### Conveners

#### Theoretical Developments: Theoretical Developments I

- Simon Catterall

#### Theoretical Developments: Theoretical Developments II

- Alexander Rothkopf (University of Stavanger)

#### Theoretical Developments: Theoretical Developments III

- Leonardo Giusti

#### Theoretical Developments: Theoretical Developments IV

- Roberto Frezzotti (University and INFN of Roma Tor Vergata)

#### Theoretical Developments: Theoretical Developments V

- Alberto Ramos Martinez (IFIC)

#### Theoretical Developments: Theoretical Developments VI

- Marina Krstic Marinkovic (ETH Zurich)

We report novel lattice QCD results for the three-gluon vertex from quenched lattice-QCD simulations. Using standard Wilson action, we have computed the three gluon vertex beyond the usual kinematic restriction to the symmetric (q² = r² = p²) and soft-gluon (p = 0) cases where it depends on a single momentum scale. We will present a detailed analysis of the asymmetric case (r² = q² ≠ p²) where...

In this talk we present numerical simulations of N = 4 super Yang-Mills for 3 color gauge theory over a wide range of ’t Hooft coupling 5 ≤ λ ≤ 30 using a supersymmetric lattice action. By explicit computations of the fermion Pfaffian we present evidence that the theory possesses no sign problem and exists in a single phase out to arbitrarily strong coupling. Furthermore, preliminary work...

Master-field simulations offer an approach to lattice QCD in which calculations are performed on a small number of large-volume gauge-field configurations. This is advantageous for simulations in which the global topological charge is frozen due to a very fine lattice spacing, as the effect of this on observables is suppressed by the spacetime volume. Here we make use of the recently developed...

We study two different SU(2) gauge-scalar theories in 3 and 4 spacetime

dimensions. Firstly, we focus on the 4 dimensional theory with 2 sets of

fundamental scalar (Higgs) fields, which is relevant to the 2 Higgs Doublet Model

(2HDM), a proposed extension to the Standard Model of particle physics.

The goal is to understand the particle spectrum of the theory at zero temperature

and the...

Topological Data Analysis (TDA) is a field that leverages tools and ideas from algebraic topology to provide robust methods for analysing geometric and topological aspects of data. One of the principal tools of TDA, persistent homology, produces a quantitative description of how the connectivity and structure of data changes when viewed over a sequence of scales. We propose that this presents...

The Hamiltonian formalism for lattice gauge theories has experienced a resurgence of interest in recent years due to its relevance for quantum simulation, a major goal of which is the solution of sign problems in QCD. The particular formulation of the Hamiltonian formalism is itself an important design decision, where factors to consider include (non)locality of the degrees of freedom,...

The 2D O(N) non-linear sigma models are exactly solvable theories and, on the lattice, they have many applications from statistical mechanics to QCD toy models. In this talk, I will consider a particular generalization of the O(N) model, i.e. the non-linear sigma model on the supersphere. The global symmetry group of this model – the OSp(N+2M|2M) supergroup – mixes bosonic and fermionic...

A generalization of Wilsonian lattice gauge theory may be obtained by considering the possible self-adjoint extensions of the electric field operator in the Hamiltonian formalism. In the special case of $3D$ $U(1)$ gauge theory these are parametrised by a phase $\theta$, and the ordinary Wilson theory is recovered for $\theta=0$. We consider the case $\theta=\pi$, which, upon dualization,...

Recent studies on the 't Hooft anomaly matching condition have suggested

a nontrivial phase structure in 4D SU($N$) gauge theory at $\theta=\pi$.

In the large-$N$ limit, it has been found that CP symmetry at $\theta=\pi$ is broken

in the confined phase, while it restores in the deconfined phase,

which is indeed one of the possible scenarios.

However, at small $N$, one may find other...

The 3D Ising conformal field theory (CFT) describes different physical systems, such as uniaxial magnets or fluids, at their critical points. In absence of an analytical solution for the 3D Ising model, the scaling dimensions and operator product expansion (OPE) coefficients characterizing this CFT must be determined numerically. The currently most-cited values for these quantities have been...

For the 2d Ising model on a triangular lattice, we determine the exact values of the three critical coupling coefficients which restore conformal invariance in the continuum limit as a function of an affine transformation of the triangle geometry. On a torus with a non-trivial modular parameter, we present numerical results showing agreement with the exact CFT solution. Finally, we discuss how...

We study the massless Schwinger model with an additional 4-fermi interaction and a topological term. For topological angle $\theta = \pi$ charge conjugation is implemented in a non-trivial way and we study its spontaneous breaking. We use staggered fermions and the Villain action for the gauge fields, where the topological term is an integer and charge conjugation at $\theta = \pi$ is an exact...

We show how staggered fermions can be coupled to gravity by generalizing them to Kaehler-Dirac fermions. The latter experience a perturbative gravitational anomaly which breaks

a U(1) symmetry down to Z_4. This anomaly is captured exactly by the lattice theory. Furthermore we show that this theory exhibits a second

non-perturbative 't Hooft anomaly which can be seen

by considering...

This research aims to analyze the integrability condition of the chiral determinant of 4D overlap fermions and construct lattice chiral gauge theories.

$\quad$ We formulate the integrability condition with 5D and 6D lattice domain wall fermions. Our formulation parallels the recent cobordism classification of the global ‘t Hooft anomaly using the $\eta$-invariant based on the Dai-Freed...

