Beyond Lorentzian Geometry

Oct 28, 2019, 9:30 AM → Oct 29, 2019, 5:00 PM UTC

ICMS

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

• Igal Arav (Imperial College London)
• Glenn Barnich (Université Libre de Bruxelles)
• Eric Bergshoeff (University of Groningen)
• Dieter Van den Bleeken (Boğaziçi University)
• Shira Chapman (University of Amsterdam)
• Troels Harmark (Niels Bohr Institute)
• Niels Obers (Nordita and Niels Bohr Institute)
• Stefan Prohazka (Université Libre de Bruxelles)
• Valentina Giangreco Puletti (University of Iceland)
• Jan Rosseel (University of Vienna)

Organisers

For questions please contact:

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

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

 

Sponsors

Partial support for this activity comes from the Edinburgh Mathematical Society via their Research Support Fund and from the Glasgow Mathematical Journal Trust via their Learning and Research Support Fund. We are very grateful to these Scottish institutions for supporting our workshop.

      

Monday, October 28

9:30 AM → 10:00 AM Welcome and registration

10:00 AM → 10:45 AM Oddities in non-relativistic strong gravity

I will review the nonrelativisic, or large c, expansion of general relativity and will argue why dynamic matter that sources strong gravitational fields requires the presence of odd powers in this expansion. I will report on ongoing work constructing the effective non-relativistic theory including these odd terms. A number of other peculiarities of the strong field, nonrelativistic corner of GR will be pointed out.

Speaker: Dieter Van den Bleeken

10:45 AM → 11:15 AM Coffee break

11:15 AM → 12:00 PM Non-relativistic String Theory and Branes

The aim of this talk is to describe what we can learn about basic non-relativistic brane solutions in non-relativistic string theory from non-relativistic T-duality in the same way that relativistic T-duality has been applied in the past to relate different relativistic brane solutions. The first part of the talk will be a review of non-relativistic string theory, the equations of motion of the background fields and the T-duality symmetry. In the he second part of the talk, which will be more speculative, we will discuss how we think that non-relativistic branes fit into the picture.

Speaker: Eric Bergshoeff

12:10 PM → 12:55 PM Maximally symmetric spacetimes reconsidered

Spacetimes, like Minkowski space, are omnipresent in physics. I will
introduce a recent classification of spacetimes that generalizes the
classification of maximally symmetric lorentzian geometries and
includes further physically interesting ones. Among them are galilean,
carrollian and aristotelian geometries for which there is renewed
interest due to applications in holography. These spacetimes posses
infinite dimensional (BMS-like) symmetries which we will also discuss.

Speaker: Stefan Prohazka

1:00 PM → 2:30 PM Lunch

2:30 PM → 3:15 PM Soft degrees of freedom, Gibbons-Hawking contribution and Casimir effect

The semiclassical contribution to the partition function is obtained by evaluating the Euclidean action improved through suitable boundary terms. We address the question of which degrees of freedom are responsible for this contribution. A physical toy model for the gravitational problem is a charged vacuum capacitor. For a planar charged vacuum capacitor with perfectly conducting plates, we identify the degrees of freedom that, in the quantum theory, give rise to additional contributions to the standard black body result proportional to the area of the plates. They allow for a microscopic derivation of the thermodynamics of the charged capacitor and contribute to the Casimir effect at finite temperature and thus to the entropy.

Speaker: Glenn Barnich

3:15 PM → 3:45 PM Tea

3:45 PM → 4:30 PM Renormalization Group Flows of Scalar Galilean Electrodynamics in 2 + 1 Dimensions

I will discuss the theory of Galilean electrodynamics coupled to a single Schrödinger scalar in 2+1 dimensions. This theory, originally obtained from a null-reduction of relativistic Maxwell's theory coupled to a complex scalar field in 3+1 dimensions, suffers an infinite series of quantum corrections. I will explain how these corrections can be handled systematically using the background field method, leading to a continuous manifold of fixed points where the non-relativistic conformal symmetry is preserved.

