Quivers, Symmetries and SCFTs

1 Sept 2025, 10:00 → 5 Sept 2025, 16:00 Europe/Rome

Giambiagi (Adriatico, ICTP)

Amihay Hanany (Imperial College, London), Julius Grimminger (Oxford University), Sara Pasquetti (Milano Bicocca), Sergio Benvenuti (Istituto Nazionale di Fisica Nucleare)

Strongly coupled quantum field theories (QFTs) are key to understanding physics across many scales. Conformal field theories (CFTs), the fixed points of renormalization group flow, are crucial for this understanding, yet analyzing them in d>2 is tough. Supersymmetry offers powerful tools; in d>4, superconformal field theories (SCFTs) are our only known interacting CFTs. Lacking standard Lagrangian descriptions, SCFTs provide unique insights into strong coupling. Recent progress using string theory and geometric methods, especially quivers, has proven very effective in tackling these challenges.

Speakers:

Alessandro Tomasiello
Antoine Bourget
Chiung Hwang
Futoshi Yagi
Gabi Zafrir
Hee-Cheol Kim 
Kimyeong Lee
Marcus Sperling
Michele Del Zotto
Saghar Hosseini
Shlomo Razamat
Simone Rota

 

 

Monday 1 September

11:00 → 12:00 Registration

12:00 → 13:00 Generalized Schur partition functions and RG flows

We revisit a double-scaled limit of the superconformal index of ${\cal N}=2$ superconformal field theories (SCFTs) which generalizes the Schur index. The resulting partition function, $\hat {\cal Z}(q,\alpha)$, has a standard $q$-expansion with coefficients depending on a continuous parameter $\alpha$. The Schur index is a special case with $\alpha=1$. Through explicit computations we argue that this partition function is an invariant of certain mass deformations and vacuum expectation value (vev) deformations of the SCFT. In particular, two SCFTs residing in different corners of the same Coulomb branch, satisfying certain restrictive conditions, have the same partition function with a non-trivial map of the parameters, $\hat {\cal Z}_1(q,\alpha_1)=\hat {\cal Z}_2(q,\alpha_2(\alpha_1))$. For example, we show that the Schur index of all the SCFTs in the Deligne-Cvitanovi\'c series is given by special values of $\alpha$ of the partition function of the $SU(2)$ $N_f=4$ ${\cal N}=2$ SQCD.

Speaker: Shlomo Razamat

16:00 → 17:00 New punctures for six-dimensional CFT compactifications

Compactifying 6D SCFTs with N=(1,0) supersymmetry on Riemann surfaces is expected to produce N=1 analogues of the famous Class S models. I will study holographic defects in massive IIA string theory AdS7 solutions, and use the results to obtain information about the punctures of these N=1 models, and their contribution to central charges.

Speaker: Alessandro Tomasiello

17:30 → 19:30 Reception

Tuesday 2 September

10:15 → 11:15 S-duality for N=4 SYM in the IR

It is well known that N=4 SYM has modular invariance, which includes S-duality. In this talk, I will review subtle incarnations of this fact in the infrared. First, I describe the interplay between modular invariances and global forms of the theory as seen from the moduli space of vacua, through the lens of the special Kahler structure on the Coulomb branch. Then, I show how these effects can be seen from a classical integrable system (the elliptic Calogero-Moser system) upon mass deformation. I will also touch on some conundrums. This is based on [2504.01502] and future work with P. Argyres, J. Grimminger, M. Lotito and M. Weaver.

Speaker: Antoine Bourget

11:15 → 12:00 Coffee break

12:00 → 13:00 Magnetic Quivers, Quantum Branches, and Chern-Simons Matter Theories

Supersymmetric quantum field theories with eight supercharges in dimensions 3–6 feature rich moduli spaces, with Higgs branches- often singular hyper-Kähler spaces- playing a central role. The framework of magnetic quivers provides a combinatorial tool to encode these geometries, while the decay and fission algorithm efficiently determines their phase structure and renormalization group (RG) flows through convex linear algebra techniques.

In this talk, I will present a unified perspective on quantum hyper-Kähler branches and RG flows in SCFTs across dimensions 3-6, focusing in particular on recent advances for three-dimensional N=3 Chern-Simons matter (CSM) theories. Utilizing Type IIB brane constructions, I will derive magnetic quivers that capture the maximal hyper-Kähler branches of both N=3 and N=4 CSM theories, including cases with non-trivial Chern–Simons levels beyond the reach of standard dualities. This yields a systematic characterization of their moduli spaces and RG flows.

Based on work with F. Marino (arXiv:2503.02744), and work in progress with F. Marino and S. Moura Soysüren.

