### The large charge expansion

The large-charge approach consists in studying conformal field theories in sectors of fixed and large global charge. This allows performing a perturbative expansion of a generically strongly-coupled theory with the inverse charge acting as a controlling parameter. In this talk, I will present the basic idea of the large quantum number expansion using the simplest example of the 3D O(2) model at the Wilson-Fisher fixed point at large global charge and then extend its treatment to the O(2N) vector model. New lattice results confirm our predictions to high accuracy.
I will further show that the large-charge expansion can also be successfully applied to non-relativistic CFTs.

**Tuesday, 7th of May 2019, 14:30, sala Wataghin**

In a remarkable recent work by Arkani-Hamed et al, the amplituhedron program was extended to the realm of non-supersymmetric scattering amplitudes. In particular it was shown that for tree-level planar diagrams in massless $\phi^3$ theory (and its close cousin, bi-adjoint $\phi^3$ theory) a polytope known as the associahedron sits inside the kinematic space and is the amplituhedron for the theory. Precisely as in the case of amplituhedron, it was shown that scattering amplitude is nothing but residue of the canonical form associated to the associahedron. Combinatorial and geometric properties of associahedron naturally encode properties like locality and unitarity of (tree level) scattering amplitudes.

In this talk after briefly reviewing their work we attempt to extend this program to planar amplitudes in massless $\phi^4$ theory. We show that tree-level planar amplitudes in this theory can be obtained from geometry of objects known as the Stokes polytope which sits naturally inside the kinematic space. As in the case of associahedron we show that residues of the canonical form on these Stokes polytopes can be used to compute scattering amplitudes for quartic interactions. However unlike associahedron, Stokes polytope of a given dimension is not unique and as we show, one must sum over all of them to obtain the complete scattering amplitude. We shall finally discuss some ongoing work about generalisation of the program to all $\phi^p$ ($p>4$) theories.

**Wednesday, 10th of April 2019, 14:30, sala Wataghin**

### Noncommutative gauge theories on D-branes in non-geometric backgrounds

I will describe some new perspectives on non-geometric backgrounds of string theory from the open string perspective, by a detailed analysis of the low-energy effective gauge theory on D-branes in these backgrounds. This theory is a noncommutative Yang-Mills theory wherein the T-duality monodromies of the non-geometric background become Morita duality monodromies of the noncommutative gauge theory. We elaborate on this perspective in detail for T-folds arising via T-duality from twisted tori, and extend the considerations to backgrounds with R-flux where the noncommutative Yang-Mills theories have a dependence on the dual coordinates, and so have no formulation in a conventional spacetime.

**Tuesday, 9th of April 2019, 14:30, sala Wataghin**

We start by a review of numerical and analytical conformal bootstrap techniques at our disposal.
We then use these tool to approach the "simplest" Argyres-Douglas theory, a four-dimensional N=2 strongly coupled superconformal field theory. We "zoom in" to the theory by specifying Coulomb branch data, and obtain strong constraints on its operator spectrum and OPE coefficients. We conclude with an outlook for the prospects of approaching other strongly coupled N=2 conformal theories.

**Tuesday, 12th of March 2019, 14:30, sala Wataghin**

### On the holographic origin of the Bekenstein-Hawking entropy of 1/16 BPS $AdS_5$ black holes

Providing a microscopic derivation of the entropy of supersymmetric asymptotically $AdS_5$ black holes has been an open problem for some time. In the talk I will present progress towards such a derivation. On the gravity side of the AdS/CFT correspondence, I will define a BPS limit of black hole thermodynamics by first focussing on a supersymmetric family of complexified solutions and then reaching extremality. I will show that in this limit the black hole entropy is the Legendre transform of the on-shell gravitational action with respect to a set of chemical potentials subject to a constraint. This constraint follows from supersymmetry and regularity in the Euclidean bulk geometry. The gravitational analysis instructs us that the dual N=1 superconformal field theory is defined on a twisted $S^1 \times S^3$ with complexified chemical potentials obeying the constraint, and localization allows to compute the corresponding partition function exactly. This computation defines a generalization of the supersymmetric Casimir energy, whose Legendre transform at large N precisely reproduces the Bekenstein-Hawking entropy of the black hole.

