Workshop on Symmetries and Gravity

Dates: January 21-24, 2025

Location: Harvard CMSA, 20 Garden Street, Cambridge, MA 02138

Organizers: Ibrahima Bah (Johns Hopkins University), Patrick Jefferson (Johns Hopkins University), Yiming Chen (Stanford University)

Description: There is a widespread belief, that has its origins in work from the 70s, that a theory of quantum gravity cannot admit global symmetries. Traditionally, this was seen only as a qualitative statement about ordinary symmetries, but there have since been a number of developments that have both widened its scope and sharpened its implications. Recent work has greatly broadened the definition of global symmetries, and characterizes them in terms of topological operators in quantum systems. Concurrently, insights from quantum gravity have suggested ways to quantify the extent of global symmetry violation. Additionally, advances in the swampland program, along with amplitudes and bootstrap techniques, have shown ways to turn high-energy statements into constraints on low-energy effective field theories. In string theory, there are more concrete statements on charge violation in gravity, with proofs in limited context. In general, however, “no global symmetries in quantum gravity” continues to be an open conjecture with broad implications on the nature of quantum gravity and low-energy effective field theory. The main goal of the meeting is to bring together experts in the various arenas of research above, to reassess and develop new strategies for making progress on this long-standing open problem. Some objectives include understanding the violation of various generalized and categorical symmetries in gravity more cohesively, and putting concrete bounds on global charge-violating amplitudes at low energies.

Partially funded by the Simons Collaboration on Global Categorical Symmetries.

 

Confirmed Participants

• Tom Banks, Rutgers
• Federico Bonetti, Durham University
• Christian Copetti, Oxford
• Hector Parra De Freitas, Harvard
• Damian van de Heisteeg, Harvard CMSA
• Matilda Delgado, IFT
• Michele Del-Zotto, Uppsala University
• Muldrow Etheredge, UMass Amherst
• Iñaki Garcia-Etxebarria, Durham University
• Eduardo Garcia-Valdecasas, SISSA, Trieste
• Naomi Gendler, Harvard
• Kelian Haring, CERN
• Daniel Harlow, MIT
• Jonathan Heckman, University of Pennsylvania
• Ben Heidenreich, UMass Amherst
• Aidan Herderschee, IAS
• Max Huebner, Uppsala University
• Jesús Huertas, Instituto de Física Teórica
• Theo Johnson-Freyd, Dalhousie University
• Ho Tat Lam, MIT
• Adam Levine, MIT
• Yue-Zhou Li, Princeton
• Jacob McNamara, Caltech
• Ruben Minasian, Institute of Theoretical Physics Saclay
• Amineh Mohseni, Harvard
• Miguel Montero, IFT
• Gregory Moore, Rutgers
• Leonardo Rastelli, Stony Brook
• Matt Reece, Harvard University
• Grant Remmen, New York University
• Diego Rodriguez-Gomez, University of Oviedo
• Konstantinos Roumpedakis, Johns Hopkins
• Tom Rudelius, Durham University
• Vivek Saxena, Stony Brook and Rutgers
• Edgar Shaghoulian, UC Santa Cruz
• Shu-Heng Shao, Stony Brook and MIT
• Adar Sharon, Simons Center for Geometry and Physics, Stony Brook
• Irene Valenzuela, IFT and CERN
• Thomas Waddleton, Johns Hopkins
• Hao Xu, University of Göttingen
• Xingyang Yu, Virginia Tech

 

Schedule 

Tuesday, Jan. 21, 2025

9:00 – 9:30 am
Breakfast

9:30 – 11:00 am
Review
Leonardo Rastelli, Stony Brook University
Youtube Video

11:00 – 11:15 am
Break

11:15 am– 12:00 pm
Kelian Haring, CERN
Title: S-matrix bootstrap and black hole production
Abstract: I will review the expected effects of black hole production in scattering amplitudes. I will consider both symmetry-breaking and elastic amplitudes. I will argue that, in the elastic case, this input can be computationally useful. Then, I will discuss an example of a symmetry-breaking Wilson coefficient as a concrete target for the bootstrap.
Youtube Video

