Beyond Lorentzian Geometry II

Feb 6, 2023, 8:00 AM → Feb 8, 2023, 4:30 PM UTC

5.10 (ICMS)

This is the second edition of the "Beyond Lorentzian Geometry" workshops.  The first was held in Edinburgh in October 2019 and it was a resounding success.

Recent years have witnessed a growing interest in the study and application of non-Lorentzian geometries such as Newton-Cartan and Carrollian geometries. They feature in such diverse areas such as

• approximations of general relativity
• fluid dynamics and (soft)-condensed matter physics
• string theory
• holography
• asymptotically flat spacetimes (BMS symmetries)
• black hole physics

Geometry plays an important role in all of these areas and non-Lorentzian structures have been found to appear in worldsheet geometries, spacetime boundaries, string target spacetimes, near horizon geometries, non-relativistic field theories on nontrivial backgrounds, etc.

In this workshop we would like to bring together researchers working on both mathematical and physical aspects of these novel geometries.

 

Speakers

• Jay Armas
• Arjun Bagchi
• Eric Bergshoeff
• Jan de Boer
• Laura Donnay
• Joaquim Gomis
• Kevin Grosvenor
• Daniel Grumiller
• Troels Harmark
• Akash Jain
• Niels Obers
• Gerben Oling
• Giandomenico Palumbo
• Noémie Parrini
• Silvia Penati
• Stefan Vandoren
• Ziqi Yan

Organisers

For questions please contact:

José Figueroa-O'Farrill (j.m.figueroa@ed.ac.uk)

Jelle Hartong (j.hartong@ed.ac.uk)

 

Sponsors

 

We are grateful for the financial support from the Glasgow Mathematical Journal Trust Learning and Research Support Fund and from the Royal Society.

       

Monday, February 6

9:00 AM → 9:30 AM Welcome

9:30 AM → 10:30 AM Review talk: Non-relativistic gravity and non-Lorentzian geometry

I will review Newton-Cartan gravity with an emphasis on recent developments, including the covariant, off-shell large speed of light expansion of general relativity. Depending on the matter content, this expansion either leads to Newton-Cartan geometry with absolute time or to Newton-Cartan geometry with non-relativistic gravitational time dilation effects. The latter shows that non-relativistic gravity includes a strong field regime and goes beyond Newtonian gravity. Earlier work on Newton-Cartan geometry will be briefly discussed, after which we turn to modern approaches, which include the gauging of the Bargmann algebra, as well as a new notion of `type II' notion of Newton-Cartan geometry which arises from the large speed of light (c) expansion of General Relativity.  Finally, I will mention matter couplings, solutions and odd powers in 1/c, as well as a summary of related topics.

Speaker: Niels Obers

Slides_NielsObers.pdf

10:30 AM → 11:00 AM Coffee

11:00 AM → 11:45 AM Comment on Carroll Quantum Fields

Speaker: Jan de Boer

11:45 AM → 12:30 PM QFT in Galilean Superspace

I will discuss quantum properties of galilean N=2 supersymmetric theories in d =2+1, primarily focusing on the non-relativistic version of the Wess-Zumino model and SuperQED. Compared with their relativistic cousins, these models exhibit very different behavior. The non-relativistic Wess-Zumino model is one-loop exact, as a consequence of robust non-renormalisation theorems. The non-relativistic electrodynamics is featured by an infinite number of marginal couplings that turn on along the RG flows. Superconformal invariance is preserved in correspondence of a non-trivial conformal manifold of fixed points where the theory is gauge-invariant and interacting.

Speaker: Silvia Penati

Slides_SilviaPenati.pdf

12:30 PM → 2:00 PM Lunch

2:00 PM → 2:45 PM Towards a hydrodynamic theory for condensed matter systems

I will discuss a new hydrodynamic theory using Aristotelian geometry that accounts for pinning, phase, and momentum relaxation effects due to translational disorder, diffusion due to the presence of interstitials and vacancies, and strain relaxation due to plasticity and dislocations. I will focus on signatures of plastic deformations in electronic crystals and show that proliferation of dislocations de-pins the spatially resolved conductivity until the crystal melts, after which point a new phase of a pinned electronic liquid emerges. The framework is applicable to a large class of physical systems including electronic Wigner crystals, multicomponent charge density waves, metals and ordinary crystals.

Speaker: Jay Armas

Slides_JayArmas.pdf

2:45 PM → 3:15 PM Tea

3:15 PM → 4:00 PM The Panorama of Spin Matrix Theory

I will review some of the features of Spin Matrix theory to motivate why it seems a promising road to a non-relativistic version of the holographic correspondence. As part of this I will mention recent progress on the understanding of the Spin Matrix theory that should include a black hole as its dual.

Speaker: Troels Harmark

4:00 PM → 4:45 PM Carrollian black holes

Speaker: Daniel Grumiller

Slides_DanielGrumiller.pdf

Tuesday, February 7

9:30 AM → 10:30 AM Review Talk: Some aspects of non-relativistic strings

It has been known for some time that there exists a self-consistent limit of string theory with a non-relativistic spectrum. Over the last few years, many aspects of the resulting non-relativistic string theory have been developed, including its coupling to curved non-Lorentzian backgrounds. In this talk, by means of the analogous constructions for non-relativistic point particles, I will attempt to give an accessible introduction to some of the foundations of these recent developments in non-relativistic string theory. I will also summarize related results on the bulk interpretation of Spin Matrix limits in terms of strings on AdS, which give rises to strings with non-Lorentzian worldsheets.

