### Conveners

#### Theoretical developments and applications beyond particle physics

- Jun Nishimura (High Energy Accelerator Research Organization (KEK))

#### Theoretical developments and applications beyond particle physics

- Antonio Rago (University of Plymouth (GB))
- Andrea Pelissetto (University of Rome "La Sapienza" and INFN)

#### Theoretical developments and applications beyond particle physics

- Simon Catterall (Syracuse University )

#### Theoretical developments and applications beyond particle physics

- C.-J. David Lin

#### Theoretical developments and applications beyond particle physics

- Daniel Nogradi
- Simon Hands

#### Theoretical developments and applications beyond particle physics

- Agostino Patella (Humboldt-Universitรคt zu Berlin)

#### Theoretical developments and applications beyond particle physics

- Richard Brower (Boston University)

Hamiltonian formulation of lattice gauge theories provides the natural framework for the purpose of quantum simulation, an area of research that is growing with advances in quantum-computing algorithms and hardware. It is therefore important to identify the most accurate, while computationally economic, Hamiltonian formulation(s) of lattice gauge theories along with necessary truncation...

Quantum link models (QLMs) are extensions of Wilson-type lattice gauge theories, and show rich physics beyond the phenomena of conventional Wilson gauge theories. Here we explore the physics of U(1) symmetric QLMs, both using a more conventional quantum spin-1/2 representation, as well as a fermionic representation. In 2D, we show that both bosonic and fermionic QLMs have the same physics. We...

In the Hamiltonian formulation, free spin-1/2 massless Dirac fermions on a bipartite lattice have an $O(4)$ (spin-charge) symmetry. Lattice interaction terms usually break this symmetry down to some subgroups. For example, the Hubbard interaction at half-filling breaks the symmetry down to $SO(4)$ by breaking the spin-charge flip symmetry. In this work, we construct a lattice model with a new...

In the Hamiltonian picture, free spin-1/2 Dirac fermions on a bipartite lattice have an O(4) (spin-charge) symmetry. Here we construct an interacting lattice model with an interaction V, which is similar to the Hubbard interaction but preserves the spin-charge flip symmetry. By tuning the coupling V, we show that we can study the phase transition between the massless fermion phase at small V...

I present lattice Monte Carlo evidence of localized quantum excitations of the fields surrounding static electric charges in the q=2 abelian Higgs model; such excitations would appear as excited states of isolated fermions. Since the q=2 abelian Higgs model is a relativistic version of the Landau-Ginzburg effective model of superconductivity, these results may have some application in a...

To investigate the properties of the large $N$ limit of $\mathcal{N}=1$ SUSY Yang-Mills theory, we have started a feasibility study for a reduced matrix model with an adjoint Majorana fermion. The gauge action is based on the Wilson action and the adjoint-fermion is the Wilson-Dirac action on a reduced lattice with twisted gauge boundary condition. We employ the RHMC algorithm in which the...

The Lorentzian type IIB matrix model is a promising candidate for a non-perturbative formulation of superstring theory. In previous studies, Monte Carlo calculations provided interesting results indicating the spontaneous breaking of SO(9) to SO(3) and the emergence of (3+1)-dimensional space-time. However, an approximation was used to avoid the sign problem, which seemed to make the...

The type IIB matrix model was proposed as a nonperturbative formulation of superstring theory in 1996. We simulate this model by applying the complex Langevin method to overcome the sign problem. Here, we clarify the relationship between the Euclidean and Lorentzian versions of the type IIB matrix model in a new phase we discovered recently.

Gauge theories admit a generalisation in which the gauge group is replaced by a finer algebraic structure, known as a 2-group. The first model of this type is a Topological Quantum Field Theory introduced by Yetter. I would like to discuss a common generalisation of both the Yetterโs model and Yang-Mills theory. I will focus on the lattice formulation of such model for finite 2-groups. After...

In this talk, I discuss a simple model based on the symmetry group $Z_2$ belonging to the class of 2-group gauge systems. Particular limits of such systems correspond to certain types of topological quantum field theories. In the selected model, independent degrees of freedom are associated to both links and faces of a four-dimensional lattice and are subject to a certain constraint. I present...

The Thirring model describes relativistic fermions with a contact interaction between conserved fermion currents. In 2+1 spacetime dimensions its U($2N$) global symmetry is broken at strong coupling to U($N)\otimes$U($N$) through generation of a non-vanishing bilinear condensate $\langle\bar\psi\psi\rangle\not=0$. I present results of numerical simulations of the single-flavour model using...

Modelling the behaviour of strongly interacting fermion sytems with correct symmetry properties presents significant challenges for lattice field theories. Investigating the suitability of domain wall fermions, we explore the locality and the Ginsparg-Wilson error of the Dirac operator in the context of a dynamical 2+1D non-compact Thirring model. We further investigate the eigenvalues of the...

