Non-Lorentzian Geometries and their Applications

29 Apr 2025, 09:00 → 1 May 2025, 12:35 Europe/Dublin

Hamilton Mathematics Institute, Trinity College Dublin

 

Topics covered

This workshop will be structured around three key themes, one for each day:

1. Non-Relativistic String and M-theory, Non-Relativistic Holography, Post-Newtonian approximation;

2. Carroll-related phenomena: Black Holes, Hydrodynamics, Cosmology, Flat Space Holography and Fractons;

3. Mathematics of Non-Lorentzian Geometries.

Motivations

In recent years, Non-Lorentzian geometries have attracted growing interest due to their applications across various fields, including high-energy physics, hydrodynamics, cosmology, and condensed matter physics.

Non-Lorentzian geometries can naturally arise from two distinct limit procedures: the non-relativistic limit and its counterpart, the Carroll limit. Applying the non-relativistic limit to string and M-theory allows us to zoom into exactly solvable sectors of more complicated theories. This approach has led to exciting recent developments, such as the formulation of a novel non-AdS holography via the Non-Relativistic AdS/CFT correspondence, the geometric description of a frame-independent post-Newtonian expansion of gravity theories, new applications of integrability in non-relativistic sigma models, and the study of massive non-relativistic higher-spin modes in the fractional quantum Hall effect.

Conversely, the Carroll limit has proven valuable in flat-space holography, as the asymptotic symmetry group of flat spacetime includes a conformal extension of the Carroll group. This limit has also found important applications in hydrodynamics, cosmology, the study of null manifolds (such as black hole horizons), and in understanding quasiparticles with limited mobility, known as fractons.

A common feature of theories emerging from both the non-relativistic and Carroll limits is that their spacetime geometry is described by singular foliated manifolds, such as Newton-Cartan manifolds. These geometries are currently well-studied in mathematics and twistor theory.

Given the wide-ranging applications of Non-Lorentzian geometries, this interdisciplinary workshop aims to bring together participants from diverse backgrounds to exchange ideas and explore new directions.

Registration

Registration is now closed.

 

Organisers

Eric Bergshoeff (Groningen), Andrea Fontanella (Trinity College Dublin)

Sponsors

The workshop is financially supported by the Simons Foundation through HMI, and by the University of Groningen. 

       

 

 

 

 

Tuesday 29 April

09:30 Registration

Non-relativistic: Plenary talk (Chair: ...)

Convener: Niels Obers

11:00 Coffee break

Non-relativistic: Plenary talk (Chair: ...)

Convener: Neil Lambert

11:30 Coffee break

12:30 Lunch

Non-relativistic: Contributed Talk (Chair: ...)

Convener: Juan Miguel Nieto García

1 Symmetries, holography and integrability in NR string theory in SNC AdS5×S5

Integrability and holography have played a huge role in understanding string theory in AdS$_5 \times$S$^5$, so it is worth studying if they survive in the non-relativistic string theory. In this talk, I will show that the Maldacena's construction of the AdS$_5$/CFT$_4$ correspondence survives the limit process, giving us a duality between NR string theory in SNC AdS$_5 \times$S$^5$ and Galilean Electrodynamics with additional scalar fields. I will also discuss the symmetries of both theories and the non-diagonalisable integrability of the string theory.

Speaker: Juan Miguel Nieto García (Universität Hamburg)

Non-relativistic: Contributed Talk (Chair: ...)

Convener: Ziqi Yan (Nordita)

2 M(atrix)-Theory from Nonrelativistic Sigma Models

I will talk about two classes of nonrelativistic sigma models and their roles in M-theory and matrix theory. I will start with the quantum critical supermembrane and its quantization, which is described by a renormalizable three-dimensional sigma model at a z=2 Lifshitz point. This model provides a natural candidate high-energy completion of the supermembrane in M-theory, where the latter is described by a nonrenormalizable sigma model that is relativistic. A more standard approach to the quantization of supermembranes is via matrix theory. I will show that the fundamental string associated with matrix theory is described by a two-dimensional Carrollian sigma model. I will illustrate how these two approaches to M-theory are related to each other.

Speaker: Dr Ziqi Yan (Nordita)

15:00 Coffee break

Non-relativistic: Contributed Talk (Chair: ...)

Convener: Chris Blair

3 The Surprising Structure of Non-Relativistic 11-dimensional Supergravity OR TTbar deformations as non-Lorentzian limits in reverse

I can give one of two talks.

In one, I can discuss the surprising structure of non-relativistic 11-dimensional supergravity, based on https://arxiv.org/abs/2407.21648

In the other, I can explain a surprising link between decoupling limits leading to non-Lorentzian corners of string theory and the TTbar deformation. The latter in its original incarnation is a deformation of 2d field theories with many remarkable properties. It turns out that the non-relativistic string limit can be viewed in reverse as a TTbar deformation, which takes a theory of free bosons to the Nambu-Goto action. This observation can be exploited to derive new field theory deformations - in higher dimensions - using other non-Lorentzian limits. For instance, these provide deformations which take Maxwell theory to the DBI action. This talk would be based on https://arxiv.org/abs/2002.12413 and https://arxiv.org/abs/2410.03591

Speaker: Chris Blair

Non-relativistic: Contributed Talk (Chair: ...)