Speaker: Marcus Sperling

16:00 → 17:00 A 2d/2d unitary/non-unitary correspondence

Dimensional reduction often implies non-trivial connections between field theories in different dimensions. A well-known example is the AGT (Alday-Gaiotto-Tachikawa) type relation that connects partition function of different theories sharing a common higher dimensional ancestor. In this talk we shall exploit this relation to study the compactification of the 4d H0 SCFT on Riemann surfaces to get 2d (2,2) theories. Specifically, we shall argue for a 2d/2d unitary/non-unitary correspondence of AGT type between the resulting 2d theories and the Lee-Yang minimal model. We use this to identify the resulting 2d theories for certain choices of the Riemann surfaces, and test them with a variety of consistency checks.

Speaker: Gabi Zafrir

Wednesday 3 September

10:15 → 11:15 From anomaly cancellation in string theory to symmetry descent in QFT

In Type I string theory and related models, perturbative anomalies are cancelled by the Green–Schwarz mechanism. I will show how, more generally, both perturbative and global anomalies cancellations can be explained using Ramond–Ramond fields understood as boundary modes of an 11-dimensional bulk theory in differential KO-theory. Dimensional reduction of this bulk leads to a symmetry descent procedure for lower-dimensional QFTs, providing a systematic framework to analyse their anomalies and categorical symmetry structures. Examples include higher-group symmetries in quiver gauge theories, mod-2 Witten anomalies, and mixed anomalies with R-symmetries.

Speaker: Saghar Hosseini

11:15 → 12:00 Coffee break

12:00 → 13:00 Gapped phases of 4d QFTs with non-invertibile symmetries

Abstract: I will discuss a coarse classification of gapped phases of 4d QFTs with non-invertibile finite symmetries. Applications to spntaneous breaking, anomalies and symmetry protected gaplessness will be discussed along with some examples. Based on joint work with Elias Riedel Gårding and Azeem Hasan.

Speaker: Michele Del Zotto

Thursday 4 September

10:15 → 11:15 3D N=8 Super Yang-Mills theory Revisited

I will present an approach to understanding the low-energy behavior of 3d bad quiver gauge theories through the mirror dualization algorithm. This algorithm provides a systematic method for constructing mirror duals of 3d linear and circular quivers, extending beyond the “good” theories classified by Gaiotto and Witten. As an application, I will discuss N=8 super Yang–Mills theory, which exhibits a novel Higgs mechanism triggered by monopole operators carrying non-unit magnetic flux. This analysis highlights new structures in the dynamics of 3d gauge theories and broadens the scope of known mirror dualities.

Speaker: Chiung Hwang

11:15 → 12:00 Coffee break

12:00 → 13:00 Planar Abelian duals of 3d (S)QCD

We propose Abelian mirror duals for 3d Chern-Simons SQCD theories. We test these dualities by analyzing supersymmetric partition functions and their consistency under mass deformations. We discuss the implications of these dualities
and propose analogous dualities for 3d QCD theories in the absence supersymmetry.

Speaker: Simone Rota

16:00 → 17:00 Finite Landscape of 6d (1,0) Supergravity

I will talk about a bottom-up proof of the finiteness of the number of massless fields in any 6d supergravity theories preserving 8 supercharges. From this, sharp bounds on the number of tensor multiplets and the rank of gauge algebras will be derived. I will also show that these bounds are saturated by specific theories realized through F-theory compactifications on elliptic Calabi-Yau threefolds.

Speaker: Hee-Cheol Kim

Friday 5 September

10:15 → 11:15 Topological vertex for 5-brane web with orientifold

Motivated by the equivalence between 5-brane web diagrams and toric Calabi-Yau 3-folds, we propose a generalization for the topological vertex formalism applied to 5-brane web diagrams with orientifold planes. We confirm that the Nekrasov's instanton partition functions for the corresponding 5d N=1 gauge theories are reproduced.

Speaker: Futoshi Yagi

11:15 → 12:00 Coffee break

12:00 → 13:00 2d Conformal Field Theories on Magic Triangle

The magic triangle due to Cvitanovic and Deligne–Gross is an extension of the Freudenthal–Tits magic square of semisimple Lie algebras. In this paper, we identify all 2d rational conformal field theories associated to the magic triangle.
These include various Wess–Zumino–Witten (WZW) models, Virasoro minimal models, compact bosons and their non-diagonal modular invariants. At level one, we find a two-parameter family of modular linear differential equation (MLDE) of fourth order whose solutions produce the affine characters of all elements in the magic triangle. We also find a universal coset relation which generalizes the dual pairs with respect to (E8)1 in the Cvitanovic–Deligne exceptional series. This suggests that five atomic models form the constitutes for all theories in the triangle.

Speaker: Kimyeong Lee