12:00 – 1:45 pm
Lunch Break

1:45 – 2:30 pm
Ho Tat Lam, MIT
Title: Global Aspects of Exactly Marginal Current-Current Deformations
Abstract: Conformal field theories connected by exactly marginal deformations form conformal manifolds. In two dimensions, a large class of conformal manifolds is generated by bilinears of currents, known as current-current deformations. In this talk, we will revisit these deformations and prove that a dense set of points on the conformal manifolds are related to the seed theory through discrete gauging. This perspective enables us to connect the topology of the conformal manifolds with the anomalies of the currents and to show that enhanced invertible symmetries reorganized into non-invertible symmetries away from the symmetry enhanced points. We will also discuss how current-current deformation can be understood from the recently proposed continuous abelian symmetry topological field theory.
Youtube Video

2:30 – 3:15 pm
Tom Banks, Rutgers University
Title: Symmetries in the Hilbert Bundle Formulation of Quantum Gravity
Abstract: Results of Jacobson, Carlip and Solodukhin from the 1990s, as extended by Banks and Zurek in 2021, point to a solution of Einstein’s equations as a hydrodynamic approximation to a quantum gravitational system, which determines the density matrix assigned to each subsystem corresponding to a hydrodynamic causal diamond in terms of the Virasoro generator of a cut off 1 + 1 dimensional CFT. The full quantum system can be viewed as a Hilbert bundle over the space of timelike geodesics on the hydrodynamic background. Isometries of the background generically map one fiber of the bundle to another and don’t act on a fixed Hilbert space. Time evolution along each geodesic is given by an analog of “one sided modular flow in QFT”, which in this context is a sequence of unitary embeddings of smaller diamond Hilbert spaces into larger ones. A full unitary map on the entire Hilbert space of a fiber requires a “Quantum Principle of Relativity” equating the entanglement spectrum of the density matrix of the largest diamond in the overlap between diamonds on different geodesics. In principle, this implies asymptotic symmetries for spacetimes which have them. For the case of asymptotically AdS space, this can be worked out in a hand waving way by using the Tensor Network Renormalization Group of Evenbly and Vidal. For asymptotically flat space we probably require a better non-perturbative definition of the space of asymptotic states to understand the action of the Poincare group. For de Sitter space there is no sense in which the de Sitter group acts on any set of asymptotic observables. Ironically, there IS an approximate de Sitter invariance of at least low point inflationary correlation functions, but I will not have time to discuss that.
Youtube Video

3:15 – 3:45 pm
Break

3:45 – 4:30 pm
Christian Copetti, Oxford University
Title: Non-Invertible Symmetries, Generalized Gauging and Factorization
Abstract: We analyze a toy model for low dimensional holography, in which the dual theory is an ensemble over 2d RCFTs. This simple model lacks factorization on multi-boundary geometries and at the same time has a (generalized) bulk global symmetry. We show that both problems are solved if the path integral prescription is modified by a generalized gauging operation, which can also be interpreted as the insertion of (topological) EOW branes.
Youtube Video

4:30 – 5:00 pm
Free Discussion

Wednesday, Jan. 22, 2025

9:00 – 9:30 am
Breakfast

9:30 – 11:00 am
Review
Daniel Harlow, MIT
Youtube Video

11:00 – 11:15 am
Break

11:15 am– 12:00 pm
Jacob McNamara, Caltech
Title: Conserved Charges of Closed Universes
Abstract: In quantum gravity, while our standard notions of symmetry operator become hard to define, the notion of conserved charge continues to make sense. After a general discussion of conserved charges in quantum gravity, I will present a new kinematic invariant of a gravitational path integral that refines the cobordism groups of quantum gravity: the (higher) category of closed universe charges. By categorifying an argument of Coleman, Giddings, and Strominger, I will argue that conserved charges in quantum gravity of any form degree arise only due to a categorical version of ensemble holography.
Youtube Video

12:00 – 1:45 pm
Lunch Break

1:45 – 2:30 pm
Federico Bonetti, Durham University
Title: Aspects of Categorical Symmetries for Branes
Youtube Video