The Hubbard model is an important tool to understand the electrical properties of various materials. More specifically, on the honeycomb lattice it features a quantum phase transition from a semimetal to a Mott insulating state which falls into the Gross-Neveu universality class. In this talk I am going to explain how we confirmed said quantum phase transition by taking advantage of recent...

Quantizing topological excitations beyond a semiclassical approximation is a nontrivial issue. Examples of relevant topological excitations are vortices in (2+1) dimensions. They are the condensed matter analogs of monopoles in particle physics and arise in Bose-Einstein condensates and superfluids. These systems can be described by the (2+1)-d O(2) model, where vortices are present through...

$\mathcal{N}=1$ SUSY Yang-Mills theory is an appealing theoretical framework that has been studied in the literature using different methods, including standard lattice simulations. Among these, the volume-reduced twisted Eguchi-Kawai model, endowed with one adjoint Majorana fermion, could play an important role in studying its large-$N$ limit via the Curci-Veneziano prescription. In this...

We report on an ongoing study of the running coupling of SU(N) pure Yang-Mills theory in the twisted gradient flow scheme (TGF). The study exploits the idea that twisted boundary conditions reduce finite volume effects, leading to an effective size in the twisted plane that combines the number of colours and the torus period. We test this hypothesis by computing the TGF running coupling and...

We describe new theoretical opportunities arising from the possibility to solve the gradient flow (GF) equations taking into account the fermion determinant exactly employing non-iterative solvers. Using this exact GF we can find real saddle points of the lattice action at zero chemical potential and trace their evolution in complex space at non-zero chemical potential. We show that these...

We describe the systematic treatment of the gradient flow at higher orders in perturbation theory and its application within the small flow-time expansion. The results include the coefficients of the gradient-flow definition of the energy-momentum tensor, the quark and the gluon condensates, as well as the hadronic vacuum polarization at next-to-next-to-leading order in the strong coupling....

The 1-loop RG flows in the most general local, renormalizable, Euclidean, classically scale invariant and globally SU(N) invariant theory of vector fields is computed. The total number of dimensionless couplings is 7 and several asymptotically free RG flows are found which are not gauge theories but nonetheless perfectly well-defined Euclidean QFT's. The set of couplings is extended to 9 with...

The one-loop determination of the coefficient $c_{\text{SW}}$ of the Wilson quark

action has been useful, in conjunction with non-perturbative

determinations of $c_{\text{SW}}$, to push the leading cut-off effects for on-shell

quantities to $\mathcal{O}(\alpha^2 a)$, or eventually $\mathcal{O}(a^2)$, if no link-smearing is

employed. These days it is common practice to include some...

In this talk I examine the algorithmic problem of minimal coupling gauge fields of the Yang--Mills type to Quantum Gravity in the approach known as Causal Dynamical Triangulations (CDT) as a step towards studying, ultimately, systems of gravity coupled with bosonic and fermionic matter. I first describe the algorithm for general dimensions and gauge groups and then focus on the results...

Quantizing gravity is one big problem of theoretical physics and it's well-known that general relativity is not renormalizable perturbatively. Yet studies of quantum gravity on lattice have given evidence of the asymptotic safety scenario in which there is a strongly coupled UV fixed point. In this talk, I will talk about our study of the interaction of two scalar particles propagating on...

After a brief introduction of Euclidean dynamical triangulations (EDT) as a lattice approach to quantum gravity, I will discuss the emergence of de Sitter space in 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. This allows to verify that the EDT geometries...

Recent work in Euclidean dynamical triangulations (EDT) has provided compelling evidence for its viability as a formulation of quantum gravity. In particular the lattice value of the renormalized Newton's constant has been obtained by two distinct methods (the binding energy of scalar particles on the lattice, and comparison with the Hawking-Moss instanton). That these calculations yield...

We present a new method to numerically investigate the gravitational collapse of a free, massless scalar quantum field in the semiclassical approximation from a spherically symmetric, coherent initial state. Numerical results are presented for a small ($r_s=3.5 l_p$) wave packet in the l=0 approximation. We observe evidence for the formation of a horizon and study various systematic effects...

If and how gauge theories thermalize is an unanswered question. Partly, this is due to the inability of lattice gauge theory (LGT) simulations to simulate out-of-equilibrium quantum dynamics on classical computers, but also due the difficulty of defining entanglement entropy in lattice gauge theories and finding schemes for its practical computation.

In this work, we study real-time...

We compute a real-time inclusive scattering processes from the spectral function of a Euclidean two-point correlation function in the two-dimensional O(3) model. The intractable inverse problem is overcome using a recently-proposed algorithm to compute the desired spectral function smeared with a variety of finite-width kernels. Systematic errors due to finite volume, continuum limit, and...

