### Conference

#### Resurgence and Modularity in QFT and String Theory

**May 06, 2024 - May 10, 2024**

**Abstract**

Modularity is a particularly powerful symmetry with many applications in theoretical physics and mathematics, in particular quantum field theory and string theory. Resurgence is a general framework for advanced asymptotics which effectively unifies perturbative and non-perturbative physics via an intricate network of algebraic relations known as Ecalle’s bridge equations. Modularity and resurgence overlap strongly in the goal of exploring non-perturbative completions of perturbative data, leading to profound new insights into the connection between weak coupling and strong coupling, and in the study of dualities, black holes and quantum gravity. The goal of this GGI Workshop is to bring together experts from these two frontier areas in theoretical and mathematical physics to foster further interaction between different scientific communities and to develop novel strategies to address truly significant problems.

**Organizers**

Daniele Dorigoni (Durham University) daniele.dorigoni@durham.ac.uk

Gerald Dunne (University of Connecticut) gerald.dunne@uconn.edu

Michael Green (DAMTP, Cambridge) mbg15@cam.ac.uk

Luca Griguolo (University of Parma) luca.griguolo@unipr.it

Sarah Harrison (Northeastern University) s.harrison@northeastern.edu

Yasuyuki Hatsuda (Rikkyo University, Japan) yhatsuda@rikkyo.ac.jp

Axel Kleinschmidt (Albert Einstein Institute, Potsdam) axel.kleinschmidt@aei.mpg.de

Sameer Murthy (King’s College London) sameer.murthy@kcl.ac.uk

Anne Taormina (Durham University) anne.taormina@durham.ac.uk

**Local organizer**

Li Gan (GGI)

**Contact**

daniele.dorigoni@durham.ac.uk

**Main event**

Resurgence and Modularity in QFT and String Theory (Workshop) - Apr 08, 2024

**Confirmed Speakers:**

- Abhiram Kidambi (Leipzig & Vienna)

- Campbell Wheeler (Bonn)

- Congkao Wen (QMUL)

- Elba Garcia-Falide (Jussieu)

- Gregory Korchemsky (IPhT Saclay)

- Ioana Coman (IPMU)

- Kim Klinger-Logan (Kansas State)

- Marialuisa Frau (Torino University)

- Nathan Benjamin (Caltech)

- Ovidiu Costin (Ohio State)

- Sergei Gukov (Caltech & DIAS Dublin)

- Shai Chester (Imperial College)

- Sungjay Lee (KIAS)

- Veronica Fantini (IHES)

**Talks**

Date | Speaker | Title | Type | Useful Links | ||||
---|---|---|---|---|---|---|---|---|

May 06, 2024 - 11:00-12:00 | Ovidiu Costin |
Unique continuation through natural boundaries using resurgence | Seminar |
Abstract
Resurgence theory is a wide-ranging extension of analyticity and of Borel summability, known to apply in many problems of natural origin. I will give an overview of some elements of this theory and discuss new results on unique continuation through natural boundaries, such as the unit circle for q-series, from a theoretical as well as numerical perspective. Work in collaboration with G. Dunne, A. Gruen and S. Gukov |
Video | |||

May 06, 2024 - 14:30-15:30 | Shai Chester |
Bootstrapping F-theory | Seminar | Video | ||||

May 06, 2024 - 16:30-17:30 | Marialuisa Frau |
Strong coupling results in N=2 gauge theories | Seminar |
Abstract
We will discuss recent developments in the study of correlation functions of chiral scalar operators and integrated correlators in four-dimensional N=2 quiver gauge theories. Using supersymmetric localization, it is possible to map the computation of these observables to an interacting matrix model and obtain expressions that are valid for any value of the ’t Hooft coupling in the planar limit of the theory. In particular, we will focus on the strong-coupling regime, where these expressions allow us to compute the leading and subleading orders behavior of the observables in an analytic way |
Video | |||

May 07, 2024 - 11:00-12:00 | Veronica Fantini |
Modular resurgent structures of fermionic spectral traces on local P^2 | Seminar |
Abstract
In a joint project with C. Rella, we propose a new paradigm of modular resurgence that focuses on the role of the Stokes constants and the interplay of the their generating functions in form of q-series with the corresponding L-functions. Resurgent series with a modular resurgent structure are conjectured to have specific summability properties as well as to be closely related to quantum modular forms. Remarkably, a pivotal example arises from topological string theory, in the study of the resurgence structure of the first fermionic spectral traces of local P^2. In this talk, after discussing the general paradigm of modular resurgent series, I will focus on the example of local P^2. In particular, I will show that the generating functions of the Stokes constants (both in the weak and strong coupling regimes) are quantum modular forms. This talk is based on arxiv:2404.11550 and arxiv:2404.10695. |
Video | |||

May 07, 2024 - 14:30-15:30 | Nathan Benjamin |
Scalar modular bootstrap and zeros of the zeta function | Seminar | Video | ||||

May 07, 2024 - 16:30-17:30 | Abhiram Kidambi |
Generalized Narain VOAs, and Ensemble Averages from real analytic Eisenstein series associated to indefinite lattices | Seminar | Video | ||||

May 08, 2024 - 11:00-12:00 | Congkao Wen |
Exact results and modularity of correlators in N=4 super Yang-Mills theory | Seminar | Video | ||||

May 08, 2024 - 14:30-15:30 | Sungjay Lee |
Classification of Fermionic RCFTs and Topological Phases Revisited | Seminar | |||||

May 08, 2024 - 16:30-17:30 | Kim Klinger-Logan |
A summary of methods for solving differential equations involving automorphic forms | Seminar | Video | ||||

May 09, 2024 - 11:00-12:00 | Ioana Coman |
3d modularity revisited - defect 3-manifold invariants and VOAs | Seminar |
Abstract
In this talk I will revisit some results regarding the modularity of a particular type of topological 3-manifold invariants, which were originally defined as q-series to categorify WRT invariants. These invariants are related to characters of logarithmic vertex operator algebras, and give examples of quantum modular forms. I will explain how, by introducing defects, a structure of vector-valued quantum modular forms emerges for families of defect invariants. These furthermore form false-mock pairs, where the proposed mock invariants are regularised indefinite theta-functions. In this form, similarly to the false invariants, the mock counterparts can also be related to corresponding vertex operator algebras. |
Video | |||

May 09, 2024 - 14:30-15:30 | Campbell Wheeler |
Computing Stokes constants with quantum modularity | Seminar | Video | ||||

May 09, 2024 - 16:30-17:30 | Sergei Gukov |
Resurgence and Quantum: Topology, Algebra, and Physics |
Seminar | Video | ||||

May 10, 2024 - 11:00-12:00 | Elba Garcia-Falide |
Resurgent large genus asymptotics of intersection numbers | Seminar | Video | ||||

May 10, 2024 - 14:30-15:30 | Gregory Korchemsky |
Tracy-Widom distribution in four-dimensional super-Yang-Mills theories | Seminar | Video |