### Workshop

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

**Apr 08, 2024 - May 17, 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.

**Topics**

Focus topics include:

- Modular graph forms and the low-energy expansion of string theory.

- Resurgence, duality and modularity in AdS/CFT.

- Automorphic forms and non-perturbative scattering amplitudes.

- Resurgence and (Mock)-modularity in 3d Chern-Simons theories.

- Exact results in localizable superconformal quantum field theories.

- Resurgence and modularity in black holes and quantum information.

The GGI environment is ideal for starting new collaborations, and learning new methods. A particular goal of the workshop is to attract outstanding junior scientists to this field. We plan a week-long introductory school at the beginning of the workshop, and a one-week conference later in the workshop. Junior scientists will be given priority in presenting their current work in informal “chalk talks” throughout the workshop.

**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

**Related events**

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

Resurgence and Modularity in QFT and String Theory (Conference) - May 06, 2024

**Talks**

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

Apr 15, 2024 - 14:30-15:30 | Luigi Guerrini |
BPS Wilson loops and mass deformations in ABJM | Seminar | Video | ||||

Apr 16, 2024 - 14:30-15:30 | Kimyeong Lee |
Strings in 6d SCFTs and Little String Theories | Seminar | Video | ||||

Apr 17, 2024 - 14:30-15:30 | Arkady Tseytlin |
Semiclassical supermembranes and AdS/CFT | Seminar | Video | ||||

Apr 18, 2024 - 14:30-15:30 | Alberto Lerda |
Exact Results in N=2 Conformal Theories | Seminar | Video | ||||

Apr 19, 2024 - 14:30-15:30 | Jacopo Papalini |
SEMINAR CANCELLED -- Towards the bulk dual of double-scaled SYK | Seminar | |||||

Apr 22, 2024 - 14:30-15:30 | Lorenzo Russo |
Examples of resurgence effects in JT gravity: Spectral Form Factor and Weyl-Petersson Volumes | Seminar | Video | ||||

Apr 23, 2024 - 14:30-15:30 | Rudolfs Treilis |
Modular resurgence for integrated correlators at large N | Seminar | Video | ||||

Apr 24, 2024 - 11:00-12:00 | Zoltan Bajnok |
The complete trans-series for energy densities in integrable models | Seminar | Video | ||||

Apr 24, 2024 - 15:00-16:00 | Alejandro Cabo-Bizet |
The Schwarzian from gauge theories (NOTE DIFFERENT STARTING TIME!) | Seminar | Video | ||||

Apr 26, 2024 - 14:30-15:30 | Marco Billò |
Localization for BPS Wilson loops in N=2, d=4 theories | Seminar | Video | ||||

Apr 29, 2024 - 14:30-15:30 | Masazumi Honda |
Resurgence in Lorentzian quantum cosmology: no-boundary saddles and resummation of quantum gravity corrections around tunneling saddles | Seminar | Video | ||||

Apr 30, 2024 - 11:00-12:00 | Martí Rosselló |
The Giant Graviton Expansion in AdS5xS5 | Seminar | Video | ||||

Apr 30, 2024 - 14:30-15:30 | David Broadhurst |
Resonant resurgence and quasi-modularity from QFT | Seminar |
Abstract
This talk concerns two studies of Feynman integrals in QFT. In a massless case, resurgence in a Dyson-Schwinger equation leads to a trans-series with resonances between instantons producing 6 Stokes constants. In a massive case, periods of modular forms result from quasi-modularity of Lambert series. This led to 20 ways of using complex multiplication to improve Ramanujan's evaluations of zeta values. |
Video | |||

May 02, 2024 - 11:00-12:00 | Guglielmo Lockhart |
The ALE partition functions of 6d SCFTs | Seminar | Video | ||||

May 02, 2024 - 14:30-15:30 | Jens Funke |
Indefinite Theta Series | Seminar | Video | ||||

May 03, 2024 - 14:30-15:30 | Alexander van Spaendonck |
Exact instanton transseries for quantum mechanics | Seminar | Video | ||||

May 13, 2024 - 14:30-15:30 | Mehregan Doroudiani |
Modular graph forms and their integrals | Seminar | Video | ||||

May 14, 2024 - 11:00-12:00 | Guillaume Bossard |
String theory at U-duality corners | Seminar | Video | ||||

May 14, 2024 - 14:30-15:30 | Federico Zerbini |
Modularity and monodromy | Seminar | Video | ||||

May 15, 2024 - 14:30-15:30 | Francesco Galvagno |
Modular properties of brane scattering from integrated correlators | Seminar |
Abstract
Integrated correlators in N=4 SYM represent a powerful tool to obtain exact results in the coupling constant, and can be used as constraints for dual scattering amplitudes in AdS. In this talk we consider a correlation function in presence of determinant operators, which in the planar limit are heavy operators realizing a giant graviton D3-brane in the dual space. We compute their integrated correlator via supersymmetric localization exactly in the 't Hooft coupling, interpreting such results as the integrated disc and annulus amplitudes from the worldsheet perspective. Next, we derive the SL(2,Z) completion of the result, that nicely matches the holographic expectations for string/brane scattering amplitude. In the end, we discuss the differences with respect to integrated correlators in presence of line defects, which are dual to extended (p,q)-string scattering and transform non-trivially under SL(2,Z). Based on arxiv:2403.17263 and arxiv:2308.16575 |
Video | |||

May 16, 2024 - 11:00-12:00 | Sergey Alexandrov |
Modularity and resurgence in Calabi-Yau compactifications | Seminar |
Abstract
I'll review some open open problems in determination of the effective action for Calabi-Yau compactifications of type II string theory, and argue that their solution requires a combination of modularity and resurgence. |
Video | |||

May 16, 2024 - 14:30-15:40 | Claudia Rella |
Strong-weak symmetry and quantum modularity of resurgent topological strings | Seminar |
Abstract
Quantizing the mirror curve to a toric Calabi-Yau threefold gives rise to quantum operators whose fermionic spectral traces produce factorially divergent series in the Planck constant and its inverse. These are captured by the Nekrasov-Shatashvili and standard topological strings via the TS/ST correspondence. In this talk, I will discuss the resurgence of these dual asymptotic series and present an exact solution for the spectral trace of local P^2. A full-fledged strong-weak symmetry is at play, exchanging the perturbative/nonperturbative contributions to the holomorphic and anti-holomorphic blocks in the factorization of the spectral trace. This relies on a network of relations connecting the dual regimes and building upon the analytic properties of the L-functions with coefficients given by the Stokes constants and the q-series acting as their generating functions. Finally, I will mention how these results fit into a broader paradigm linking resurgence and quantum modularity. This talk is based on arXiv:2212.10606, 2404.10695, and 2404.11550. |
||||

May 17, 2024 - 11:00-12:00 | Paolo Gregori |
Non-perturbative Topological Recursion in Jackiw-Teitelboim Gravity | Seminar |
Abstract
The connection between matrix models and two-dimensional gravitational theories (including JT gravity) is a very well-established one. For this reason, Topological Recursion has proved to be an invaluable tool for computing observables perturbatively in such theories. In this talk, I will introduce a non-perturbative generalization of Topological Recursion which is particularly well-suited for the study of instanton effects (more specifically, of the ZZ brane type), and apply it to the case of JT gravity. Moreover, by making use of resurgent large order relations, I will show how our results lead to large genus asymptotics of Weil-Petersson volumes. |