions to type IIB supergravity with S8 horizon topology that dominate the theory in the microcanonical ensemble at small energies. At higher energies, there is a first-order phase transition to AdS5-Schwarzschild×S5. By the AdS/CFT correspondence, this transition is dual to spontaneously breaking the SO(6) R-symmetry of N = 4 super Yang-Mills down to SO(5). We pinpointed the location of this phase transition and computed the expectation value of the resulting scalar operators in the low energy phase Still in the context of the gauge/gravity correspondence, at low energies or temperatures, maximally supersymmetric Yang-Mills theory on R(t) × S1 with large N gauge group SU(N) and strong t'Hooft coupling is conjectured to be dual to the low energy dynamics of a collection of D0-branes on a circle. We constructed thermal states in the gravitational side of the correspondence where we find a first-order phase transition between states that are uniform on the S1 and states that are localised on it. When compared with lattice computations that are now available, these critical values provide the first instance where a first-order phase transition is tested on both sides of gauge/gravity duality. In the last years we also have pathbreaking contributions in the fields of differential equations and numerical solvers of Einstein's PDEs. Indeed, we have been involved in a long-term program to understand reformulations of Einstein's equation as a manifestly elliptic system of PDEs (for symmetric ansätz) and developing numerical schemes to solve the (non-)linear systems of coupled PDEs of Einstein's gravity. Accordingly, we were invited to write a Topical Review for Classical and Quantum Gravity entitled `Numerical Methods for Finding Stationary Gravitational Solutions' with the state-of-the-art technical tools. As an illustrative sharp example, to construct the BHs with a single isometry aforementioned we had to solve a coupled system of ten (10) non-linear 2nd order PDEs that depend on three (3) variables. |
| Exploitation Route | My research is on theoretical physics and mainly on black holes. Therefore it does not have an immediate direct impact on technological and economical applications. However, it is fundamental to complement the investment done (also by STFC-UK) on the LIGO international collaboration that recently detected the first gravitational waves generated by the merger and collision of two black holes. In one of our key results, we found the characteristic oscillation frequencies that black holes emit when perturbed. We made these results available on open source websites and LIGO will need this database to identify the properties of black holes involved on future detections. |
| Sectors | Education,Other |
| Title | Characteristic oscillation frequencies for Kerr-Newman black holes |
| Description | The LIGO collaboration recently announced the so much awaited detection of gravitational waves. These waves were emitted when two black holes collided and merged. To identify the characteristics of the black holes involved in the collision LIGO needs to know the characteristic oscillation frequencies (called quasinormal modes) of the black holes. Astrophysical black holes rotate but should not have electric charge (i.e. they can have it but are expected to discharge in a very short timescale). However, LIGO needs to have a database with the characteristic oscillation frequencies of charged rotating black holes to compare their detection against. Computing these frequencies was a 30 year old problem that was finally solved in our recent publication in Physical Review Letters ( Phys.Rev.Lett. 114 (2015) 15, 151101 ). A database with some of the main frequencies is already publically available on the two websites: 1) http://centra.tecnico.ulisboa.pt/network/grit/files/ringdown/ 2) http://www.phy.olemiss.edu/~berti/ringdown/ and we are currently collecting more data to release. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2015 |
| Provided To Others? | Yes |
| Impact | LIGO will need to use this data to characterise the mass, spin and electric charge of future gravitational wave detections (that will typically involve violent astrophysical processes with black holes). LIGO will measure the frequencies of the gravitational waves and then will match it with the database to find the corresponding mass, spin and electric charge. |
| URL | http://centra.tecnico.ulisboa.pt/network/grit/files/ringdown/ |
| Description | "Squaring the sphere": holography, black holes, fluids and turbulence |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Public/other audiences |
| Results and Impact | Outreach lecture at Summer School on String Theory and Holography, Instituto Superior T ´ecnico, Lisbon, Portugal. July 2014. Target Public: University students and professors, and general public. Webpage: http://faraday.fc.up.pt/cfp-pages/School/program.html |
| Year(s) Of Engagement Activity | 2014 |
| URL | http://faraday.fc.up.pt/cfp-pages/School/program.html |
| Description | Outreach activity: Royal Society Summer Exhibit in London 3-9 July 2017 |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Public/other audiences |
| Results and Impact | The Gravitational group of Mathematical School of university of Southampton is part of a consortium that provides a gravitational-wave exhibit during the Royal Society Summer Exhibit in London 3-9 July, 2017. This takes place at the Royal Society and attracts many thousand visitors. |
| Year(s) Of Engagement Activity | 2017 |
| Description | Participation in an activity, workshop or similar - , Winchester Science Cafe, Discovery Centre of Winchester |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Local |
| Primary Audience | Public/other audiences |
| Results and Impact | Outreach Activity: talk "Black holes as soap bubles", November 2019, Winchester Science Cafe, Discovery Centre of Winchester, Winchester, UK. Target Public: general public. |
| Year(s) Of Engagement Activity | 2019 |
| URL | http://www.wincafesci.org.uk |
| Description | Science Day, Outreach activity, University of Southampton, 18 March 2017 |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Public/other audiences |
| Results and Impact | "Black holes - Einstein's enigma", Science Day, Outreach activity (posters and personal interaction/discussions), University of Southampton, 18 March 2017 |
| Year(s) Of Engagement Activity | 2017 |
| Description | Winchester Science Festival |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Public/other audiences |
| Results and Impact | "Winchester Science Festival", 12-13 May 2018, Winchester Science Centre, Winchester, UK. Member of the team responsible for the organization and presentation of one of the 10 invited hands-on exhibitions: "Playing with Maths". Target Public: general young public (mainly kids with their parents). |
| Year(s) Of Engagement Activity | 2018 |