2023 Simons Collaboration on Global Categorical Symmetries Annual Meeting

Ibrahima Bah
Johns Hopkins University

Aspects of Symmetry and Branes in Holography

String theory and holography provide important points of view on the topological nature of symmetries acting on quantum systems. In this talk, Ibrahima Bah will discuss how symmetry structure can be described from the bulk in AdS/CFT, both from top down, in string theory, and bottom-up perspectives. Bah will discuss how branes can realize non-invertible symmetry operators and the various properties associated to them, such as fusion rules.
 

Clay Córdova
University of Chicago

Anomalies of Non-Invertible Symmetries

Non-invertible symmetries, i.e., topological operators with general fusion rules, have recently emerged as a new tool to study dynamics of quantum field theories. Clay Córdova will formulate the notion of anomalies of non-invertible symmetries, which are obstructions to realizing the non-invertible symmetry in a trivially gapped/invertible phase. As Córdova describes, such anomalies are intimately connected to finding topological boundary conditions of an associated topological field theory that encodes the symmetry. Córdova will compute these anomalies both for 2d and 4d quantum field theories which have a duality symmetry captured by a (higher) fusion category. Along the way, Córdova will show an interesting, decorated domain wall construction which is useful for understanding the contribution to the anomaly of Frobenius-Schur indicators.
 

Thomas Dumitrescu
UCLA

Invertible TQFTs and Gauge Theory Phases

Gauge theory phases are characterized by the breaking pattern of global symmetries. Typically, these are higher symmetries acting on extended operators. Gauge theories with fundamental matter, e.g., QCD, typically do not have such higher symmetries, obstructing sharp definitions of confining and Higgs phases.

In this talk, Thomas Dumitrescu will discuss examples in which confining and Higgs phases are naturally characterized by certain invertible TQFTs, or equivalently via symmetry protected topological (SPT) phases, which involve only ordinary symmetries. Dumitrescu will conclude with applications to the QCD phase diagram.
 

Iñaki García Etxebarria
Durham University

Deriving SymTFTs from Geometry

Symmetry TFTs (aka, SymTFTs), and the related “sandwich construction,” provide a principled way of discussing various subtle aspects of many systems with categorical symmetries. These objects also appear very naturally when studying quantum field theory using geometric methods in string theory. In this talk, Iñaki García Etxebarria will review some elementary aspects of this description of symmetries and explain how it arises in string theory and holography.
 

Nicolai Reshetikhin
UC Berkeley & Tsinghua University

Topological Invariants Related to Quantum Groups at Roots of Unity

Quantum groups at roots of unity can be used to construct invariants of links and 3-manifolds. Part of it is a well-known story. In this talk, Nicolai Reshetikhin will focus on recent progress on invariants of links with flat $G$-connections in the complement. This is unfolding story, closely related to invariants related to non-semisimple categories.
 

Claudia Scheimbauer
TU Munich

Finite Gauge Theory as an Extended Topological Field Theory

Following Freed-Hopkins-Lurie-Teleman’s proposal, we construct finite gauge theory as an extended topological field theory by following two steps: first, from a theory defined depending on choices of principle bundles, construct a theory valued in “spans” or “correspondences,” and then compose with a variant of a finite path integral summing over the choices. Claudia Scheimbauer will explain how to construct the second part in a higher categorical setting using the crucial property “m-semiadditivity” and a universal property of the higher category of spans. This generalizes Harpaz’s result and is joint work in progress with Tashi Walde.
 

Nathan Seiberg
Institute for Advanced Study

Emanant Symmetries

Based on joint work with Meng Cheng (arXiv:2211.12543), with Shu-Heng Shao (arXiv: 2307.02534) and with Shu-Heng Shao and Sahand Seifnashri (to appear), Nathan Seiberg will discuss some aspects of global symmetries and their ‘t Hooft anomalies.

Seiberg will define a notion of an emanant global symmetry. It is not a symmetry of the UV theory, but unlike emergent (accidental) symmetries, it is not violated by any relevant or irrelevant operators in the IR theory. It is an exact symmetry of the low-energy theory.

Seiberg will demonstrate this notion in several well-known examples and will discuss in detail the Majorana chain, the transverse field Ising model, a continuum system with a chemical potential, and the Heisenberg chain. In all these models emanant symmetries exist, and, in one case, it is a non-invertible emanant symmetry.
 

Ashvin Vishwanath
Harvard University

Superconductors as Dual Topological Insulators and Higher-Form Symmetry

In recent years, significant progress has been made in understanding the intricate relationship between symmetry and topology, bringing within reach a complete classification of gapped quantum phases. However, it remains unclear how to incorporate superconductivity and more generally condensates of bosons coupled to the electromagnetic field, within this framework. In this talk, Ashvin Vishwanath will describe an approach that captures the long distance properties of superconductors and connects them to topological phases enabled by symmetry.

Central to this theoretical framework is the utilization of symmetry to encode an implicit yet vital assumption — the absence of magnetic monopoles. This approach not only connects seemingly distinct phenomena, including other dissipationless mechanisms of conductivity such as the Thouless pump, but it also offers a promising avenue to going beyond the mean-field Landau-Ginzburg approach, particularly in the regime of strong fluctuations.