We investigate the Casimir effect for relativistic lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion with the periodic or antiperiodic boundary condition. We also discuss anomalous behaviors for nonrelativistic particles. We apply our approaches to condensed matter systems described by low-energy effective Hamiltonian of Dirac semimetals such as Cd3As2 and Na3Bi.

Lattice simulations of Yang-Mills theories coupled with $N_f$ flavours of fermions in the adjoint representation provide a way to probe the non-perturbative regime of a plethora of different physical scenarios, such as Supersymmetric Yang-Mills theory to BSM models. Although the large-$N_c$ limit of these theories can give important insight into the strongly coupled regime of these models, the...

Standard lattice formulations of non-relativistic Fermi gases with two spin components suffer from a sign problem in the cases of repulsive contact interactions and attractive contact interactions with spin imbalance. We discuss the nature of this sign problem and the applicability of the complex Langevin method in both cases. For repulsive interactions, we find the results to converge well...

The non-local dependence of the fermion determinant on the gauge field limits our ability of simulating Quantum Chromodynamics on the lattice. Here we present a factorization of the gauge field dependence of the fermion determinant based on an overlapping four-dimensional domain decomposition of the lattice. The resulting action is block-local in the gauge and in the auxiliary bosonic fields....

Padé approximants are employed in order to study the analytic structure of the four-dimensional SU(2) Landau-gauge gluon and ghost propagators in the infrared regime. The approximants, which are model independent, are used as fitting functions to lattice data for the propagators, carefully propagating uncertainties due to the fit procedure taking into account all possible correlations....

In this talk, I will revisit the emergence of de Sitter space in Euclidean dynamical triangulations (EDT). Working within the semi-classical approximation, it is possible to relate the lattice parameters entering the simulations to the partition function of Euclidean quantum gravity. We verify that the EDT geometries behave semi-classically, and by making contact with the Hawking-Moss...

In Non Destructive Testings (NDT), ultrasonic Time Revesal based Nonlinear Elastic Wave Spectroscopy (TR-NEWS) turned out to be an efficient method. In order to find out anomalies in the convolution of scattered phonetic waves one of which is time reversed (TR) phonon of the other, it is necessary to perform Fourier transforms of signals.

The energy flow of nonlinear waves detected in...

Using different observables we test the approach to the continuum limit of several lattice gauge actions. We use lattice spacings in the range that are usually found in typical lattice QCD simulations. As observables we use different flow observables. This allows to check the scaling properties of the different discretizations with high statistical precision.

We study U(1) lattice field theory in the Villain formulation and couple electrically as well as magnetically charged bosonic matter. The system has a manifest self-duality that allows to establish a relation between the weak and strong coupling regimes. The complex action problem can be overcome with a worldline representation such that numerical simulations are possible. We study the...

We present our progresses in the use of the non-perturbative renormalization framework based on considering QCD at finite temperature with shifted and twisted (for quarks only) boundary conditions in the compact direction. We report our final results in the application of this method for the non-perturbative renormalization of the flavor-singlet local vector current. We then discuss the more...

Numerical Stochastic Perturbation Theory (NSPT) has over the years proved to be a valuable tool, in particular being able to reach unprecedented orders for Lattice Gauge Theories, whose perturbative expansions are notoriously cumbersome. One of the key features of the method is the possibility to expand around non-trivial vacua.

While this idea has been around for a while, and it has been...

The Szymanzik improvement program for gauge theories is most commonly implemented using forward finite difference corrections to the Wilson action. Central symmetric schemes (see e.g. [1]) naively applied, suffer from a doubling of degrees of freedom, identical to the well known fermion doubling phenomenon. And while adding a complex Wilson term remedies the problem for fermions, it does not...

A class of non-linear, massive electrodynamics theories known as Generalized Proca (GP) was proposed in 2014 in the context of classical effective field theories and has held a prominent role in cosmology. As a quantum field theory GP has the potential to describe phenomena in condensed matter, optics, and lattice field theories. In this talk, we show how to quantize a family of GP theories...

Flavor observables are usually computed with the help of the electroweak Hamiltonian which separates the perturbative from the non-perturbative regime. The Wilson coefficients are calculated perturbatively, while matrix elements of the operators require non-perturbative treatment, e.g. through lattice simulations. The resulting necessity to compute the transformation between the different...

The Lorentzian type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. However, it was found recently that a Euclidean space-time appears in the conventional large-$N$ limit. In this work, we add a Lorentz invariant mass term and consider a limit, in which the coefficient of the mass term vanishes at large $N$. By performing complex Langevin...

When designing lattice actions, gauge field smearing is frequently used to define the lattice Dirac operator. Since the smearing procedure removes effects of ultraviolet fluctuations, the fermions effectively see a larger lattice spacing than the gauge fields. Creutz ratios, formed from ratios of rectangular Wilson loops, based on smeared gauge fields are an adequate observable to investigate...

We report on the development of a lattice formalism for studying the realtime behaviour of radially symmetric configurations of massless scalar fields in radially symmetric, curved spacetimes in 3+1 dimensions.

It is intended to numerically study back reaction effects due to semiclassical gravity in the time evolution of scalar field configurations, especially for those that will eventually...