To mark the end of the first year of QFT and Geometry seminars, this 2 day workshop will provide an overview of recent advances in QFT and Geometry. No registration required -- details of zoom link will be circulated through the QFT and Geometry seminar list.

• Pietro Benetti Genolini (Cambridge)
  Instantons, symmetries and anomalies in five dimensions
  Five-dimensional non-abelian gauge theories have a U(1) global symmetry associated with instantonic particles. I will describe a mixed ’t Hooft anomaly between this and other global symmetries of the theory, namely the one-form center symmetry or ordinary flavor symmetry for theories with fundamental matter. I will explore some general dynamical properties of the candidate phases implied by the anomaly, and apply our results to supersymmetric gauge theories in five dimensions, analysing the symmetry enhancement patterns occurring at their conjectured RG fixed points.

• Antoine Bourget (Imperial College)
  Moduli space of 5d SCFTs, a walk in the tropical rainforest
  We characterize the full moduli space of large classes of 5d SCFTs using generalized toric polygons, magnetic quivers and Hasse diagrams. This allows us to understand how the Higgs branch gets modified as one moves along the extended Coulomb branch, giving a global picture of the phases of the theory, including trees generated by successive decoupling of hypermultiplet matter and RG-flow.

• Ioana-Alexandra Coman (Amsterdam)
  A geometric description of topological string partition functions from quantum curves and integrability
  I will give a progress update on work relating topological string partition functions Z top for Class S theories to quantum Seiberg-Witten curves and integrability. In particular, I will discuss a geometric characterisation of the Z top functions in terms of a line bundle over the moduli space of quantum curves, building up this picture through examples. Part of this discussion will review earlier results, showing how the Z top functions enter particular types of series expansions of isomonodromic tau functions associated to quantised SW curves. The new insight then concerns the existence of certain preferred coordinates on the moduli space of quantum curves, which are defined from the curves and which enter theta-series expansions of normalised tau functions in a way that generates the functions Z top. Understanding these coordinates and how they are related leads to the proposed geometric characterisation of the tau functions and Z top.

• Christopher Couzens (Utrecht)
  Rotating Black hole near-horizons in M-theory
  In this talk we will discuss work classifying supersymmetric fibered AdS_2 solutions in M-theory. These geometries arise as the near-horizon of a rotating black hole and can be seen as the generalization of GK geometries away from the static black hole case. We show that the 9d internal manifold is a U(1) bundle over a balanced manifold base which must solve a master equation constraining the curvature. We construct an action for the theory and show that upon imposing supersymmetry it reduces to a simple form which gives the entropy of the black hole. We conclude with some comments about the geometric extremization problem dual to I-extremization for rotating AdS_4 black holes.

• Simone Giacomelli (Oxford)
  Superconformal theories from S-fold geometries
  The term S-folds denotes F-theory compactifications which involve non-trivial S-duality transformations. In this talk I will discuss 4d N=2 preserving S-folds and the worldvolume theories on D3-branes probing them. They consist of two new infinite series of superconformal theories whose distinction lies in the discrete torsion carried by the S-fold and in the difference in the asymptotic holonomy of the gauge bundle on the 7-brane. These models are connected by an interesting web of RG flows and their Higgs branches provide new examples of instanton moduli spaces.

• Seyed Morteza Hosseini (IPMU)
  Anomalies, Black strings and the charged Cardy formula
  I derive the general anomaly polynomial for a class of two-dimensional CFTs arising as twisted compactifications of a higher-dimensional theory on compact manifolds, including the contribution of its isometries. The results are then used to perform a counting of microstates for dyonic rotating supersymmetric black strings in AdS(5) x S^5 and AdS(7) x S^4 via a charged version of the Cardy formula.