2:30 – 3:15 pm
Konstantinos Roumpedakis, Johns Hopkins University
Title: Symmetry Operators and Gravity
Abstract: It is widely believed that there are no conserved charges in a theory of gravity, based on arguments involving black holes. Moreover, the modern approach to study global symmetries is the language of topological operators. In this talk, I will revisit the absence of global symmetries in a theory of gravity from the perspective of topological operators. More specifically, I will argue that topological operators for continuous symmetries written in terms of currents need regularization, which effectively gives them a small but finite width. The regulated operator is a finite tension object which fluctuates. In the zero-width limit these fluctuations freeze, recovering the properties of a topological operator. When gravity is turned on, the zero-width limit becomes ill-defined, thereby prohibiting the existence of topological operators. This talk is based on work in collaboration with Ibrahima Bah, Patrick Jefferson, and Thomas Waddleton.
Youtube Video

3:15 – 3:45 pm
Break

3:45 – 4:30 pm
Iñaki Garcia-Etxebarria, Durham University
Title: Some aspects of symmetry descent
Abstract: SymTFTs allow us to encode the symmetry structure of Quantum Field Theories in a convenient way. For those QFTs that arise in geometric engineering, or holography, we expect to be able to derive the SymTFT from the geometric data of the string background. This talk will describe some recent progress in this direction, together with S. Hosseini and with F. Gagliano.
Youtube Video

4:30 – 5:00 pm
Free Discussion

6:00 pm
Dinner at Changsho Restaurant

Thursday, Jan. 23, 2025

9:00 – 9:30 am
Breakfast

9:30 – 11:00 am
Review
Irene Valenzuela, IFT and CERN
Title: Breaking of Symmetries in Gravity
Abstract: Global symmetries are expected to be broken (or gauged) in quantum gravity. However, we can still learn a lot from understanding the mechanisms by which quantum gravity avoids them and quantifying their breaking. Remarkably, several Swampland constraints can be reinterpreted as consequences of breaking global symmetries. I will first focus on quantifying the minimal symmetry violation of axionic shift symmetries, and show how the bottom-up expectation based on black holes seems to hold in string theory examples. I will then discuss how this symmetry violation changes as we move in the moduli space, implying a drop-off of the quantum gravity cut-off when the symmetry is approximate. Finally, I will discuss the fate of non-invertible symmetries in string theory, and how they are typically broken at loop level. Nevertheless, these approximate non-invertible symmetries are still useful to fill in the gaps in the worldsheet proofs of some Swampland conjectures.

11:00 – 11:15 am
Break

11:15 am– 12:00 pm
Tom Rudelius, Durham University
Title: A Symmetry-Centric Perspective on the Geometry of the Landscape and the Swampland
Abstract: As famously observed by Ooguri and Vafa nearly twenty years ago, scalar field moduli spaces in quantum gravity appear to exhibit various universal features. For instance, they seem to be infinite in diameter, have trivial fundamental group, and feature towers of massive particles that become light in their asymptotic limits. In this talk, I will explain how these features can be reformulated in more modern language using generalized notions of global symmetries. Such symmetries are ubiquitous in non-gravitational quantum field theories, but it is widely believed that they must be either gauged or broken in quantum gravity. We will see that the observations of Ooguri and Vafa can be understood as consequences of such gauging or breaking.

12:00 – 1:45 pm
Lunch Break

1:45 – 2:30 pm
Miguel Montero, IFT
Title: Parity symmetry breaking and the membrane Weak Gravity Conjecture
Abstract: Symmetries are expected to be broken or gauged in any consistent theory of quantum gravity, and this also applies to spacetime symmetries such as parity. I will argue that, in the context of 4d N=1 AdS vacua of string theory, the Weak Gravity Conjecture for membranes case only holds if the vacuum has an exact (i.e. gauged) parity symmetry of Pin+ type. I will give top-down examples of M-theory vacua illustrating this, and show that in the DGKT scenario (a putative massive IIA vacuum with scale separation, whose full consistency is the subject of some debate in the literature) there is no parity symmetry, and the membrane WGC is violated. Thus, there is either a pathology in DGKT, or the membrane WGC is wrong. Both possibilities would have interesting consequences, and I will outline ongoing work to figure out which one is it.