Speaker: Gerben Oling

10:30 AM → 11:00 AM Coffee

11:00 AM → 11:45 AM Non-relativistic massive higher-spin modes in the Fractional Quantum Hall Effect

It is quite well known that quantum area-preserving diffeomorphisms play a key role in the fractional quantum Hall states (FQHs) and explain, for instance, the incompressibility of the quantum Hall fluids. Moreover, quantum area-preserving diffeomorphisms in two space dimensions are naturally encoded in the so-called Girvin-MacDonald-Plazman (GMP) algebra or in its dual version known as W_{\infinity} algebra. In this talk, firstly I will introduce an effective-field-theory approach that shows the relation between the GMP algebra and the emergence of a non-relativistic massive spin-2 mode in the bulk state of FQHs through the existence of a nematic order. The corresponding nematic order parameter is nothing but a symmetric rank-2 tensor that can be naturally identified with  an emergent metric tensor. Secondly, I will generalize this approach by showing how higher-rank symmetric tensors and their corresponding non-relativistic massive higher-spin modes, which should naturally emerge from quantum area-preserving diffeomorphisms, can be indeed introduced and analyzed by considering generalized nematic FQHs. It remains an open question how and if these modes can be derived from a suitable non-relativistic version of linearized higher-spin gravity.

Speaker: Giandomenico Palumbo

11:45 AM → 12:30 PM Higher-form symmetries and topological phase transitions

Symmetries and their breaking patterns are a valuable tool in physics for classifying and describing phases of matter. In recent years, a new generalised notion of symmetries has emerged, dubbed "higher-form symmetries", where the associated conserved charges are carried by higher-dimensional objects like strings and surfaces, instead of the usual point-like particles. In this talk, I will give a brief overview of higher-form symmetries and their spontaneous and explicit breaking patterns. In particular, the explicit breaking of higher-form symmetries is associated with the emergence of topological defects in many-body systems. We will outline a new hydrodynamic framework for systems with (approximate) higher-form symmetries and use this to study transitions between topological phases of matter. This includes the melting phase transition in smectic
crystals, the plasma phase transition from polarised gases to magnetohydrodynamics, the superfluid to neutral fluid phase transition, and the Meissner effect in superconductors, among many others. The talk will be based on: https://arxiv.org/abs/2301.09628.

Speaker: Akash Jain

Slides_AkashJain.pdf

12:30 PM → 2:00 PM Lunch

2:00 PM → 2:45 PM Carroll Stories

Speaker: Stefan Vandoren

2:45 PM → 3:15 PM Tea

3:15 PM → 4:00 PM Gravitational S-matrix and Carrollian holography

In this talk, I will present recent advances towards a holographic formulation of gravity in asymptotically flat spacetime in terms of a putative conformal Carrollian field theory living at null infinity. I will also comment on how this approach relates to the celestial holography program.

Speaker: Laura Donnay

Slides_LauraDonnay.pdf

4:00 PM → 4:45 PM A New Consistent Limit of Eleven-Dimensional Supergravity

Speaker: Eric Bergshoeff

Slides_EricBergshoeff.pdf

8:00 PM → 10:30 PM Workshop Dinner

Dinner at Howies Waterloo Place (29 Waterloo Place, EH1 3BQ)

Wednesday, February 8

9:30 AM → 10:30 AM Review Talk: Quirks, Novelties, and Curiosities of Fractons

A Fracton is an excitation whose mobility when in isolation is restricted by various types of symmetry (e.g., multipole or subsystem symmetries). However, when these come together, the composite states they form may move much more freely. I will briefly discuss the history of this field and point out some of the conceptual puzzles that have fueled their study. I will focus particularly on the question of UV/IR mixing and how it affects renormalization.

Speaker: Kevin Grosvenor

Slides_KevinGrosvenor.pdf

10:30 AM → 11:00 AM Coffee

11:00 AM → 11:45 AM Non-Lorentzian Torus and SL(2, Z) Duality

I will talk about some recent progress on non-perturbative SL(2,Z) duality in nonrelativistic string theory, which is a self-contained string theory that has a string spectrum with a Galilean invariant dispersion relation. I will show that the SL(2,Z) duality in this string theory exhibits intriguing new structure. This study provides a precursor towards realizing novel U-duality relations between nonrelativistic and discrete light-cone quantization (DLCQ) string/M-theory, where DLCQ appears in non-perturbative approaches to quantum field theory and string/M-theory, such as in matrix model.

Speaker: Ziqi Yan

Slides_ZiqiYan.pdf

11:45 AM → 12:30 PM Geometry of the super Null Infinity

Through the study of homogeneous spaces and thanks to the orbit decomposition of compactified super Minkowski space, I will discuss different geometrical aspects of the supersymmetric version of Null Infinity. The purpose is to tend to a proposition of definition for a super conformal carrollian geometry.

Speaker: Noémie Parrini

Slides_NoemieParrini.pdf

12:30 PM → 2:00 PM Lunch

2:00 PM → 2:45 PM Non-Lorentzian theories with or without constraints

We exhibit a new method of constructing further non-Lorentzian models by applying a method we refer to as starting from a so-called seed Lagrangian. This method typically produces additional constraints in the system that can drastically alter the physical content of the model. We demonstrate our method for particles, strings, scalars, vector fields and JT gravity.

Speaker: Joaquim Gomis

2:45 PM → 3:15 PM Tea

3:15 PM → 4:00 PM The Carrollian Kaleidoscope

Speaker: Arjun Bagchi