### Strange Symbol Structures for a Sufficiently Supplemented Sunrise

The symbol is a powerful formalism used to manipulate and understand certain classes of Feynman diagrams. It can dramatically simplify expressions, reveal analytic structure, and even allow perturbative amplitudes to be bootstrapped from first principles to high loop orders. However, many classes of diagrams involve functions for which an appropriate symbol formalism is not known. The simplest such class, the sunrise diagrams, consist of a family of massive propagator corrections that can be thought of as integrals over the Calabi-Yau manifolds coincidentally explored by string theorists. We explore an extension of the symbol formalism to this class of diagrams. There are many choices involved in setting up such a formalism, and we comment on the challenge of finding ways to make those choices that achieve the amplitudes community's aims.

**the 29th November 2022, 14:30**

### Some remarks on thermal CFTs and massless Feynman graphs

I will elaborate on a recently observed, curious relationship between thermal one-point partition functions of free massive theories in odd dimensions and multilloop Feynman ladder graphs in d=4.

**the 22nd November 2022, 14:30**

### Classical observables of General Relativity from scattering amplitudes in the PM expansion

We start discussing the elastic scattering of two massive particles with different masses and from their scattering amplitude we extract the eikonal that is a classical quantity and from it the classical deflection angle up to 3PM (two loops).

Then, we consider the inelastic process in which an extra soft graviton is emitted in the final state and we show how in this case the c-number elastic eikonal becomes an operator containing the creation and annihilation operators of the graviton. Then we compute the waveform and the zero frequency limit (ZFL) of the emitted energy.

Finally we show that both the elastic and inelastic observables are universal at high energy as expected from the fact that the graviton is the massless particle with the highest spin.

**the 15th November 2022, 14:30**

### Bootstrapping line defects with O(2) symmetry

Line defects play an important role in our understanding of QFTs, explaining interesting phenomena in both condensed matter physics and high-energy theories, and giving access to new data and observables.
I will discuss recent work in which we explore 1d conformal line defects with an additional O(2) symmetry using the numerical bootstrap. The starting point is an agnostic approach, where we perfom a systematic bootstrap study of correlation functions between two canonical defect operators: the displacement and the tilt. We then move on to study two specific defects: a monodromy line defect and a localized magnetic field line defect. I will highlight the results of the latter one, where we found a series of intriguing cusps which we investigate.

**the 8th November 2022, 14:30**

### Bootstrability in defect CFT

We study how the exact non-perturbative integrability methods in 4D N = 4 Super-Yang-Mills can work efficiently together with the numerical conformal bootstrap techniques to go beyond the spectral observables and access previously unreachable quantities such as correlation functions at finite coupling. We consider the 1D defect CFT living on a 1/2-BPS Wilson line, whose non-perturbative spectrum is governed by the Quantum Spectral Curve (QSC). In addition, we use that the deformed setup of a cusped Wilson line is also controlled by the QSC. In terms of the defect CFT, this translates into two nontrivial relations connecting integrated 4-point correlators to cusp spectral data, such as the Bremsstrahlung and Curvature functions – known analytically from the QSC. Combining these new constraints and the spectrum of the 10 lowest-lying states with the Numerical Conformal Bootstrap, we obtain very sharp rigorous numerical bounds for the structure constants of the first non-protected states. Furthermore, we also develop analytic functional bootstrability obtaining weak coupling results for several structure constants.

**the 25th of October 2022, 14:30**

A longstanding problem of the metric-affine approach to gravity is the fact that four degrees of freedom of the connection are not fixed by the field equations of the theory. This is a consequence of an underlying invariance of a large class of gravity theories usually referred to as projective symmetry. In this talk, we propose a solution to this problem by revisiting and generalizing the interpretation of the projective symmetry as a gauging of the conformal transformations. Furthermore, we provide strong arguments to establish that any consistent metric-affine gravity theory has to be conformal invariant. Assuming that the gauge field associated to the conformal symmetry is dynamical, a Stueckelberg symmetry breaking is realized in a natural way, paving the way to a possible restoration of the conformal symmetry below the Plank scale. Remarkably, we show how to solve the field equation associated to the connection, making manifest the role of the gauge vector of the conformal symmetry as a possible ingredient to solve some of the current issues regarding gravitational interaction.

**the 20th of October 2022, 14:30**

### Bootstrapping string dynamics in the 6d N = (2, 0) theories

The 6d N = (2, 0) theories are superconformal field theories believed to describe the low-energy dynamics of N coincident M5-branes. These theories don’t have a known lagrangian description and remain largely mysterious, so it is an interesting question how one might calculate observables there. An exciting prospect is to use the analytical conformal bootstrap, which offers a way to systematically calculate 1/N corrections at large N. In this talk I will present the bootstrap approach to a case study, that of calculating the 2-point function of stress tensors in the presence of a surface defect. This setup turns out to be remarkably simple and helps us address some technical issues faced in similar calculations, notably we can derive a supersymmetric inversion formula and check crossing symmetry explicitly. I will also comment on the interpretation of our result in the context of holography, of the chiral algebra construction of Beem et al. and on what it can reveal about the interactions between M2 and M5-branes.

**the 18th of October 2022, 14:30**

Within a holographic framework, we explore the physical consequences
of embedding Einstein-AdS gravity in Conformal Gravity in four and six dimensions.
In the bulk, the procedure is equivalent to Holographic Renormalization, as the
Einstein-AdS action appears augmented by the correct boundary counterterms.
In codimension-2 surfaces, 4D Conformal Gravity induces a conformal invariant
which, for given conditions on the ambient space and the surface itself, reproduces different
functionals: Renormalized Area, Willmore Energy and Reduced Hawking Mass.

**the 13th of October 2022, 14:30**

### Misaligned SUSY and the effective central charge criterion

In this talk I will present a criterion from which it is possible to see whether tachyons are present in the tree level spectrum for closed string models. I will review the ideas that have come out since the mid 90's to clarify their role and their meaning before presenting a general argument, through which the criterion is built, and providing some examples. Afterwards I will give some hints on how the construction can be adapted in the case of open strings.

**the 11th of October 2022, 14:30**

### 2d Integrable field theories from 4d CS theory with 2d systems and its lattice discretization

The 4d Chern-Simons (CS) theory proposed by Costello,Yamazaki and Witten is proposed as a framework that allows a systematic description not only of (1+1)-d integrable lattice models, but also of 2d classical integrable field theories. This would allow for a unified description of the relationship between integrable lattice models and field theories in terms of a single gauge theory. In this talk, as a first step towards understanding this relation, I derive the Faddeev-Reshetikhin (FR) model, which can be discretised preserving the quantum integrability, from a 4d CS theory coupled with 2d free field theories. The derivation is based on my work [2012.07370] with K.Yoshida and O.Fukushima in Kyoto university.
Then, I give a rough sketch of the lattice discretisation of the FR model in the context of 4d CS theory. This is achieved by discretising the 2d theory coupled to the 4d CS theory into Wilson lines, which would provide a framework for studying the lattice discretisation of 2d integrable field theories. The work on this discretisation is in progress with M.Yamazaki and M.Ashwinkumar in IPMU.

**the 27th of September 2022, 14:30**