2:30 – 3:15 pm
Matilda Delgado, IFT
Title: Dualities, Defects and Duality Defects
Abstract: I will outline how duality symmetries in quantum gravity theories naturally predict the existence of defects associated with duality transformations. While some of these objects are well-understood and extensively studied, others remain enigmatic; I will discuss this with examples. I will conclude by discussing the potential role of dualities in characterising the UV defects predicted by cobordism conjecture (and more generally by the no global symmetries conjecture). Based on: [2412.03640]

3:15 – 3:45 pm
Break

3:45 – 4:30 pm
Max Hübner, Uppsala University
Title: Metric Isometries, Holography, and Continuous Symmetry Operators
Abstract: In the AdS/CFT correspondence, a topological symmetry operator of the boundary CFT is dual to a dynamical brane in the gravitational AdS bulk. Said differently, this predicts a dynamical brane for every global symmetry of the boundary CFT. We analyze this correspondence for continuous symmetries which arise from a consistent truncation of isometries on the “internal” factor X of AdS × X. We discuss how this perspective can be used to both derive properties of the topological symmetry operators and non-topological properties of their bulk duals.

4:30 – 5:00 pm
Free Discussion

 

Friday, Jan. 24, 2025

9:00 – 9:30 am
Breakfast

9:30 – 10:15 am
Jonathan Heckman, University of Pennsylvania
Title: Cobordism Utopia
Abstract: On general grounds one expects that global symmetries are absent in quantum gravity. We discuss some aspects of this issue, focusing on the recently proposed Swampland Cobordism Conjecture, and related conjectures connected with completeness of the spectrum of states charged under symmetries. In particular, the U-dualities of M-theory provide an excellent arena both for testing aspects of these conjectures, as well as predicting the existence of new dynamical objects. We also comment on how this approach connects to related top down and holographic approaches to constructing and studying gauging and breaking symmetries in quantum gravity. Based on joint work to appear with Braeger, Debray, Dierigl, and Montero.

10:15 – 11:00 am
Naomi Gendler, Harvard University

11:00 – 11:15 am
Break

11:15 am – 12:00 pm
Diego Rodriguez-Gomez, University of Oviedo
Title: Non-BPS branes as holographic symmetry operators
Abstract: We propose a holographic description of the operators implementing continuous global symmetries that are dual to superstring gauge fields in terms of non-BPS D- branes, and consider some possible further extensions.

12:00 – 12:45 pm
Greg Moore, Rutgers University
Title: Summing Over Bordisms In 2d TQFT: Déjà Vu
Abstract: This is basically a rerun of a talk I gave on zoom for the CMSA on March 16, 2022. I will review the contents of a paper I wrote with Anindya Banerjee 2201.00903, but including a few minor updates. I will describe a construction in Topological Field Theory (TFT) which was motivated by developments in the quantum gravity community. The goal is to provide an interpretation of a model discussed by D. Marolf and H. Maxfield 2002.08950 aimed at fitting their model within the functorial framework of Quantum Field Theory (QFT). Given a TFT one can consider – formally – the sum over all bordisms between fixed ingoing and outgoing spatial slices (with appropriate weight factors for the bordisms) of the amplitudes associated to the bordism by the TFT. This construction leads to convergent sums in d\leq 2 dimensions, at least for for generic parameters of the TFT. I will describe a curious splitting property satisfied by the total amplitude. I view the splitting property as an alternative to ensemble-type interpretations. There will be a cameo appearance of a very interesting paper by Daniel Friedan 2306.00019 which purports to give an axiomatic framework for Euclidean Quantum Gravity (EQG) analogous to the functorial formalism of QFT. I will also note, in passing, that these extremely simple, low-dimensional, baby baby baby models of EQG admit global symmetries and continuous parameters.

1:00 pm
Farewell Lunch