Workshop “Conformal higher spins, twistors and boundary calculus”
Conformal geometry and its generalisations emerge in many different areas, including CFT, (flat space) holography, boundary calculus and asymptotic symmetries, as well as twistor methods in field theory. Remarkably, all these themes become intertwined around conformal higher spin (CHS) gravities which are higher spin extensions of conformal (Weyl) gravities, and these theories suggest a vast generalisation of conformal geometry. In particular, CHS gravities generate various conformally-invariant operators and are closely related to conformal anomalies. Moreover, CHS fields can be identified as boundary values of massless fields in AdS space via Feffermann-Graham expansion. In low dimensions, another kind of geometry becomes important, namely twistor geometry, which is crucial for studying self-dual (conformal) theories, including higher spin gravities. The purpose of this workshop is to bring together mathematicians and physicists interested in these research directions.
- Tim Adamo* (University of Edinburgh)
- Xavier Bekaert (U. Tours)
- Andreas Čap (University of Vienna)
- Michael Eastwood (University of Adelaide)
- Yannick Herfray (U. Tours)
- Euihun Joung (Kyung Hee University)
- Kirill Krasnov (University of Nottingham)
- Sergei Kuzenko (University of Western Australia)
- Ruben Manvelyan (Yerevan Physics Institute)
- Tristan McLoughlin (Trinity College Dublin)
- Rodrigo Olea (Pontificia Universidad Católica de Valparaíso)
- Jan Slovák (Masaryk University)
- Dmitri Sorokin (University of Padova)
- Arkady Tseytlin* (Imperial College London)
- Andrew Waldron (UC Davis)
Xavier Bekaert | BMS particles: continuous spins and higher spins
Abstract: Generic unitary irreducible representations (UIRs) of the Bondi-Metzner-Sachs (BMS) group are considered. They are shown to describe quantum superpositions of (Poincaré) particles propagating on inequivalent gravity vacua. This follows from reconsidering McCarthy’s classification of BMS group UIRs through a unique, Lorentz-invariant but non-linear, decomposition of supermomenta into hard and soft pieces. The branching rules of generic UIRs for the restriction of BMS group to a Poincaré subgroup typically include continuous spins and higher spins in the BMS multiplet.
Rod Gover | Higher Yang-Mills energies and conformal Yang-Mills renormalisation
Abstract: Given a gauge connection on a Riemannian 4-manifold, the norm squared of its curvature gives a Lagrangian density whose integral is the Yang-Mills action/energy -- the variation of which gives the celebrated Yang-Mills equations. An important feature of both this energy and the equations is their conformal invariance in dimension 4.
A natural question is whether there are analogous objects in higher dimensions. We prove that there are such conformally invariant objects on even dimensional manifolds equipped with a connection. One proof, in dimension six, uses a type of Q-curvature that one can associate to connections, and we investigate applications of the result to conformal gravity type equations. Another proof uses a Poincaré-Einstein manifold in one higher dimension and a suitable Dirichlet problem for the interior Yang-Mills equations on this structure. The higher Yang-Mills equations arise from an obstruction to smoothly solving the asymptotic problem, while the higher energy is a log term (the so-called anomaly term) in the asymptotic expansion of the divergent interior energy. More arises including links to the non-local renormalised Yang-Mills energy, and a related higher non-linear Dirichlet-Neumann operator.
This is joint work with Emanuele Latini, Andrew Waldron, and Yongbing Zhang.
Kirill Krasnov | 4D gravity via triples of 2-forms
Abstract: Generic unitary irreducible representations (UIRs) of the Bondi-Metzner-Sachs (BMS) group are considered. They are shown to describe quantum superpositions of (Poincaré) particles propagating on inequivalent gravity vacua. This follows from reconsidering McCarthy’s classification of BMS group UIRs through a unique, Lorentz-invariant but non-linear, decomposition of supermomenta into hard and soft pieces. The branching rules of generic UIRs for the restriction of BMS group to a Poincaré subgroup typically include continuous spins and higher spins in the BMS multiplet.
Rod Gover | Higher Yang-Mills energies and conformal Yang-Mills renormalisation
Abstract: Given a gauge connection on a Riemannian 4-manifold, the norm squared of its curvature gives a Lagrangian density whose integral is the Yang-Mills action/energy -- the variation of which gives the celebrated Yang-Mills equations. An important feature of both this energy and the equations is their conformal invariance in dimension 4.
A natural question is whether there are analogous objects in higher dimensions. We prove that there are such conformally invariant objects on even dimensional manifolds equipped with a connection. One proof, in dimension six, uses a type of Q-curvature that one can associate to connections, and we investigate applications of the result to conformal gravity type equations. Another proof uses a Poincaré-Einstein manifold in one higher dimension and a suitable Dirichlet problem for the interior Yang-Mills equations on this structure. The higher Yang-Mills equations arise from an obstruction to smoothly solving the asymptotic problem, while the higher energy is a log term (the so-called anomaly term) in the asymptotic expansion of the divergent interior energy. More arises including links to the non-local renormalised Yang-Mills energy, and a related higher non-linear Dirichlet-Neumann operator.
This is joint work with Emanuele Latini, Andrew Waldron, and Yongbing Zhang.
Kirill Krasnov | 4D gravity via triples of 2-forms
- Xavier Bekaert (University of Tours)
- Andreas Čap (University of Vienna)
- Minkyu Cho (Kyung Hee University)
- Raikhik Das (University of Edinburgh)
- Ivan Dneprov (UMONS)
- Michael Eastwood (University of Adelaide)
- Alejandro García Rivas (University of Bologna)
- Yannick Herfray (University of Tours)
- Euihun Joung (Kyung Hee University)
- Kirill Krasnov (University of Nottingham)
- Sergei Kuzenko (University of Western Australia)
- Julian Lang (Okinawa Institute of Science and Technology)
- Iva Lovrekovic (Technischen Universität Wien)
- Mikhail Markov (UMONS)
- Tristan McLoughlin (Trinity College Dublin)
- TaeHwan Oh (Korean Institute of Advanced Studies)
- Rodrigo Olea (Pontificia Universidad Católica de Valparaíso)
- Simon Pekar (Scuola Internazionale Superiore di Studi Avanzati)
- Davide Rovere (University of Padova)
- Jan Slovák (Masaryk University)
- Andrew Waldron (University of California, Davis)
Registration
If you wish to attend the meeting please send an email to Evgeny.SKVORTSOV@umons.ac.beHow to reach the conference venue
- Direct trains from Zaventem airport to Mons are available every hour. You only have to be careful to look for trains directed to Bergen, which is the Dutch name of Mons; alternatively, you can reach the station Brussels Midi and take a train to Mons;
- Charleroi airport is connected to Mons by a shuttle bus (bus schedule);
- Trains from Brussels to Mons are running every half an hour, starting around h:25 and h:56 from Midi station (please crosscheck the train schedule!);
- The workshop will take place in the UMONS campus “Plaine de Nimy”, that can be reached from Mons train station in 20/25 minutes by walk (see the precise address below). A limited number of blue-bikes is also available at the train station;
- The talks will take place in the building De Vinci (map of the campus).
Accommodation
- B&B Hotel Mons Centre (10 min by foot from the workshop venue)
Address
Avenue Maistriau, 19
7000 Mons, Belgium
7000 Mons, Belgium