Quantum gravity, random geometry and holography

9 janv. 2023, 08:30 → 17 févr. 2023, 20:30 Europe/Paris

Amphitheater Darboux (IHP)

Thematic six-weeks program at Institut Henri Poincaré, Paris.

January 09th - February 17th, 2023.

The scope of the program is to bring together researchers who are working on quantum gravity from various perspectives and approaches, with an emphasis on the random geometry point of view and on more recent holographic developments. The main goal is to intensify the fruitful interactions between the researchers in these and related communities in order to make significant progress on the outstanding problems in quantum gravity.

Program :

The thematic six-weeks program will include two workshops (weeks 2 and 5), introductory lectures (weeks 1 and 4), two general public lectures, and more (informal gatherings and seminars).

 

Videos of most of the lectures and workshop seminars are available on carmin.tv.

Workshops:

Week 2 (January 16-20, 2023): Quantum Gravity and Random Geometry

Week 5 (February 6-10, 2023): Tensor Models and Holography

Introductory lectures:

Week 1 (January 9-13, 2023): 

Jan Ambjorn (NBI, Denmark): "Lattice gravity"

Florian Girelli (U. Waterloo, Canada): "Quantum groups in a (coco) nutshell"

Simone Speziale (CPT, Marseille, France): "Twisted geometries and spin network states"

Week 4 (January 30 to February 3, 2023): 

Robert de Mello Koch (Univ. Witwatersrand, South Africa): "Holography for Higher Spin Gravity" 

Razvan Gurau (Heidelberg U., Germany): "From random tensors to tensor field theory"

Sanjaye Ramgoolam (Queen Mary U., UK): "Groups, algebras and hidden symmetries of matrix/tensor models"

Public lectures:

January 16, 2023: Lecture for general public* by François David (CEA Saclay, France) [video].

January 30, 2023: Lecture for high school students* by Frank Ferrari (Univ. Libre Bruxelles, Belgium)

*in French

Organizing committee :

John Barrett (University of Nottingham)

Dario Benedetti (CNRS, École Polytechnique)

Joseph Ben Geloun (Université Sorbonne Paris Nord)

Renate Loll (Radboud University Nijmegen)

 

Poster :

 

Poster T1 A 2023-1.pdf

lundi 9 janvier

14:00 → 14:10 Welcome address

14:10 → 15:10 Twisted geometries and spin network states

Loop quantum gravity is a background-independent approach to the
quantization of general relativity. The fundamental states of the
theory are described by spin networks, states associated with graphs
whose quantum numbers give the spectra of discrete and non-commuting
geometric operators. On a fixed graph, the quantum numbers can be
interpreted as a collection of fuzzy polyhedra describing a twisted
geometry. The maths describing the twisted geometry uses an amusing
interplay of symplectic geometry, group theory and Regge geometry
which I will describe in some details. There is also a connection to
twistors that I will briefly discuss.

Orateur: Simone Speziale (CPT, Marseille)

15:10 → 15:40 coffee break

15:40 → 16:40 Twisted geometries and spin network states

Loop quantum gravity is a background-independent approach to the
quantization of general relativity. The fundamental states of the
theory are described by spin networks, states associated with graphs
whose quantum numbers give the spectra of discrete and non-commuting
geometric operators. On a fixed graph, the quantum numbers can be
interpreted as a collection of fuzzy polyhedra describing a twisted
geometry. The maths describing the twisted geometry uses an amusing
interplay of symplectic geometry, group theory and Regge geometry
which I will describe in some details. There is also a connection to
twistors that I will briefly discuss.

Orateur: Simone Speziale (CPT, Marseille)

mardi 10 janvier

09:30 → 10:30 Twisted geometries and spin network states

Loop quantum gravity is a background-independent approach to the
quantization of general relativity. The fundamental states of the
theory are described by spin networks, states associated with graphs
whose quantum numbers give the spectra of discrete and non-commuting
geometric operators. On a fixed graph, the quantum numbers can be
interpreted as a collection of fuzzy polyhedra describing a twisted
geometry. The maths describing the twisted geometry uses an amusing
interplay of symplectic geometry, group theory and Regge geometry
which I will describe in some details. There is also a connection to
twistors that I will briefly discuss.

Orateur: Simone Speziale (CPT, Marseille)

10:30 → 11:00 coffee break

11:00 → 12:00 Twisted geometries and spin network states

Loop quantum gravity is a background-independent approach to the
quantization of general relativity. The fundamental states of the
theory are described by spin networks, states associated with graphs
whose quantum numbers give the spectra of discrete and non-commuting
geometric operators. On a fixed graph, the quantum numbers can be
interpreted as a collection of fuzzy polyhedra describing a twisted
geometry. The maths describing the twisted geometry uses an amusing
interplay of symplectic geometry, group theory and Regge geometry
which I will describe in some details. There is also a connection to
twistors that I will briefly discuss.