Speaker: Shira Chapman

Tuesday, October 29

10:00 AM → 10:45 AM Quantum Critical and Supersymmetric Lifshitz Field Theories

I will discuss non-boost-invariant field theories with "time domain" supersymmetry, in which the supersymmetric algebra closes on the Hamiltonian alone. I will briefly review the N=1 (two real supercharges) construction, and then introduce an N=2 family of field theories with four real supercharges and a holomorphic structure. I will show how this relatively simple construction exhibits some surprising properties: Mainly, the marginal subcases realize lines of quantum exact, interacting Lifshitz fixed points with vanishing beta functions in various space dimensions. Additionally, these theories enjoy a rich moduli space of vacua with spontaneously broken translation symmetry.

Speaker: Igal Arav

10:45 AM → 11:15 AM Coffee

11:15 AM → 12:00 PM Non-relativistic gravity and strings

I will start by motivating the recent interest in non-relativistic gravity and strings, and introduce the basics of Newton-Cartan geometry.
Newton-Cartan (NC) geometry was introduced more than 90 years ago in order to find a geometric formulation of Newtonian gravity. This geometry (including recent novel generalisation
and extensions) has gained renewed interest as it appears in a variety of settings in modern theory involving gravity, string theory and holography. I will then talk about recent work on an action principle for non-relativistic gravity, including its Newtonian limit. This requires a new notion of NC geometry, which naturally arises in a covariant 1/c expansion of general relativity, with c being the speed of light. The corresponding truncation of general relativity yields a non-relativistic gravity theory that goes beyond Newtonian gravity and is able to correctly describe gravitational time dilation. Finally, I will discuss the relevance and appearance of non-relativistic geometry in connection with non-relativistric string theory and holography.

Speaker: Niels Obers

12:10 PM → 12:55 PM Non-relativistic Strings from Quantum Mechanics

This talk is about a new type of string theory with a non-relativistic conformal field theory on the world-sheet, as well as a non-relativistic target space geometry. Starting with the relativistic Polyakov action with a fixed momentum along a non-compact null-isometry, we can take a scaling limit that gives the non-relativistic string, including an interesting intermediate step. This can in particular be applied to a string on AdS5 x S5. In this case the scaling limit realizes a limit of AdS/CFT that on the field theory side gives a quantum mechanical theory known as Spin Matrix theory. We review that Spin Matrix theory is a finite-N version of nearest neighbor spin chains, from which one can find a long-wavelength semi-classical description using sigma-model such as the Landau-Lifshitz sigma-model. Hence, we can show that both sides of the AdS/CFT gives, in this limit, equivalent non-relativistic sigma-models that we are able to write down in a fully covariant manner, and show that it has a non-relativistic local symmetry that realizes the Galilean Conformal Algebra (GCA). This suggests that one has a holographic duality between the quantum mechanical theory of Spin Matrix theory, and the non-relativistic string. This could provide a more tractable holographic duality in which one can study the emergence of non-relativistic strings, geometry and gravity.

Speaker: Troels Harmark

1:00 PM → 2:30 PM Lunch

2:30 PM → 3:15 PM Entanglement measures in generalised quantum Lifshitz models

The talk focusses on the computation and analysis of entanglement measures in generalised quantum Lifshitz models. These are free field theories with Lifshitz scaling symmetry which extend the (2+1)-dimensional quantum Lifshitz model to higher dimension, and provide us with simple models for non-relativistic critical theories. I will introduce various entanglement measures, such as entanglement entropy and logarithmic negativity (suitable to characterising quantum entanglement for pure and mixed states respectively), outline their computation in generalised quantum Lifshitz theories, and discuss the results.

Speaker: Valentina Giangreco Puletti

3:15 PM → 3:45 PM Tea

3:45 PM → 4:30 PM Non-relativistic supersymmetry on curved backgrounds

In this talk, I will briefly review how curved Riemannian manifolds, on which relativistic supersymmetric field theories can be defined, are found by studying a suitable set of differential Killing spinor equations. These Killing spinor equations are determined by the supersymmetry transformation rules of the fermionic fields of off-shell relativistic supergravity. I will then argue that one can obtain curved Newton-Cartan backgrounds, on which non-relativistic supersymmetric field theories can be put, by studying a set of non-relativistic Killing spinor equations, that include both algebraic and differential equations. Finally, some examples and properties of these curved backgrounds will be discussed.

Speaker: Jan Rosseel