# Aldo Riello

PSI Fellow

Perimeter Institute for Theoretical Physics

Areas of research:

### Research Interests

My main research interests are in quantum gravity. Quantum gravity is ultimately the problem of devising a theory of quantum matter which interacts gravitationally. Since our understanding of gravitation is in terms of a dynamical spacetime, quantum gravity is often restated as the problem of finding a quantum theory of spacetime itself. My work focuses on the interface between non-perturbative background independent approaches to quantum gravity, topological quantum field theories, and discrete quantum geometries. In the last year, I focused on various projects.
Together with the faculty member B.Dittrich and her PhD student C. Delcamp, I developed a new representation for non-perturbative 2+1 dimensional quantum gravity, dual to the usual Ashtekar-Lewandowski representation of Loop Quantum Gravity (more specifically, although slightly loosely, it is based on curvature, rather than metric, defects). We used this basis for developing a new approach to the calculation of entanglement entropy. [JHEP 1611 (2016) 102, JHEP 1702 (2017) 061]
In collaboration with H. Gomes, another postdoc at PI, I put forward a proposal for a gauge-invariant form of symplectic geometry in finite spacetime regions; the main tool employed is a connection 1-form in field-space, that can be thought as providing an abstract observer and whose algebraic properties are closely related to the BRST ghosts. [JHEP 1705 (2017) 017]
I also kept working on an older project of mine, that is 4d Loop Quantum Gravity with a cosmological constant. Investigations in this area led me to propose a deformed, completely self-dual, version of the Yang-Mills phase space on a lattice. This deformed, self-dual, phase space, bears interesting relationships with recent work in (3+1)d Topological Quantum Field Theories, in the Hamiltonian framework, by Walker & Wang, and more recently Dittrich [arXiv:1706.07811 hep-th].
Finally, I am finalizing (two papers under reduction, and another one in project) the study of Euclidean 3d Loop Quantum Gravity on a (filled) torus. The interest of this study is comparing the Loop Quantum Gravity non-perturbative results with the 1-loop exact calculations done in the usual QFT framework. Quite remarkably, and via totally different techniques (deeply rooted in the finiteness of the "spacetime" region under study, rather than on an Euclidean path integral on an infinite space and periodic time), the results are perfectly compatible, modulo some interesting non-perturbative corrections. This project is done in collaboration with B. Dittrich (PI), E. Livine (ENS Lyon), and C. Goeller (PI & ENS Lyon), a PhD student I supervised during his master project. [to appear soon]

### Positions Held

- 2017-now Perimeter Institute, Waterloo, Canada, Senior Postdoctoral Researcher
- 2014-2017 Perimeter Institute, Waterloo, Canada, Postdoctoral Researcher
- 2011-2014 Aix-Marseille University, France, Teaching Assistant
- 2011-2014 Centre de Physique Théorique, Aix-Marseille University, France, PhD Student

### Recent Publications

- M. Han, H.M. Haggard, W. Kaminski, AR. "SL(2,C) Chern-Simons Theory, Flat Connections, and Four-dimensional Quantum Geometry" arXiv: hep-th/1512.07690 Accepted in Advances in Theoretical and Mathematical Physics (to be published in Volume 23, Issue 4)
- H. Gomes, F. Hopfmüller, AR "A unified geometric framework for boundary charges and dressings: non-Abelian theory and matter" Nucl.Phys. B941 (2019) 249-315 DOI: 10.1016/j.nuclphysb.2019.02.020 arXiv: 1808.02074
- H. Gomes, AR "Unified geometric framework for boundary charges and particle dressings" Phys.Rev. D98 (2018) no.2, 025013 DOI: 10.1103/PhysRevD.98.025013 arXiv: 1804.01919
- B. Dittrich, C. Goeller, E. Livine, AR "Quasi-local holographic dualities in non-perturbative 3d quantum gravity" Class.Quant.Grav. 35 (2018) no.13, 13LT01 DOI: 10.1088/1361-6382/aac606 arXiv: 1803.02759
- AR "Quantum edge modes in 3d gravity and 2+1d topological phases of matter" Phys.Rev. D98 (2018) no.10, 106002 DOI: 10.1103/PhysRevD.98.106002 arXiv: 1802.02588
- B.Dittrich, C. Goeller, E. Livine, AR "Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS3 characters" Nucl.Phys. B938 (2019) 878-934 DOI: 10.1016/j.nuclphysb.2018.06.010 arXiv: 1710.04237
- B. Dittrich, C. Goeller, E. Livine, AR "Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals". Nucl.Phys. B938 (2019) 807-877 DOI: 10.1016/j.nuclphysb.2018.06.007 arXiv: 1710.04202
- AR. "Self-dual phase space for ( 3+1 )-dimensional lattice Yang-Mills theory". Phys.Rev. D97 (2018) no.2, 025003 DOI: 10.1103/PhysRevD.97.025003 arXiv: 1706.07811
- C. Delcamp, B. Dittrich, AR. "On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity". JHEP 1611 (2016) 102, [arXiv: 1609.04806 hep-th]
- H. Gomes, AR. "The observer"s ghost: notes on a field space connection". JHEP 1705 (2017) 017, May 2017. [arXiv: 1608.08226 math-phys]
- C. Delcamp, B. Dittrich, AR. "Fusion basis for lattice gauge theory and loop quantum gravity" JHEP 1702 (2017) 061, [arXiv: 1607.08881 hep-th]
- H.M. Haggard, M. Han, W. Kaminski, AR, "Four-dimensional Quantum Gravity with a Cosmological Constant from Three-dimensional Holomorphic Blocks". Phys.Lett.B, 752, pp. 258-2622015, January 2016. [arXiv: 1509.00458 hep-th]
- M. Han, H.M. Haggard, AR. "Encoding Curved Tetrahedra in Face Holonomies: a Phase Space of Shapes from Group-Valued Moment Maps". Ann. Henri Poicaré 2016. [arXiv: 1506.03053 math-ph]
- M. Han, H.M. Haggard, W. Kaminski, AR. "SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry." Nucl.Phys.B, 900, pp. 1-79, September 2015. [arXiv: 1412.7546 hep-th]
- G. Chirco, H.M. Haggard, AR, C. Rovelli. "Spacetime thermodynamics without hidden degrees of freedom". Phys.Rev.D 90, 044044, August 2014, [arXiv: 1401.5262 gr-qc]
- AR. "Radiative corrections to the Lorentzian Engle-Pereira-Rovelli-Livine and Freidel-Krasnov spinfoam graviton". Phys.Rev.D 89, 06402, March 2014, [arXiv: 1310.2174 gr-qc]
- AR. "Self-energy of the Lorentzian Engle-Pereira-Rovelli-Livine and Freidel-Krasnov model of quantum gravity". Phys.Rev.D 88, 024011, July 2013, [arXiv: 1302.1781 gr-qc]
- M. Christodoulou, M. Långvik, AR, C. Röken, C. Rovelli. "Divergences and Orientation in Spinfoams". Classical Quant.Grav., 30(5): 055009, February 2013. [arXiv: 1207.5156 gr-qc]
- M. Christodoulou, AR, C. Rovelli. "How to detect an anti-spacetime". Int.J.Mod.Phys.D, 21(11):1242014, October 2012. [arXiv: 1206.3903 gr-qc]
- V. Bonzom, R. Gurau, AR, V. Rivasseau. "Critical behavior of colored tensor models in the large N limit". Nucl.Phys.B, 853(1):174-195, December 2011. [arXiv: 1105.3122 hep-th]
- S. Asante, B. Dittrich, F. Girelli, AR, P. Tsimiklis "Quantum geometry from higher gauge theory" e-Print: arXiv: 1908.05970
- H. Gomes, AR "Quasilocal degrees of freedom in Yang-Mills theory" arXiv: 1906.00992
- AR "Soft charges from the geometry of field space" arXiv: 1904.07410

