# Applied Newton-Cartan Geometry

Europe/Berlin
02.430 (Mainz Institute for Theoretical Physics, Johannes Gutenberg University)

### 02.430

#### Mainz Institute for Theoretical Physics, Johannes Gutenberg University

Staudingerweg 9 / 2nd floor, 55128 Mainz
Description

The field of Applied Newton-Cartan Geometry is currently a rapidly developing field which is attracting researchers from different directions. Recent studies of non-AdS holography involving Lifshitz spacetimes have led to field theories with non-relativistic scaling, that are coupled to an extension of Newton-Cartan geometry that includes so-called twistless torsion. Parallel to this development, effective field theories in a Newton-Cartan background have been studied in Condensed Matter Physics and used to describe a variety of non-relativistic systems such as the Fractional Quantum Hall Effect, chiral superfluids and simple fluids. Besides the holographic and effective field theory applications, there have been many other recent applications of Newton-Cartan geometry in different fields ranging from hydrodynamics to modified gravity, and even connections to String Theory. For instance, it has been shown that Hořava-Lifshitz gravity and novel extensions can be described using dynamical Newton-Cartan geometry. Furthermore, Newton-Cartan geometry obeys a duality with its ultra-relativistic cousin, Carroll geometry. Carroll symmetries have been shown to occur as symmetries of strongly coupled gravity and, more recently, of plane gravitational waves while a conformal extension of it is related to the so-called BMS symmetry of flat-space holography. Finally, studying supersymmetric non-relativistic field theories on curved Newton–Cartan backgrounds enables one to apply powerful localization techniques to extract exact non-perturbative results for these field theories such as the partition function and the vacuum expectation value of Wilson lines.

The aim of this interdisciplinary topical workshop is to advance these recent exciting applications of NC geometry in different directions. It will enable participants from different backgrounds (Condensed Matter Physics, Mathematics, Statistical Physics, Gravity and String Theory) to interact and exchange new ideas. The first topical workshop on Applied Newton-Cartan Geometry was organised in March 2017 at the Simons Center for Geometry and Physics in Stony Brook (USA), see the webpage http://scgp.stonybrook.edu/archives/18337. This workshop was a huge success and led to many contacts across different disciplines which otherwise would never have been established. New directions where set in motion like novel applications of massive gravity in the Fractional Quantum Hall Effect, the role of hydrodynamics without boost invariance and new applications of torsion in holography and Condensed Matter Physics.The aim of this workshop is to repeat the success of the Simons workshop and to give a significant boost to the emerging field of Applied Newton-Cartan Geometry and its cross-disciplinary opportunities.

Participants include:

• Alejandra Castro (University of Amsterdam)
• Jose Figueroa-O'Farrill (University of Edingburgh)
• Jelle Hartong (University of Amsterdam)
• Petr Horava (UC Berkeley)
• Robert Leigh (University of Illinois, Urbana)
• Djordje Minic (Virginia Tech)
• Jan Rosseel (University of Vienna)
• Marika Taylor (University of Southampton)

(see the pdf file on left for the full list of final partipants)

