The aim of my talk is to give an introduction to the Lorentzian inversion formula in Conformal Field Theory. First I will briefly review the properties of correlators in conformal theories. In particular I will show that they are completely fixed once we know the CFT data, namely conformal dimensions, spins and three-point functions of the operators. Then I will review an inversion formula which allows to recover precisely these data from the lorentzian singularities of the four-point function. I will also comment on closely related dispersion relations that directly compute the full four-point function from the same singularities. Finally I will show some applications.
the 29th of March 2022, 14:30
Hibert series and gauge invariants
I review the notion of Moduli Space of Vacua in the context of 4d $\mathcal{N}=1$ gauge theories. From a geometrical point of view this is an algebraic variety that can be efficiently characterized using a generating function called the "Hilbert series" . I introduce this quantity and its properties through some explicit examples and I explain how it can be computed in a theory with a connected gauge group. Then, in the second part of the talk, I generalize this construction in the context of gauge theories based on a particular type of disconnected gauge group called "principal extension". In particular, via the Hilbert series computation, I discuss how the different global structure of the gauge group can affect properties of the corresponding moduli space of vacua.
the 15th of March 2022, 14:30
The critical O(N) CFT
Fifty years ago Wilson and Fisher published their renowned paper on the
epsilon-expansion of the critical $O(N)$ model. Nowadays we may think of
the critical $O(N)$ model as a two-parameter family of conformal field
theories, labeled by $N$ and spacetime dimension $d$. Advances in both
diagrammatic technology and CFT methods have led to a constant supply of
new results for the $O(N)$ CFT, both perturbatively and
non-perturbatively. In this talk, I will give an introduction to the
$O(N)$ CFT from the perspective of conformal field theory, with a focus
on the often-implicit assumption of spectrum continuity, which is the
conjectural assumption that all conformal data, such as critical
exponents and operator scaling dimensions, depend continuously on the
parameters $N$ and $d$.
the 8th of March 2021, 14:30
D-branes in AdS3 x S3 x T4 at k=1 and their holographic duals
Following the recent work of Eberhardt, Gaberdiel and Gopakumar, exact comparison between various quantities living on the two sides of the AdS/CFT duality has become a possibility. The goal of this talk will be to extend the existing holographic dictionary to include some non-perturbative vacua on both sides. I will start by reviewing the original, purely closed-string setup, giving arguments that string theory on ${\rm AdS}_3\times {\rm S}^3 \times \mathbb{T}^4$ with minimal $k=1$ NS-NS flux is exactly dual to the symmetric-product orbifold CFT with the $\mathbb{T}^4$ as the seed. I will then construct various D-branes of this string theory and calculate their associated cylinder amplitudes. We will observe that these amplitudes match with the cylinder correlators of certain boundary states of the dual CFT, thus suggesting a direct correspondence between these boundary conditions. I will also show that the disk amplitudes of these D-branes localise to those points in the worldsheet moduli space where the worldsheet disk holomorphically covers the spacetime disk. This talk is based on https://arxiv.org/abs/2110.05509.
the 22nd of February 2021, 14:30
In this talk I will review some recent developments that allow us to completely solve a large family of Matrix models in the planar limit. Armed with these new techniques, we will compute the full planar series of relevant observables of N=2 Lagrangian superconformal field theories on S^4 such as the planar free energy, the Wilson loop and n-point functions. Finally, we obtain the exact expression for the maximally transcendental part of the 2 and 3-point function of Chiral Primary Operators.
23rd of November 2021, 14:30
Defect Central Charges
Conformal defects can be characterised by their contributions to the Weyl anomaly. The coefficients of these terms, often called defect central charges, depend on the particular defect insertion in a given conformal field theory. I will review what is currently known about defect central charges across dimensions, and present novel results. I will discuss many examples where they can be computed exactly without requiring any approximations or limits. These include defects in free theories, and recently developed tools for defects in superconformal field theories.
16th of November 2021, 14:30
In this talk, I will consider two examples of TTbar deformed theories and discuss the crucial role played by nonperturbative corrections in the deformation parameter. The first part is dedicated to JT gravity at finite cutoff, as given by its proposed formulation in terms of a deformed Schwarzian quantum mechanics. Resurgence gives a prescription to fix the instantonic terms shaping the spectrum of the theory on arbitrary topologies. The second part is devoted to TTbar deformed two-dimensional Yang-Mills theory. I will show how to extend previous results to any finite value of the gauge rank and how to characterize the rich phase diagram that the theory exhibits for both positive and negative values of the deformation parameter.
9th of November 2021, 14:30
Emergent strings and duality with broken supersymmetry
We explore the dramatic consequences of string-scale supersymmetry breaking. We focus on the USp(32) and U(32) orientifolds of the type IIB and type 0B strings, as well as the SO(16) x SO(16) projection of the exceptional heterotic string, which provide non-tachyonic settings with no moduli directly in ten dimensions. While deceptively innocuous at the level of worldsheet perturbation theory, dynamical gravitational tadpoles backreact on spacetime in a dramatic fashion. We discuss how branes can tame this effect to a certain extent, finding that spacetime universally breaks down at a finite distance, ending in a strongly coupled, highly curved singularity. Remarkably, the dynamics of branes in these settings remains consistent among different complementary regimes despite the absence of supersymmetric protection. We connect the resulting picture with a number of swampland criteria, including the weak gravity, de Sitter and distance conjectures, which are realized via novel mechanisms and provide tantalizing hints for a candidate S-dual heterotic construction of the USp(32) orientifold with “brane supersymmetry breaking”.
19th of October 2021, 14:30
Exact solutions to N=2 D=4 Gauged Supergravity coupled to abelian vector multiplets
Known exact solutions to N=2, D=4 and their properties will be discussed. In particular I will focus on new non BPS solution that consists in a closed universe with two extremal black holes of equal size, surrounding two singularities. They have opposite magnetic charges (and no electric charges), but stay in static equilibrium thanks to the positive pressure of a cosmological constant. The geometry is perfectly symmetric under the exchange of the black holes and the flip of the sign of the charges. However the scalar field is non constant and non symmetric, with different values at the horizons, which depend on a real modulus, remarkably we show that it satisfies the attractor mechanism and the entropy indeed depends only on the magnetic charges. At one of the horizon the solution becomes 1/2-BPS supersymmetric, while at the other one there is no supersymmetry, but the entropy remains independent from the scalar modulus
Sala Fubini
12th of October 2021, 14:30
N=1 inherithed S-duality for oriented quivers
We study necklace quiver gauge theories obtained from type IIA string theory with
O-planes. It has been recently observed that such models, that describe different singularities before the projection,
become dual after the addition of the O-planes and of the necessary amount of fractional branes, enforcing
anomaly cancellations. In this talk we provide the field theory interpretation of this process, in terms of
inherited S-duality on the conformal manifold. We then extend the class of conformally S-dual models obtained
through orientifold projections and provide further checks of the duality, matching the central charges,
the t’ Hooft anomalies and, for low gauge ranks, the superconformal index. We conclude by discussing various
extensions and generalizations.
5th of October 2021, 14:30, sala Wataghin