• Evyatar Sabag (Technion)
  New 4d Lagrangians from 6d RG-flows
  SCFTs in six dimensions are interrelated by networks of RG flows. Compactifying such models on a Riemann surface with flux for the 6d global symmetry, one can obtain a wide variety of theories in four dimensions. These four dimensional models are also related by a network of RG flows. In this talk I will show how mappings between such 6d and 4d RG flows were established for the 6d (1,0) SCFTs described by a stack of M5-branes probing an A-type singularity. These relations were then used to find new 4d Lagrangians in a similar setup but with a D-type singularity. Finally, I will show how symmetry enhancement allowed finding an even greater variety of 4d Lagrangians for A- and D-type compactifications.

• Matteo Sacchi (Milano Bicocca)
  Swimming against the tide: a bottom-up perspective on 4d and 3d supersymmetric gauge theories
  In the last years, the geometric approach of constructing 4d and 3d supersymmetric gauge theories from compactification of 6d theories have proved to be very successful. In this talk I present an alternative bottom-up route based on a series of limits that relate 4d N=1 theories to 3d N=2 theories and eventually to 2d CFT free field correlators. Knowing these limits one can indeed try to reverse the logic and find dualities and symmetry enhancements in 4d and 3d of a genuinely new type from known results for 2d free field correlators. Among these, I will present a family of 4d theories related by a novel type of infra-red duality that reduces upon circle compactification to the three-dimensional mirror symmetry, for which a higher dimensional origin was not known.

• Orr Sela (Technion)
  A Nilpotency Index of Conformal Manifolds
  We show that exactly marginal operators of supersymmetric conformal field theories with four supercharges cannot obtain a vacuum expectation value at a generic point on the conformal manifold. Exactly marginal operators are therefore nilpotent in the chiral ring. This allows us to associate an integer to the conformal manifold, which we call the nilpotency index of the conformal manifold. We discuss several examples in diverse dimensions where we demonstrate these facts and compute the nilpotency index.

• Luigi Tizzano (SCGP)
  Delayed Deconfinement and the Hawking-Page Transition
  We revisit the confinement/deconfinement transition in N=4 super Yang-Mills (SYM) theory and its relation to the Hawking-Page transition in gravity. Recently there has been substantial progress on counting the microstates of 1/16-BPS extremal black holes. In this context, we discuss a phenomenon in complex matrix models which we call "delayed deconfinement". It turns out that when the action is complex, due to destructive interference, tachyonic modes do not necessarily condense. We demonstrate this phenomenon in a simple unitary matrix model and finally in the context of N=4 SYM. Delayed deconfinement implies a first-order transition, in contrast to the more familiar cases of higher-order transitions in unitary matrix models. We determine the deconfinement line and find remarkable agreement with the prediction of gravity.

• Jingxiang Wu (Perimeter)
  Integrable Kondo line defect, 4D Chern Simons, and ODE/IM correspondence
  In two dimensional conformal field theory, Kondo line defect arises when a local impurity is chirally coupled to the bulk CFT. In general, it encodes the integrability structure of the bulk CFT and provides a large class of interesting defect RG flow starting from topological lines. I will discuss the integrability and wall-crossing properties of Kondo line defects using ODE/IM correspondence and four dimensional Chern Simons theory. Along the way, I will explain how 4d Chern Simons provides a new perspective in understanding the ODE/IM correspondence. This work is part of a multi-pronged exploration of studying 4D Chern-Simons theory as an overarching structure for integrable systems. The talk is based on [2003.06694] and [2010.07325] in collaboration with D. Gaiotto, J Lee, B. Vicedo.

• Gianluca Zoccarato (UPenn)
  S-folds, String Junctions, and 4D N=2 SCFTs
  In this talk I will discuss N=2 SCFTs realised on the worldvolume of D3-branes probing an S-fold plane with 7-branes. I will show how to formulate a projection on string junctions ending on 7-branes that generalises the usual orientifold projection of perturbative string theory to the case of S-fold planes. Using this technique it is possible to read off the flavour symmetry of the SCFT for all possible S-fold planes including the cases with discrete torsion. As a byproduct of this analysis it is possible to understand which representations of the flavour symmetry group are allowed. Finally, I will discuss the computation of central charges of these theories and discuss how to define F-theory in the presence of S-folds with discrete torsion.