### Conveners

#### Formal Theory

- Silvia Penati (Istituto Nazionale di Fisica Nucleare)
- Jaroslav Trnka (UC Davis)

#### Formal Theory

- Jaroslav Trnka (UC Davis)
- Silvia Penati (Istituto Nazionale di Fisica Nucleare)

#### Formal Theory

- Davide Fioravanti (Istituto Nazionale di Fisica Nucleare)
- Patrick Dorey (Durham University)

#### Formal Theory

- Davide Fioravanti (Istituto Nazionale di Fisica Nucleare)
- Patrick Dorey (Durham University)

#### Formal Theory

- Silvia Penati (Istituto Nazionale di Fisica Nucleare)
- Davide Fioravanti (Istituto Nazionale di Fisica Nucleare)

We go beyond the state-of-the-art by combining first principle lattice results and effective field theory approach as Polyakov Loop model to explore the non-perturbative dark deconfinement-confinement phase transition and the generation of gravitational-waves in a pure gluon dark Yang-Mills theory. We further include fermions with different representations in the dark sector. Employing the...

Physics in (canonical) quantum gravity needs to be manifestly diffeomorphism-invariant. Consequently, physical observables need to be formulated in terms of manifestly diffeomorphism-invariant operators, which are necessarily composite. This makes an evaluation in general involved, even if the concrete implementation of quantum gravity should be treatable (semi-)perturbatively in general.

A...

The all-order structure of scattering amplitudes is greatly simplified by the use of (generalized) Wilson line operators, describing (subleading) soft emissions from straight lines extending to infinity. In this talk I will review how these techniques (originally developed for QCD phenomenology) can be naturally applied to gravitational scattering. At the quantum level, we find a convenient...

The radion equilibrium in the Randall-Sundrum model is guaranteed by the backreaction of a bulk scalar field. We studied the radion dynamics in an extended scenario, where an intermediate brane exists in-between the UV and IR branes. We conducted an analysis in terms of the Einsteinโs equations and effective Lagrangian after applying the Goldberger-Wise mechanism. Our result elucidates that in...

We present a method to obtain a scalar potential at tree level from a pure gauge theory on nilmanifolds, a class of negatively-curved compact spaces, and discuss the spontaneous symmetry breaking mechanism induced in the residual Minkowski space after compactification at low energy. We show that the scalar potential is completely determined by the gauge symmetries and the geometry of the...

While CP violation has not been observed so far in processes mediated by the strong force, the QCD Lagrangian admits a CP-odd topological term proportional to the so-called theta angle, which weighs the contributions to the partition function from different topological sectors. The observational bounds are usually interpreted as demanding a severe tuning of theta against the phases of the...

The Standard Model effective field theory (SMEFT) is one of the preferred approaches for studying particle physics in the present scenario. The dimension-six SMEFT operators are the most relevant ones and have been studied in various works. The renormalization group evolution equations of these operators are available in the literature and facilitate examining the SMEFT on combined...

Due to large scale separations, matching is an essential and laborious computational step in the comparison of high-energy new physics models to experimental data.

Matchete is a Mathematica package that automates the one-loop matching from any generic ultraviolet (UV) model to a low-energy effective field theory (EFT) including, but not limited to, SMEFT. The program takes a UV Lagrangian as...

I would like to present an intriguing new perspective into such fundamental questions as 1) the origin of the gauge interactions in the Standard Model (SM), and 2) the origin of the quark, lepton and neutrino families' replication and their fundamental properties experimentally observed in Nature. These questions can be addressed by tying together in a common framework both flavour physics and...

In this talk, we present the construction of Effective Field Theories (EFTs) in which a chiral fermion, charged under both gauge and global symmetries, is integrated out. These symmetries can be spontaneously broken, and the global ones might also be anomalous. This setting is typically served to study the structure of low-energy axion EFTs, where the anomalous global symmetry can be...

We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal singular configurations of multiloop Feynman diagrams. To identify such configurations, we exploit Grover's algorithm for querying multiple solutions over...

We consider Nielsen-Olesen vortices (abelian Higgs model in $2+1$ dimensions) under Einstein gravity in an AdS$_3$ background. We find numerically non-singular solutions characterized by three parameters: the cosmological constant $\Lambda$, the winding number $n$ and the vacuum expectation value (VEV) labeled by $v$. The mass (ADM mass) of the vortex is expressed in two ways: one involves...

We discuss the phase diagram of QCD in the presence of a strong magnetic background field, providing numerical evidence, based on lattice simulations of QCD with 2+1 flavours and physical quark masses, that the QCD crossover turns into a first order phase transition for large enough magnetic field, with a critical endpoint located between $eB = 4$ GeV$^2$ (where we found an analytic crossover...

In light-front holographic QCD a Schr\"{o}dinger-like equation determines the transverse mode in the chiral limit. The supersymmetric formulation of holographic QCD each baryon has two supersymmetric partners, a meson and a tetraquark. The mass degeneracy of these partner states is lifted by the combination of two mechanisms: chiral symmetry breaking and longitudinal confinement. In this...

Scattering amplitudes are the fundamental building blocks of collider observables. Comparing high precision measurements to theory predictions requires computing them to high perturbative order. The growth in the number of loops significantly increases the complexity of the problem. Using novel mathematical methods allowed to compute QCD corrections to four-point massless processes at...