### Seminars

- "A unified geometric framework for Yang-Mills charges and dressings in finite regions" seminar of Mathematical Physics, Centre de Recherche Mathématique (CRM), U. of Montreal
- "A unified geometric framework for Yang-Mills charges and dressings in finite regions" High Energy Physics joint seminar (U. Libre de Bruxelles, Vrije U. Brussel, K.U. Leuven, U. Mons) at the unité de recherche Physics of the Universe, Fields and Gravitation, Mons U., Belgium
- "Quasi-local holography in nonperturbative 3D quantum gravity" talk at Quantum Gravity meets Lattice QCD, ECT*, Trento, Italy
- "What"s at the edge of 3d quantum gravity?" seminar at the Laboratoire de Physique The Ìorique, U. d"Orsay (Paris Sud XI), France
- "What"s at the edge of 3d quantum gravity?" seminar at the Centre for Mathematical Sciences, U. of Nottingham, UK
- "What"s at the edge of 3d quantum gravity?" seminar at the ICMS, Heriot-Watt U. & Edinburgh U., Scotland
- "Entanglement entropy in 3d gauge theories and quantum gravity", LOOPS17, Instytut Fizyki Teoretycznej, U. of Warsaw (Warsaw, Poland), 7 July 2017 [invited contribution]
- "The observer"s ghost", International Loop Quantum Gravity Seminar (ILQGS), 6 December 2016
- "On Asymptotic Symmetries in Classical General Relativity", invited contribution at the workshop Classical and Quantum Symmetries in Mathematics and Physics (Satellite meeting of 7ECM), Friedrich Schiller U. (Jena, Germany), July 2016
- "On Finite Regions, Symmetries, and Observers in General Relativity'', Carlofest 2016, Aix-Marseille U. (Marseille, France), May 2016
- "From Holonomy Observables to 3+1 QG with a Cosmological Constant", Quantum Gravity meeting in Rome, La Spaienza University, Roma, 19-23 July 2015
- "Deformed Holonomy-Flux Algebra in 3+1 Quantum Gravity with a Cosmological Constant", LOOPS15, Institute for Quantum Gravity, Friedrich-Alexander Universitaet (Erlangen, Germany), 6-10 July 2015
- "Towards Covariant Loop Quantum Gravity with a Cosmological Constant", General Relativity and Gravitation, Centennial Conference, Penn State University, June 2015
- "Toward 4d Quantum Gravity with a Cosmological Constant from SL(2,C) Chern-Simons Theory", Laboratoire de Physique Théorique de Lyon, ENS Lyon, February 2015
- "SL(2,C) Chern-Simons Theory and Spinfoam Gravity with a Cosmological Constant", International Loop Quantum Gravity Seminar, November 2014
- "The Melon Graph in the EPRL-FK Spinfoam Model", invited contribution to the fourth edition of the Workshop Quantum Gravity in Paris, March 2014
- "Radiative Corrections in Spinfoam Quantum Gravity", Quantum Vacuum and Gravitation (QVG2013), Institut de Recherche en Astrophysique et Planétologie (Toulouse, France), 4-6 November 2013
- "Field-Space Approach to Gauge Symmetries at Boundaries", Infrared Problems in QED and Quantum Gravity, Perimeter Institute (Waterloo, Canada), 7-8 December 2016
- PIRSA:13110063, "Divergences in Spinfoam Quantum Gravity", 2013-11-28, Quantum Gravity Seminar
- PIRSA:13070041, "Self-energy of the Lorentzian EPRL-FK model", 2013-07-22, Loops 13 - Spin Foams