Convener: Jørgen Sandøe Musaeus (University of Edinburgh)

4 Towards a covariant approach to post-Newtonian gravity

In this talk, I will show how we used the covariant $1/c$-expansion to construct a framework for post-Newtonian gravity that is valid in any gauge with a Newtonian regime. This is not true for every gauge as Newtonian gravity itself is a gauge fixed version of Newton-Cartan gravity. Thus, we fix the leading order gauge choice but keep full gauge freedom at all subleading orders in this framework. Due to the limited region of validity of the PN expansion, we have to construct a similarly covariant (for all post-Newtonian gauges) framework for the multipolar post-Minkowskian expansion outside the compact matter source. This is then glued together with the PN expansion through matched asymptotic expansion methods. This framework stands in contrast to the standard Blanchet-Damour approach which relies entirely on the harmonic gauge. I will show how this new framework allows us to make general statements about the structure of the equations at any order and write down the full field equations to 2.5PN order, valid for any PN gauge. I will then go on to showcase the framework in what we refer to as transverse gauge and explain why this could be an interesting alternative to the standard harmonic gauge. Particularly, I will highlight how this gauge reduces the number of relativistic wave equations (exchanging them for the simpler Poisson equation) that one has to solve for in MPM expansion as well as significantly simplifying half-PN orders in the metric as compared to harmonic gauge.

Speaker: Jørgen Sandøe Musaeus (University of Edinburgh)

Wednesday 30 April

Carroll: Plenary Talk (Chair: ...)

Convener: Stefan Vandoren

11:00 Coffe break

Carroll: Plenary Talk (Chair: ...)

Convener: Marios Petropoulos

12:30 Lunch

Carroll: Contributed Talk (Chair: ...)

Convener: Romain Ruzziconi (University of Oxford)

5 Flat Space Holography from the Flat/Carrollian Limit of AdS/CFT

Carrollian holography proposes that gravity in four-dimensional (4d) asymptotically flat spacetime is dual to a 3d Carrollian CFT living at null infinity. In this talk, I will review this framework and explain how massless amplitudes in flat space can be re-expressed as Carrollian CFT correlators at the boundary, referred to as Carrollian amplitudes. I will show that these correlators naturally emerge from the Carrollian limit of holographic CFT correlators computed via AdS Witten diagrams, establishing a correspondence between the flat limit in the bulk and the Carrollian limit at the boundary. As a concrete application, I will implement the flat/Carrollian limit of the duality between 11d supergravity on $AdS_4\times S_7$ and 3d $\mathcal{N}=8$ ABJM theory, extracting supergravity amplitudes in flat space.

Based on arXiv:2406.19343 and work in preparation with A. Y. Srikant and A. Lipstein.

Speaker: Romain Ruzziconi (University of Oxford)

Carroll: Contributed Talk (Chair: ...)

Convener: Priyadarshini Pandit (Indian Institute of Technology Kanpur)

6 Null Open Strings and Boundary Conformal CFTs

We study null open strings and establish, for the first time, that the worldsheet residual gauge symmetry algebra is the Boundary Carrollian Conformal Algebra (BCCA). We present the construction of open null strings and demonstrate that, under Dirichlet boundary conditions, Boundary Carrollian Conformal Algebra emerges as the algebra of constraints. Additionally, we show that the BCCA can be obtained by contracting a single copy of the Virasoro algebra, confirming that null open strings arise as the tensionless limit of tensile open strings. This discovery initiates a broader study of Carrollian Conformal Field Theory (CCFT) with boundaries, opening a range of new research possibilities, given the growing importance of Carrollian symmetries.

Speaker: Dr Priyadarshini Pandit (Indian Institute of Technology Kanpur)

15:00 Coffee break

Carroll: Contributed Talk (Chair: ...)

Convener: Jan Rosseel (Ruder Boskovic Institute)

7 A Conformal Approach to Carroll Gravity

In this talk, I will outline how to take the first step in the conformal program for constructing general matter couplings to Carroll gravity. In particular, I will show how a (non-conformal version of) electric/magnetic Carroll gravity arises from gauge-fixing a theory of a single massless electric/magnetic scalar coupled to conformal Carroll gravity with isotropic dilatations. Special attention will be paid to the way intrinsic torsion tensors occur in the full Carroll transformation rules. These results form a convenient starting point for constructing general matter couplings to Carroll gravity. Towards the end of the talk, I will argue that, surprisingly, the relation between dynamical matter and gravity, that forms the basis of the conformal program, does not work in the usual fashion in the Galilei case.

Speaker: Jan Rosseel (Ruder Boskovic Institute)

Carroll: Contributed Talk (Chair: ...)

Convener: Erica Bertolini (Dublin Institute for Advanced Studies)

8 From a covariant Maxwell-like theory to fractons: a new approach

The concept of fracton quasiparticle has recently emerged in many areas of physics, from mathematical physics to condensed matter and quantum information, unified by the general feature of restricted mobility.

In this talk I will show that the fracton phenomenology of Pretko's original papers [1604.05329,1606.08857] can be reproduced from first principles of QFT through a symmetry-based approach. A strong relation with Linearized Gravity naturally emerges, interesting boundary effects can be observed, and a generalized "self-duality" can be implemented. These results open the doors to the study of a new class of covariant gauge field theories.

Speaker: Dr Erica Bertolini (Dublin Institute for Advanced Studies)

16:45 Group picture

18:30 Conference dinner

Thursday 1 May

Mathematics of NL geometries: Plenary Talk (Chair: ...)

Convener: Maciej Dunajski

11:00 Coffee break

Mathematics of NL geometries: Plenary Talk (Chair: ...)

Convener: José Figueroa-O'Farrill

12:30 Closing remarks