Participation in the meeting falls into the following four categories. An individual’s participation category is communicated via their letter of invitation.

Group A – PIs and Speakers
The foundation will arrange and pay for all air and train travel to the conference as well as hotel accommodations and reimbursement of local expenses.

Group B – Out-of-town Participants
The foundation will arrange and pay for all air and train travel to the conference as well as hotel accommodations and reimbursement of local expenses.

Group C – Local Participants
Individuals in Group C will not receive financial support, but are encouraged to enjoy all conference-hosted meals.

Group D – Remote Participants
Individuals in Group D will participate in the meeting remotely. Please register at the link above and a remote participation link will be sent to you approximately two weeks prior to the meeting.

Air and Train
For individuals in Groups A and B the foundation will arrange and pay for round-trip travel from their home city to the conference.

All travel and hotel arrangements must be booked through the Simons Foundation’s preferred travel agency. Travel arrangements not booked through the preferred agency must be pre-approved by the Simons Foundation and a reimbursement quote must be obtained through the foundation’s travel agency. Travel specifications can be provided by clicking the registration link above.

Personal Car
Personal car trips over 250 miles each way require prior approval from the Simons Foundation via email.

The James NoMad Hotel offers valet parking. Please note there are no in-and-out privileges when using the hotel’s garage, therefore it is encouraged that participants walk or take public transportation to the Simons Foundation.

Hotel
Participants in Groups A & B who require accommodations are hosted by the foundation for a maximum of three nights at The James NoMad Hotel. Any additional nights are at the attendee’s own expense. To arrange accommodations, please register at the link above.

The James NoMad Hotel
22 E 29th St
New York, NY 10016
(between 28th and 29th Streets)
https://www.jameshotels.com/new-york-nomad/

For driving directions to The James NoMad, please click here.

Attendance
In-person participants and speakers are expected to attend all meeting days. Partial participation is permitted so long as the individual fully attends the first day, which is typically Thursday for two-day meetings. Participants receiving hotel and travel support wishing to arrive on meeting days which conclude at 2:00 PM will be asked to attend remotely.

COVID-19 Vaccination
Individuals accessing Simons Foundation and Flatiron Institute buildings must be fully vaccinated against COVID-19.

Entry & Building Access
Upon arrival, guests will be required to show their photo ID to enter the Simons Foundation and Flatiron Institute buildings. After checking-in at the meeting reception desk, guests will be able to show their meeting name badge to re-enter the building. If you forget your name badge, you will need to provide your photo ID.

The Simons Foundation and Flatiron Institute buildings are not considered “open campuses” and meeting participants will only have access to the spaces in which the meeting will take place. All other areas are off limits without prior approval.

If you require a private space to conduct a phone call or remote meeting, please contact your meeting manager at least 48-hours ahead of time so that they may book a space for you within the foundation’s room reservation system.

Guests
Meeting participants are required to give 24 hour advance notice of any guests meeting them at the Simons Foundation either before or after the meeting. Outside guests are discouraged from joining meeting activities, including meals.

Ad hoc meeting participants who did not receive a meeting invitation directly from the Simons Foundation are discouraged.

Children under the age of 18 are not permitted to attend meetings at the Simons Foundation. Furthermore, the Simons Foundation does not provide childcare facilities or support of any kind. Special accommodations will be made for nursing parents.

Reimbursement
Individuals in Groups A & B will be reimbursed for meals and local expenses including ground transportation. Expenses should be submitted through the foundation’s online expense reimbursement platform after the meeting’s conclusion.

Expenses accrued as a result of meetings not directly related to the Simons Foundation-hosted meeting (a satellite collaboration meeting held at another institution, for example) will not be reimbursed by the Simons Foundation and should be paid by other sources.

Below are key reimbursement takeaways; a full policy will be provided with the final logistics email circulated approximately 2 weeks prior to the meeting’s start.

Meals
The daily meal limit is $125 and itemized receipts are required for expenses over $24 USD. The foundation DOES NOT provide a meal per diem and only reimburses actual meal expenses.

• Meals taken on travel days are reimbursable.
• Meals taken outside those provided by the foundation (breakfast, lunch, breaks and/or dinner) are not reimbursable.
• If a meal was not provided on a meeting day, dinner for example, that expense is reimbursable.
• Meals taken on days not associated with Simons Foundation-coordinated events are not reimbursable.
• Minibar expenses are not reimbursable
• Meal expenses for a non-foundation guest are not reimbursable.
• Group meals consisting of fellow meeting participants paid by a single person will be reimbursed up to $65 per person per meal and the amount will count towards each individual’s $125 daily meal limit.

Ground Transportation
Expenses for ground transportation will be reimbursed for travel days (i.e. traveling to/from the airport) as well as local transportation. While in NYC, individuals are encouraged to use public transportation and not use taxi, Uber or Lyft services.

Registration and Travel Assistance
Ovation Travel Group
sfnevents@ovationtravel.com
(917) 408-8384 (24-Hours)
www.ovationtravel.com

Meeting Questions and Assistance
Meghan Fazzi
Manager, Events and Administration, MPS, Simons Foundation
mfazzi@simonsfoundation.org
(212) 524-6080