The QCD topological observables are essential inputs to obtain theoretical predictions about axion phenomenology, which are of utmost importance for current and future experimental searches for this particle. Among them, we find the topological susceptibility, related to the axion mass.

We present lattice results for the topological susceptibility in QCD at high temperatures obtained...

We calculate the relativistic six-meson scattering amplitude at low energy within the framework of QCD-like theories with $n$ degenerate quark flavors at next-to-leading order in the chiral counting. We discuss the cases of complex, real and pseudo-real representations, i.e. with global symmetry and breaking patterns $\text{SU}(n)\times\text{SU}(n)/\text{SU}(n)$ (extending the QCD case),...

In the past decade, antenna subtraction has been used to compute NNLO QCD corrections to a series of phenomenologically relevant processes. However, as for other subtraction schemes at NNLO, the application of this method proceeded in a process-dependent way, with each new calculation requiring a significant amount of work. In this talk we present an improved version of antenna subtraction...

The exact computation of partition functions of four-dimensional theories with extended supersymmetry by means of localization techniques hinges on the existence of a Lagrangian description. On the one hand, it is known that in many cases such a description is only accurate in certain regions of moduli space, such as weak-coupling phases. On the other hand, there are also many examples of...

In this talk we will talk about a large class of solvable lattice models, based on the data of conformal field theory. These models are constructed from any conformal field theory. The talk will be based on the results of a work titled โThe crossing multiplier for solvable lattice modelsโ. We consider the lattice models based on affine algebras described by Jimbo et al., for the affine...

If we start from some functional relations as definition of a quantum integrable theory, then we can derive from them a linear integral equation. It can be extended, by introducing dynamical variables, to become an equation with the form of the Marchenko one. Then, we naturally derive from the latter a classical Lax pair problem. We exemplify our method by focusing on the massive version of...

While colour-kinematics duality and double copy are a well established paradigm at tree level, their loop level generalisation remained for a long time an unsolved problem. Lifting the on-shell, scattering amplitude-based description to an action-based approach, we show that a theory that exhibits tree level colour-kinematics duality can be reformulated in a way such that its loop integrands...

In this talk, I will show a new connection between quantum integrable models and black holes perturbation theory. After an introduction to quasinormal modes and their role in gravitational waves observations, I will connect their mathematically precise definition with the integrability structures derived from the ordinary differential equation associated to the black hole perturbation. More...

The renormalization group (RG) beta function describes the running of the renormalized coupling and connects the ultraviolet and infrared regimes of quantum field theories. Performing numerical lattice field theory simulations we use gradient flow measurements to determine the RG $\beta$ function nonperturbatively for SU(3) gauge systems with $N_f$ = 2, 4 and 6 flavors in the fundamental...

We show that a recently discovered non-perturbative field-theoretical mechanism giving mass to elementary fermions, is also capable of generating a mass for the electro-weak bosons and can thus be used as a viable alternative to the Higgs scenario. A detailed analysis of this remarkable feature shows that the non-perturbatively generated fermion and $W$ masses have the parametric form...

A new criterion to extend the Standard Model (SM) of particle physics is proposed: the symmetries of physical microscopic forces originate from the automorphism groups of main CayleyโDickson algebras, from complex numbers to octonions and sedenions. This correspondence leads to a natural and minimal enlargement of the color sector, from a SU(3) gauge group to an exceptional Higgs-broken G(2)...

We present a new grand unification paradigm, where gauge couplings do not need to be equal at any give scale, instead they run towards the same fixed point in the deep ultraviolet. We provide a concrete example based on SU(5) with a compactified extra space dimension. By construction, fermions are embedded in different SU(5) bulk fields, hence baryon number is conserved and proton decay is...

Lattice simulations suggest that the spectrum of observable particles in BSM-like theories may be different than naively expected using standard methods.

We consider a GUT-like toy theory, which (despite its simplicity) shows qualitative discrepancies arising from non-trivial field theoretical effects, even at weak coupling.

These effects arise as an immediate consequence of the...

A supersymmetric extension of the Standard Model is presented, that results from the dimensional reduction of the $N=1$, $10D$ $E_8$ gauge group over a $M_4\times B_0/Z_3$ space, where $B_0$ is the nearly-Kaehler manifold $SU(3)/U(1)\times U(1)$ and $Z_3$ is a freely acting discrete group on $B_0$. The $4D$ theory -after the dimensional reduction and Wilson flux breaking- is an $N=1$...

The โflavor problemโ represents one of the greatest challenges of particle model building since SM does not provide neither โa prioriโ explanation of the number of fermion generations nor on their mass and mixing patters, which appear to be very different in the lepton and quark sector. Discrete non-abelian symmetries have gathered a lot of attention as candidates for the solutions of the...

We propose that the electroweak and flavour quantum numbers of the Standard Model (SM) could be unified at high energies in an SU(4)รSp(6)LรSp(6)R anomaly-free gauge model. All the SM fermions are packaged into two fundamental fermion fields, thereby explaining the origin of three families. The SM Higgs, being electroweakly charged, necessarily becomes charged also under flavour when embedded...