Orateur: Simone Speziale (CPT, Marseille)

mercredi 11 janvier

09:30 → 10:30 Lattice gravity

Lattice quantum field theory has been very successful as a tool to study non-perturbative aspects of quantum field theory. These lectures describe how the QUANTUM theory of General Relativity can also be formulated as a lattice theory. It is (very) successful in the case of two-dimensional spacetimes. There are several ways to generalize the two-dimensional lattice theory to higher dimensions, but amazingly they lead to the same modified Friedmann equation that seems to resolve all tension present between early time and late time cosmological data. The modified Friedmann equation has no cosmological constant. Instead the present expansion of the universe is caused by the creation of baby universes and links the dynamics of the very early universe to its final destiny.

Orateur: Jan Ambjorn (NBI, Denmark)

Ambjorn_parislectures.pdf

10:30 → 11:00 coffee break

11:00 → 12:00 Lattice gravity

Lattice quantum field theory has been very successful as a tool to study non-perturbative aspects of quantum field theory. These lectures describe how the QUANTUM theory of General Relativity can also be formulated as a lattice theory. It is (very) successful in the case of two-dimensional spacetimes. There are several ways to generalize the two-dimensional lattice theory to higher dimensions, but amazingly they lead to the same modified Friedmann equation that seems to resolve all tension present between early time and late time cosmological data. The modified Friedmann equation has no cosmological constant. Instead the present expansion of the universe is caused by the creation of baby universes and links the dynamics of the very early universe to its final destiny.

Orateur: Jan Ambjorn (NBI, Denmark)

jeudi 12 janvier

09:30 → 10:30 Quantum groups in a (coco) nutshell

(Lie) Groups are typically seen as encoding a symmetry structure. For some phase spaces, the symmetry structure might need to be equipped with a non-trivial Poisson structure, which must then be compatible with the group product (to have a well defined symmetry action). This defines the notion of Poisson Lie group. When quantizing the system, the Poisson Lie group becomes a quantum group. I will provide a compact introduction to these concepts having in mind as leading example, the 3d (quantum) gravity framework, where such Poisson Lie/quantum symmetries are key to understand the quantum theory.

Orateur: Florian Girelli (U. Waterloo)

2023 IHP lectures 1.pdf

2023 IHP lectures 3.pdf

10:30 → 11:00 coffee break

11:00 → 12:00 Quantum groups in a (coco) nutshell

(Lie) Groups are typically seen as encoding a symmetry structure. For some phase spaces, the symmetry structure might need to be equipped with a non-trivial Poisson structure, which must then be compatible with the group product (to have a well defined symmetry action). This defines the notion of Poisson Lie group. When quantizing the system, the Poisson Lie group becomes a quantum group. I will provide a compact introduction to these concepts having in mind as leading example, the 3d (quantum) gravity framework, where such Poisson Lie/quantum symmetries are key to understand the quantum theory.

Orateur: Florian Girelli (U. Waterloo)

14:00 → 15:00 Lattice gravity

Lattice quantum field theory has been very successful as a tool to study non-perturbative aspects of quantum field theory. These lectures describe how the QUANTUM theory of General Relativity can also be formulated as a lattice theory. It is (very) successful in the case of two-dimensional spacetimes. There are several ways to generalize the two-dimensional lattice theory to higher dimensions, but amazingly they lead to the same modified Friedmann equation that seems to resolve all tension present between early time and late time cosmological data. The modified Friedmann equation has no cosmological constant. Instead the present expansion of the universe is caused by the creation of baby universes and links the dynamics of the very early universe to its final destiny.

Orateur: Jan Ambjorn (NBI, Denmark)

15:00 → 15:30 coffee break

15:30 → 16:30 Lattice gravity

Lattice quantum field theory has been very successful as a tool to study non-perturbative aspects of quantum field theory. These lectures describe how the QUANTUM theory of General Relativity can also be formulated as a lattice theory. It is (very) successful in the case of two-dimensional spacetimes. There are several ways to generalize the two-dimensional lattice theory to higher dimensions, but amazingly they lead to the same modified Friedmann equation that seems to resolve all tension present between early time and late time cosmological data. The modified Friedmann equation has no cosmological constant. Instead the present expansion of the universe is caused by the creation of baby universes and links the dynamics of the very early universe to its final destiny.