**Tuesday, 5th of March 2019, 14:30, sala Wataghin**

### 3d Abelian Gauge theories at the Boundary

A four-dimensional abelian gauge theory can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFTs) parametrized by the gauge coupling \tau and by the choice of the CFT in the decoupling limit. Upon performing an Electric-Magnetic duality in the bulk and going to the decoupling limit in the new frame, one finds a different 3d CFT on the boundary, related to the original one by Witten's SL(2, Z) action. In particular the cusps on the real \tau axis correspond to the 3d gauging of the original CFT. We study general properties of this family of BCFTs. We show how to express bulk one and two-point functions, and the hemisphere free-energy, in terms of the two-point functions of the boundary electric and magnetic currents. Finally, upon assuming particle-vortex duality (and its fermionic version), we show how to turn this machinery into a powerful computational tool to study 3d gauge theories.

**Tuesday, 26th of February 2019, 14:30, sala Wataghin**

### Weyl anomaly cancellation in string theories on generalized supergravity backgrounds

Recently, there has been a fundamental and significant development
in the Green-Schwarz (GS) formulation of superstring theory.
In this formulation, the kappa-symmetry plays a central role
to ensure the consistency of the theory. In 2016, Tseytlin and Wulff
showed that the kappa-symmetry constraints of the GS superstring defined
on an arbitrary background lead to a "generalized" supergravity,
which contains an additional (non-dynamical) vector field, rather than
the standard supergravity. This result indicates that we might have
overlooked a potentially important ingredient in the low-energy
effective theory of string theory for long time, and may open up new
directions including phenomenology and cosmology.

In this talk, I will give an overview on the progress on Yang-Baxter
deformations of the $AdS_5 \times S^5$ superstring and the generalized
supergravity. Finally, I would like to discuss the cancellation of
Weyl anomaly in string theories on generalized supergravity
backgrounds.

**Tuesday, 12th of February 2019, 14:30, sala Wataghin**

### A-infinity algebra from supermanifolds.

Inspired by the analogy between different types of differential forms on
supermanifolds and string fields in superstring theory, we construct new
multilinear non-associative products of forms which yield an
$A_\infty$-algebra.

**Tuesday, 29th of January 2019, 14:30, sala Franzinetti**

### Living on the walls of Super-QCD

Super-QCD, the supersymmetric version of ordinary QCD, admits isolated vacua and dynamical domain walls between them. I will present a class of three-dimensional Chern-Simons theories to describe the effective dynamics on these walls. Our proposal passes several non-trivial checks, which I will discuss in detail. The domain wall dynamics is very rich and enjoys interesting phenomena, as for example a second order phase transition where multiple vacua coalesce into a single one and where supersymmetry gets enhanced, in some cases. Our proposal includes and extends previous results in the literature, solving also some old puzzles, and provides a complete picture of Super-QCD domain walls.

**Tuesday, 22th of January 2019, 14:30, sala Wataghin**

### 4d SCFTs via discrete gauging

I will introduce the notion of discrete gauging in the context of 4d SCFTs and I will show how, using this procedure, we can obtain new SCFTs starting from 4d SCFTs mother theories. At the beginning of the talk I will review the mathematical tools that will be employed, that is to say the Superconformal index and the Higgs branch Hilbert series. I will then apply the discrete gauging in two different contexts. In the first case I will show how starting from $\mathcal{N}=4$ SYM, and discretely gauging a $\mathbb{Z}_n$ subgroup of the global symmetry group, we can obtain new $\mathcal{N}=4$ or $\mathcal{N}=3$ SCFTs (depending on the value of $n$). I will give a prescription for how to perform the discrete gauging at the level of the superconfomal index and Higgs branch Hilbert series. Finally I will give an overview of the results that we got in this context, in particular we will see that the Coulomb branches of the daughter theories generically are not-freely generated. Then I will focus on 4d SCFTs with $\mathcal{N}=2$ supersymmetry. In this context the mother theory will be always provided by a theory with SU(N), gauge group and the daughter theory will be obtained gauging the automorphism group of the Dynkin diagram. I will then analyse the consequences of this gauging. We will see that the global symmetry of the Higgs branch is modified in a non-trivial way and that, also for this class of theories, the corresponding Coulomb branch is generically not-freely generated.

The talk will be mainly based on the following two articles:

**Tuesday, 12th of December 2018, 14:30, sala Wataghin**