The Memory of Solitons
ERC starting grant #851931
MEMBERS
Principal Investigator: Michele Del Zotto
Postdocs: Azeem Hasan, Muyang Liu, PaulKonstantin Öhlmann
PhD students: Elias RiedelGårding
Project Affiliates
Vladimir Bashmakov (Postdoc  Theoretical physics group)
Robert Moscrop (PhD student  Mathematics Department)
Description
Quantum field theory (QFT) is undoubtedly one of the most important achievements of modern theoretical physics, with broad applications ranging from condensed matter systems to elementary particle physics. Despite its successes, the current formulation of QFT is incomplete and we lack tools to address from first principles a wide variety of interesting physical systems, including the dynamics of quarks within protons, phase transitions, and high temperature superconductors.
The present project aims at addressing this issue by establishing a novel, powerful and unconventional paradigm for QFT without relying upon the existence of a perturbative expansion.
The cornerstone for such a paradigm is the following remark: in a wide variety of simple examples it is possible to compute exactly the values of several observables relying solely upon the knowledge of the spectrum of solitons of the given QFT: this effect is the memory of solitons. The main purpose of this project is to develop and exploit the memory of solitons to study nonperturbative aspects of QFTs.
Our strategy to approach this problem is twofold. On the one hand we focus on the simplest QFTs to develop intuition on concrete and explicit examples: our theoretical laboratory consists of theories having supersymmetry and/or conformal symmetry where a plethora of exact results are available. On the other, we exploit geometric engineering techniques in string theory, which gives access to the nonperturbative spectrum of QFTs from a completely different angle that allows exact computations to be performed, providing new insights into the mathematical structure of the theories involved.
The geometric engineering techniques we adopt are intertwined with the geometric structures of special holonomy manifolds and their enumerative invariants. These are tools to determine the solitonic spectrum in terms of geometric data for the models in our theoretical laboratory.
Among the first results of the project we have determined the global strucutres and higher form symmetries of a wide variety of SCFTs in 4,5 and 6 dimensions, with and without a conventional Lagrangian formulation.
ACTIVITIES
We will publish below activities related to this project
 UU Workshop: Engineering in the Landscape: Geometry, Symmetries, and Anomalies (August 2426, 2022)
 MittagLeffler Workshop: Enumerative Invariants, Quantum Fields and String Theory Correspondences (July 2529, 2022)
Since February 2020, we are coorganizing the joint stringmath seminar at Uppsala University.
Publications and Preprints

On the 6d Origin of Noninvertible Symmetries in 4d, Vladimir Bashmakov, MDZ, Azeem Hasan, ePrint: 2206.07073

Global Structures from the Infrared, MDZ and Iñaki García Etxebarria (Durham), ePrint: 2204.06495

2Group Symmetries and MTheory, MDZ, Iñaki García Etxebarria (Durham), and Sakura ShäferNameki (Oxford U), ePrint: 2203.10097

Higher Symmetries of 5d Orbifold SCFTs, MDZ, Jonathan J. Heckman (Penn U), Shani Nadir Meynet (Uppsala U and SISSA), Robert Moscrop (Uppsala U), Hao Y. Zhang (Penn U), ePrint: 2201.08372

Ftheory on 6D Symmetric Toroidal Orbifolds, Finn Bjarne Kohl (Munster U), Magdalena Larfors (Uppsala U), PaulKonstantin Öhlmann, ePrint: 2111.07998

Phases of N=1 Quivers in 2+1 Dimensions, Vladimir Bashmakov, Nicola Gorini (Bicocca U), ePrint: 2109.11862

Evidence for an Algebra of G_{2} Instantons, MDZ, Jihwan Oh (Oxford U), Yehao Zhou (PI), ePrint: 2109.01110

The Characteristic Dimension of Fourdimensional N=2 SCFTs, Sergio Cecotti (SISSA), MDZ, Mario Martone (SCGP), Robert Moscrop, ePrint: 2108.10884

MaruyoshiSong flows and defect groups of D^{b}_{p}(G) theories, Saghar Hosseini (Durham U), Robert Moscrop, Published in: JHEP 2021 119, ePrint: 2106.03878

Playing with the index of Mtheory, MDZ, Nikita Nekrasov (SCGP), Nicolò Piazzalunga (Uppsala U), and Maxim Zabzine (Uppsala U), ePrint: 2103.10271

2Group Symmetries of 6d Little String Theories and Tduality, MDZ, and Kantaro Ohmori (IAS and SCGP), Published in: Annales Henri Poincaré (2021), ePrint: 2009.03489

Higher form symmetries of ArgyresDouglas theories, MDZ, Iñaki García Etxebarria (Durham), and Saghar Hosseini (Durham), Published in: JHEP 10 (2020) 056, ePrint: 2007.15603

Higher Form Symmetries and Mtheory, Federica Albertini (Durham), MDZ, Iñaki García Etxebarria (Durham), and Saghar Hosseini (Durham), ePrint: 2005.12831 (accepted  to appear on JHEP)