Orateur: Jan Ambjorn (NBI, Denmark)

vendredi 13 janvier

09:30 → 10:30 Quantum groups in a (coco) nutshell

(Lie) Groups are typically seen as encoding a symmetry structure. For some phase spaces, the symmetry structure might need to be equipped with a non-trivial Poisson structure, which must then be compatible with the group product (to have a well defined symmetry action). This defines the notion of Poisson Lie group. When quantizing the system, the Poisson Lie group becomes a quantum group. I will provide a compact introduction to these concepts having in mind as leading example, the 3d (quantum) gravity framework, where such Poisson Lie/quantum symmetries are key to understand the quantum theory.

Orateur: Florian Girelli (U. Waterloo)

10:30 → 11:00 coffee break

11:00 → 12:00 Quantum groups in a (coco) nutshell

(Lie) Groups are typically seen as encoding a symmetry structure. For some phase spaces, the symmetry structure might need to be equipped with a non-trivial Poisson structure, which must then be compatible with the group product (to have a well defined symmetry action). This defines the notion of Poisson Lie group. When quantizing the system, the Poisson Lie group becomes a quantum group. I will provide a compact introduction to these concepts having in mind as leading example, the 3d (quantum) gravity framework, where such Poisson Lie/quantum symmetries are key to understand the quantum theory.

Orateur: Florian Girelli (U. Waterloo)

lundi 16 janvier

09:30 → 16:50 Workshop on Quantum Gravity and Random Geometry

Timetable

mardi 17 janvier

09:30 → 16:50 Workshop on Quantum Gravity and Random Geometry

Timetable

mercredi 18 janvier

09:30 → 12:30 Workshop on Quantum Gravity and Random Geometry

Timetable

jeudi 19 janvier

09:30 → 17:40 Workshop on Quantum Gravity and Random Geometry

Timetable

vendredi 20 janvier

09:30 → 12:30 Workshop on Quantum Gravity and Random Geometry

Timetable

vendredi 27 janvier

14:00 → 16:00 Enumeration of bicolored maps: investigating a holographic recursion

Orateur: Ariane Carrance

lundi 30 janvier

09:30 → 10:30 Holography for Higher Spin Gravity

After a brief review of the original argument due to Maldacena for a holographic duality between IIB string theory on
AdS$_5\times$S$^5$ and maximally supersymmetric Yang-Mills theory, we turn to the duality between the free O(N)
vector model in 2+1 dimensions and higher spin gravity on AdS$_4$. For this theory we study the spectrum of single
trace primaries of the CFT, which is dual to the spectrum of fields in higher spin gravity. By formulating the CFT in terms
of bilocal variables, using the formalism of collective field theory, we demonstrate how the gravitational theory can be
constructed. This example demonstrates a number of recently discovered phenomena in quantum gravity including the
quantum error correction interpretation of holography, entanglement wedge reconstruction and the holography of information.

Orateur: Robert de Mello Koch

Tutorial_lectures_Holography_for_higher_spin_gravity.pdf

10:30 → 11:00 Coffee break

11:00 → 12:00 Holography for Higher Spin Gravity

After a brief review of the original argument due to Maldacena for a holographic duality between IIB string theory on
AdS$_5\times$S$^5$ and maximally supersymmetric Yang-Mills theory, we turn to the duality between the free O(N)
vector model in 2+1 dimensions and higher spin gravity on AdS$_4$. For this theory we study the spectrum of single
trace primaries of the CFT, which is dual to the spectrum of fields in higher spin gravity. By formulating the CFT in terms
of bilocal variables, using the formalism of collective field theory, we demonstrate how the gravitational theory can be
constructed. This example demonstrates a number of recently discovered phenomena in quantum gravity including the
quantum error correction interpretation of holography, entanglement wedge reconstruction and the holography of information.

Orateur: Robert de Mello Koch

mardi 31 janvier

09:30 → 10:30 Holography for Higher Spin Gravity

After a brief review of the original argument due to Maldacena for a holographic duality between IIB string theory on
AdS$_5\times$S$^5$ and maximally supersymmetric Yang-Mills theory, we turn to the duality between the free O(N)
vector model in 2+1 dimensions and higher spin gravity on AdS$_4$. For this theory we study the spectrum of single
trace primaries of the CFT, which is dual to the spectrum of fields in higher spin gravity. By formulating the CFT in terms
of bilocal variables, using the formalism of collective field theory, we demonstrate how the gravitational theory can be
constructed. This example demonstrates a number of recently discovered phenomena in quantum gravity including the
quantum error correction interpretation of holography, entanglement wedge reconstruction and the holography of information.