• Monday, 12 March
• 09:30 10:30
Arrival/Registration
• 10:30 11:30
M. Roberts: Electrons in the LLL and Galilean geometry 1h
• 11:30 12:00
Coffee 30m
• 12:00 12:30
G. de Saxcé: Parameterized Post-Newtonian expansion with Galilean covariance 30m
• 12:30 14:00
Lunch 1h 30m
• 14:00 14:30
M. Dunajski: Twistor Theory of Newton Cartan Space times 30m
• 14:30 15:15
A. Castro: Wilson lines and Ishibashi states in AdS_3/CFT_2 45m
In this talk I will discuss a refined interpretation of a gravitational Wilson line in AdS_3 in terms of Ishibashi states in the dual CFT_2. Our strategy is to give a method to evaluate the Wilson line that accounts for all the information contained in the representation, and clarify the role of boundary conditions at the endpoints of the line operator. This gives a novel way to explore and reconstruct the local bulk dynamics.
• 15:15 15:45
Tea 30m
• 15:45 16:30
D. Grumiller: Higher Spin Carroll Gravity 45m
• 16:30 17:00
Break 30m
• 17:00 18:30
Welcome reception 1h 30m
• Tuesday, 13 March
• 09:30 10:30
P. Horava: Nonrelativistic Naturalness 1h
• 10:30 11:00
Coffee 30m
• 11:00 11:30
A. Bagchi: Tensionless strings and Carrollian things 30m
• 11:30 12:00
D. Van den Bleeken: Torsional Newton-Cartan and strong gravitational fields 30m
• 12:00 14:00
Lunch 2h
• 14:00 14:45
D. Minic: Towards a non-relativistic metastring theory 45m
• 14:45 15:15
Tea 30m
• 15:15 16:00
M. Petropoulos: Carrollian fluids and holographic applications 45m
General-covariant Galilean or Carrollian hydrodynamics can be reached from relativistic fluids observed from either Zermelo or Randers-Papapetrou frames, at infinite or vanishing velocity of light. I will focus on the latter case, display the general equations and describe the paramount role of Carrollian fluids in flat holography: duals of Ricci-flat spacetimes in the sense of fluid/gravity correspondence are Carrollian fluids defined at null infinity. Robinson-Trautman or Kerr-Taub-NUT families illustrate these results.
• Wednesday, 14 March
• 09:30 10:30
J. Hartong: Non-Relativistic Holographic Dualities 1h
• 10:30 11:00
Coffee 30m
• 11:00 11:30
T. Harmark: A quantum mechanical model for holography 30m
• 11:30 12:00
K. Grosvenor: Coset Representation of Newton-Cartan Geometry 30m
• 12:00 12:30
J. Lukierski: D=4 extended Galilean symmetries and N=4 Galilean superparticles with central charges 30m
• 12:30 14:00
Lunch 1h 30m
• 14:00 14:45
R. Leigh: Newton-Cartan and the Exact RG 45m
• 14:45 15:15
Tea 30m
• 15:15 16:00
S. Moroz: Effective field theory of a vortex lattice in a bosonic superfluid 45m
• Thursday, 15 March
• 09:30 10:30
M. Taylor: BMS for AdS 1h
• 10:30 11:00
Coffee 30m
• 11:00 11:30
P. Horvathy: A unified framework for Galilei and Carroll symmetry 30m
Whereas the usual Wigner-In\"on\"u contraction $c\to\infty$ of the Poincar\'e group yields the Galilei group, another $c\to0$ contraction yields the Carroll group" of L\'evy-Leblond. Both boost-invariant theories are conveniently unified within the Eisenhart-Duval'' framework. Plane gravitational waves carry a non-trivially implemented Carroll symmetry with broken rotations.
• 11:30 12:00
F. Pena-Benitez: Non-Relativistic Scaling in Semimetals 30m
I will discuss some examples of (condensed matter) systems with point like band touching but anisotropic spatial scaling. Then, I will talk about the recent attempts to describe these type of topologically non-trivial states of matter from holography.
• 12:00 14:00
Lunch 2h
• 14:00 14:45
V. Giangreco Puletti: Entanglement entropy in generalised Quantum Lifshitz theories 45m
In the first part of the talk I will review the so-called generalised quantum Lifshitz theories. These are (d+1)-dimensional field theories with Lifshitz scaling symmetry, which exhibit certain features of d-dimensional conformal theories, whenever the dynamical critical exponent is equal to the number of spatial dimensions. In the second part of the talk, I will outline the computation of entanglement entropy for spherical entangling surfaces in Lifshitz theories in (d+1)-dimensions, and finally, discuss the results.
• 14:45 15:15
Tea 30m
• 15:15 16:00
N. Pinzani Fokeeva: Schwinger-Keldysh effective field theories, a field theory and holographic perspective 45m
• Friday, 16 March
• 09:45 10:45
J. Rosseel: Non-relativistic supergravity 1h
• 10:45 11:15
Coffee 30m
• 11:15 12:00
J. Figueroa-O'Farrill: Classification of kinematical Lie algebras in arbitrary dimension 45m
• 12:00 13:30
Lunch 1h 30m
• 13:30 14:00
H. Afshar: Asymptotic Symmetries in p-Form Theories 30m
We consider (p+1)-form gauge fields in flat (2p+4)-dimensions for which the radiation and the Coulomb solutions have the same asymptotic falloff behavior. Imposing appropriate falloff behavior on fields and adopting a Maxwell-type action, we construct the boundary term which renders the action principle well-defined in the Lorenz gauge. We then compute conserved surface charges and the corresponding asymptotic charge algebra associated with nontrivial gauge transformations. We show that for p≥1 cases we have three sets of conserved asymptotic charges associated with exact, coexact and zero-mode parts of the corresponding p-form gauge transformations on the asymptotic S^{2p+2}. The coexact and zero-mode charges are higher form extensions of the four dimensional electrodynamics case (p=0), and are commuting. Charges associated with exact gauge transformations have no counterparts in four dimensions and form infinite copies of Heisenberg algebras. We briefly discuss physical implications of these charges and their algebra
• 14:00 14:30
S. Prohazka: Three-dimensional Spin-3 Theories Based on General Kinematical Algebras 30m
• 14:30 15:00
Tea 30m