The Memory of Solitons
ERC starting grant #851931
Principal Investigator: Michele Del Zotto
Postdocs: Azeem Hasan, Mario De Marco
PhD students: Elias Riedel-Gårding
Shani Nadir Meynet (Postdoc - Mathematics Department)
Kaiwen Sun (Postdoc - Theoretical physics group)
Daniele Migliorati (PhD student - Mathematics Department)
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 non-perturbative 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 non-perturbative 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.
We will publish below activities related to this project
- Nordita Program: Categorical Aspects of Symmetries (August 14-25, 2023)
- UU Workshop: Engineering in the Landscape: Geometry, Symmetries, and Anomalies (August 24-26, 2022)
- Mittag-Leffler Workshop: Enumerative Invariants, Quantum Fields and String Theory Correspondences (July 25-29, 2022)
Since February 2020, we are co-organizing the joint string-math seminar at Uppsala University.
Publications and Preprints
- The ALE Partition Functions of M-String Orbifolds, MDZ, Guglielmo Lockhart, e-Print: 2311.08462
- 5d Conformal Matter, MDZ, Mario De Marco, Michele Graffeo, Andrea Sangiovanni, e-Print: 2311.04984
- Topological defects, Nils Carqueville, MDZ, Ingo Runkel, e-Print: 2311.02449
- The ALE Partition Functions of M-Strings, MDZ, Guglielmo Lockhart, e-Print: 2309.00607
- The Higgs branch of Heterotic ALE instantons, MDZ, Marco Fazzi, Suvendu Giri, e-Print: 2307.11087
- A new vista on the Heterotic Moduli Space from Six and Three Dimensions, MDZ, Marco Fazzi, Suvendu Giri, e-Print: 2307.10356
- Higher Structure of Chiral Symmetry, Christian Copetti, MDZ, Kantaro Ohmori, Yifan Wang, e-Print: 2305.18282
- Four-manifolds and Symmetry Categories of 2d CFTs, Vladimir Bashmakov, MDZ, Azeem Hasan, e-Print: 2305.10422
- Junctions, Edge Modes, and G2G2-Holonomy Orbifolds, Bobby Acharya, MDZ, Jonathan J. Heckman, Max Hubner, Ethan Torres, e-Print: 2304.03300
- 6D Heterotic Little String Theories and F-theory Geometry: An Introduction, MDZ, Muyang Liu, Paul-Konstantin Oehlmann, e-Print: 2303.13502
- Back to Heterotic Strings on ALE Spaces: Part II -- Geometry of T-dual Little Strings, MDZ, Muyang Liu, Paul-Konstantin Oehlmann, e-Print: 2212.05311
- Non-invertible symmetries of class S theories, Vladimir Bashmakov, MDZ, Azeem Hasan, Justin Kaidi, e-Print: 2211.05138
- Back to heterotic strings on ALE spaces. Part I. Instantons, 2-groups and T-duality, MDZ, Muyang Liu, Paul-Konstantin Oehlmann, e-Print: 2209.10551
On the 6d Origin of Non-invertible Symmetries in 4d, Vladimir Bashmakov, MDZ, Azeem Hasan, e-Print: 2206.07073
The Characteristic Dimension of Four-dimensional N=2 SCFTs, Sergio Cecotti (SISSA), MDZ, Mario Martone (SCGP), Robert Moscrop, e-Print: 2108.10884
Maruyoshi-Song flows and defect groups of Dbp(G) theories, Saghar Hosseini (Durham U), Robert Moscrop, Published in: JHEP 2021 119, e-Print: 2106.03878
2-Group Symmetries of 6d Little String Theories and T-duality, MDZ, and Kantaro Ohmori (IAS and SCGP), Published in: Annales Henri Poincaré (2021), e-Print: 2009.03489
Higher form symmetries of Argyres-Douglas theories, MDZ, Iñaki García Etxebarria (Durham), and Saghar Hosseini (Durham), Published in: JHEP 10 (2020) 056, e-Print: 2007.15603