Geometry and Symmetries of SCFTs

17 Jun 2024, 01:15 → 21 Jun 2024, 16:00 Europe/Berlin

2413/2-430 - MITP Seminar Room (MITP - Mainz Institute for Theoretical Physics, Johannes Gutenberg University Mainz)

Quantum field theory (QFT) is the framework which best describes our world, yet our understanding of it is incomplete and remains one of the most important mathematical challenges. Aided by supersymmetry and string theory important progress has been made in computing exact quantities in QFT, uncovering some of its underlying mathematical structure. One particular area which has seen rapid progress over the last few years are strongly coupled superconformal QFTs (SCFTs). Many tools have been developed to compute their (generalized) global symmetries, their moduli space geometries, how they are connected through RG flows, etc.
The workshop will bring together experts in the field of SCFTs to report on most cutting edge progress and identify new directions and possibilities, addressing some of the deepest questions in QFT.

Monday, 17 June

09:00 Check-In and Coffee

1 Welcome

2 Ilka Brunner

3 Matteo Sacchi : Kutasov–Schwimmer-like dualities from deconfinement

Infrared (IR) dualities are an interesting phenomenon that can characterize the low energy dynamics of a quantum field theory. A key question is whether an organizing principle exists for known IR dualities. One approach is identifying a fundamental set of dualities from which others can be derived, often through a process called "deconfinement" when tensor matter fields are involved. In this talk, I will review the idea of the deconfinement and present recent results on how to use it to derive some Kutasov–Schwimmer-like dualities in 3d and 4d. These are dualities for theories involving a U(N) adjoint field in 3d or a USp(2N) antisymmetric field in 4d with superpotential W=A^{p+1}, for which a derivation was previously unknown and many of the standard tests present complications.

14:45 Coffe Break

Tuesday, 18 June

09:15 Coffee Break

4 Pieter Bomans : An Ode to the Spindle: From N=1 Punctures to AD Theories and Codimension 2 Defects

Over the past few years so-called spindle solutions have received a lot of attention in the liturature. However, in most cases a clear holographic interpretation of these supergravity solutions remains absent. In this talk I will clarify various aspects of the landscape of spindle solutions. In particular, I will clarify a puzzle regarding the global symmetry of the disc solution dual to a class of Argyres-Douglas theories. In addition, when breaking supersymmetry I will show that spindle solutions in seven-dimensional gauged supergravity correspond to class S theories on the sphere with two locally $\mathcal{N}=1$ preserving punctures. Finally, I will show how a different global completion of the (local) spindle solution can describe holographic co-dimension two defects and explain what class of defect observables can be accessed using holography.

11:30 Group Photo

5 Ron Donagi : On the geometry of meromorphic Higgs bundles

We explore both local and global aspects of the geometry of meromorphic Higgs moduli space and its Hitchin map. (Work with Balasubramanian, Distler, Herrero and Perez.)

14:45 Coffee Break

Wednesday, 19 June

09:15 Coffee Break

6 Max Hübner : Symmetries of SCFTs from Geometry

Many geometrically engineered field theories exhibit symmetries. These symmetries are realized via topological operators and organized by higher-dimensional symmetry theories. String theory realizes a mapping of geometry onto these structures. We review aspects of this mapping and comment on applications.

7 Eric Sharpe : An introduction to decomposition in quantum field theories

In this talk, I will give an introduction to `decomposition,' a property of d-dimensional QFTs with global (d-1)-form symmetries.
Decomposition is the observation that such quantum field theories are equivalent to disjoint unions of other quantum field theories, first observed in 2006 and studied in numerous examples and applications since.
I will outline some basic examples in two and four dimensions, and as time
permits, discuss various applications.

14:45 Coffee Break

18:00 Dinner at Ristorante alCortile, Kartäuserstraße 14, 55116 Mainz

Thursday, 20 June

09:15 Coffee Break

8 Sara Pasquetti

9 Philip Argyres : Extending the VOA of 4d N=2 SCFTs in minkowski space-time

In euclidean space, operators in the cohomology of the twisted Schur supercharge for a vertex operator algebra (VOA). In Minkowski space-time the set of such operators is greatly extended, and form a vertex algebra which admits a secondary product, giving it the structure of a quantum Poisson vertex algebra. We take some first steps in describing the properties of this extended vertex algebra.

14:45 Coffee Break

Friday, 21 June

09:15 Coffee Break

10 Shlomo Razamat

11 Michele del Zotto : Recent progress on 5d conformal matter

There are various approaches to classify higher dimensional SCFTs. In this talk we will review recent progress in the classification of 5d SCFTs from a conformal matter perspective. Results involve both the Higgs branches of generalized bifundamentals (in progress with De Marco, Grimminger and Sangiovanni), as well as results about generalized trifundamentals (in progress with De Marco, Graffeo, and Sangiovanni).

14:45 Coffee Break