Orateur: Robert de Mello Koch

10:30 → 11:00 Coffee break

11:00 → 12:00 Holography for Higher Spin Gravity

After a brief review of the original argument due to Maldacena for a holographic duality between IIB string theory on
AdS$_5\times$S$^5$ and maximally supersymmetric Yang-Mills theory, we turn to the duality between the free O(N)
vector model in 2+1 dimensions and higher spin gravity on AdS$_4$. For this theory we study the spectrum of single
trace primaries of the CFT, which is dual to the spectrum of fields in higher spin gravity. By formulating the CFT in terms
of bilocal variables, using the formalism of collective field theory, we demonstrate how the gravitational theory can be
constructed. This example demonstrates a number of recently discovered phenomena in quantum gravity including the
quantum error correction interpretation of holography, entanglement wedge reconstruction and the holography of information.

Orateur: Robert de Mello Koch

mercredi 1 février

09:30 → 10:30 Groups, algebras and hidden symmetries of matrix/tensor models

Orateur: Sanjaye Ramgoolam

10:30 → 11:00 Coffee break

11:00 → 12:00 Groups, algebras and hidden symmetries of matrix/tensor models

Orateur: Sanjaye Ramgoolam

jeudi 2 février

09:30 → 10:30 Groups, algebras and hidden symmetries of matrix/tensor models

Orateur: Sanjaye Ramgoolam

10:30 → 11:00 Coffee break

11:00 → 12:00 Groups, algebras and hidden symmetries of matrix/tensor models

Orateur: Sanjaye Ramgoolam

14:00 → 15:00 From random tensors to tensor field theory

Random tensors exhibit a 1/N expansion dominated by melonic graphs. The large N limit of these models is thus richer than the large N limit of vector models, but more amenable to computations than the one of matrix models. This series of lectures is divided into two parts. In the first part I will review the melonic large N limit in combinatorial tensor and vector/tensor models. In the second part I will discuss the O(N)^3 field theory in the large N limit.

Orateur: Razvan Gurau (ITP, Heidelberg)

15:00 → 15:30 Coffee break

15:30 → 16:30 From random tensors to tensor field theory

Random tensors exhibit a 1/N expansion dominated by melonic graphs. The large N limit of these models is thus richer than the large N limit of vector models, but more amenable to computations than the one of matrix models. This series of lectures is divided into two parts. In the first part I will review the melonic large N limit in combinatorial tensor and vector/tensor models. In the second part I will discuss the O(N)^3 field theory in the large N limit.

Orateur: Razvan Gurau (ITP, Heidelberg)

vendredi 3 février

09:30 → 10:30 From random tensors to tensor field theory

Random tensors exhibit a 1/N expansion dominated by melonic graphs. The large N limit of these models is thus richer than the large N limit of vector models, but more amenable to computations than the one of matrix models. This series of lectures is divided into two parts. In the first part I will review the melonic large N limit in combinatorial tensor and vector/tensor models. In the second part I will discuss the O(N)^3 field theory in the large N limit.

Orateur: Razvan Gurau (ITP, Heidelberg)

10:30 → 11:00 Coffee break

11:00 → 12:00 From random tensors to tensor field theory

Random tensors exhibit a 1/N expansion dominated by melonic graphs. The large N limit of these models is thus richer than the large N limit of vector models, but more amenable to computations than the one of matrix models. This series of lectures is divided into two parts. In the first part I will review the melonic large N limit in combinatorial tensor and vector/tensor models. In the second part I will discuss the O(N)^3 field theory in the large N limit.

Orateur: Razvan Gurau (ITP, Heidelberg)

lundi 6 février

09:30 → 17:00 Workshop on Tensor Models and Holography

Timetable

mardi 7 février

09:30 → 17:00 Workshop on Tensor Models and Holography

Timetable

mercredi 8 février

09:30 → 12:00 Workshop on Tensor Models and Holography

Timetable

jeudi 9 février

09:30 → 17:00 Workshop on Tensor Models and Holography

Timetable

vendredi 10 février

09:30 → 12:00 Workshop on Tensor Models and Holography

Timetable

mercredi 15 février

10:00 → 12:00 Peeking at quantum gravity with self-overlapping curves

After a brief overview of the progress in 2d quantum gravity achieved through JT gravity, we will motivate the study of self-overlapping curves. In particular, we will explore some of their surprising geometrical and combinatorial properties.

Orateur: Nicolas Delporte (OIST)