In non-Hermitian random matrix theory there are three universality classes for local spectral correlations: the Ginibre class and the nonstandard classes AI$^\dagger$ and AII$^\dagger$. We show that the continuum Dirac operator in two-color QCD coupled to a chiral U(1) gauge field or an imaginary chiral chemical potential falls in class AI$^\dagger$ (AII$^\dagger$) for fermions in pseudoreal...

Abstract: The SU(3) Yang-Mills matrix model coupled to fundamental

fermions is an approximation of quantum chromodynamics (QCD) on a

3-sphere of radius R. The spectrum of this matrix model Hamiltonian

estimated using standard variational methods, and is analyzed in the

strong coupling limit. By employing a renormalization prescription to

determine the dependence of the Yang-Mills...

Lattices on Spherical Manifolds or on the cylindrical boundary of Anti-de-Sitter

space have the potential to explore non-perturbative conformal or near conformal

gauge theories for BSM studies for composite Higgs or Dark Matter. We report

on progress in the use of **Quantum Finite Elements (QFE)** to address renormalization on maximally symmetric spherical simplicial manifolds. The...

We present the necessity of counter terms for Quantum Finite Element (QFE) simulations of $\phi^4$ theory on non-trivial simplicial manifolds with semi-regular lattice spacing. In particular, by computing the local cut-off dependence of UV divergent diagrams we found that the symmetries of the continuum theory are restored for $\phi^4$ theory on the manifolds $\mathbb{S}^2$ and $\mathbb{R}...

We explore holography with geometry fluctuation in the two-dimensional hyperbolic lattice. We present results on the behavior of the boundary-boundary correlation function of scalar fields propagating on discrete 2D random triangulations with the topology of a disk. We use a gravitational action that includes a curvature squared operator which favors a regular tessellation of hyperbolic space...

We consider a massive fermion system having a curved domain-wall

embedded in a square lattice.

As already reported in condensed matter physics, the massless chiral edge modes

appearing at the domain-wall feel "gravity" through the induced spin

connections.

In this work, we embed $S^1$ and $S^2$ domain-wall into Euclidean space

and show how the gravity is detected from the spectrum of...

We analyze the chiral phase transition of the NambuโJona-Lasinio model in the cold and dense region on the lattice developing the Grassmann version of the anisotropic tensor renormalization group algorithm. The model is formulated with the KogutโSusskind fermion action. We use the chiral condensate as an order parameter to investigate the restoration of the chiral symmetry. The first-order...

We make an analysis of the two-dimensional U(1) lattice gauge theory with a ฮธ term by using the tensor renormalization group.

Our numerical result for the free energy shows good consistency with the exact one at finite coupling constant. The topological charge density generates a finite gap at ฮธ=ฯ toward the thermodynamic limit.

In addition finite size scaling analysis of the topological...

We investigate the metal-insulator transition of the (1+1)-dimensional Hubbard model in the path-integral formalism with the tensor renormalization group method. The critical chemical potential $\mu_{\rm c}$ and the critical exponent $\nu$ are determined from the $\mu$ dependence of the electron density in the thermodynamic and zero-temperature limit. Our results for $\mu_{\rm c}$ and $\nu$...

In complex Langevin simulations, the insufficient decay of the probability density near infinity leads to boundary terms that spoil the formal argument for correctness. We present a formulation of this term that is cheaply measurable in lattice models, and in principle allows also the direct estimation of the systematic error of the CL method. Results for various lattice models from XY model...

The complex Langevin method is a general method to treat systems with

complex action, such as QCD at finite density. The formal justification

relies on the absence of certain boundary terms, both at infinity and at

the unavoidable poles of the drift force. In this talk I focus on the

boundary terms at poles for simple models, which so far have not been

discussed in detail. The main result...

Near the second order phase transition point, QCD with two flavours of massless quarks can be approximated by an $O(4)$ model, where a symmetry breaking external field $H$ can be added to play the role of quark mass. The Lee-Yang theorem states that the equation of state in this model has a branch cut along the imaginary $H$ axis for $|\text{Im}[H]|>H_c$, where $H_c$ indicates a second order...

We present a high-precision Monte Carlo study of the $O(3)$ spin theory on the lattice in $D=4$ dimensions. This model exhibits interesting dynamical features, in particular in the broken-symmetry phase, where suitable boundary conditions can be used to enforce monopole-like topological excitations. We investigate the Euclidean time propagation and the features of these excitations close to...

In this talk I present a recent proposal for a novel action for lattice gauge theory for finite systems, which accommodates non-periodic boundary conditions [1]. Drawing on the summation-by-parts formulation of finite differences and finite volume strategies of computational electrodynamics, an action is constructed that implements the proper integral form of Gauss' law and exhibits an...

The Renormalization Group (RG) is one of the central and modern techniques in quantum field theory. Indeed, quantum field theories can be understood as flows between fixed points, representing Conformal Field Theories (CFT's), of the RG. Hence, the search and classification of yet unknown non-trivial CFT's is a legitimate endeavor. Analytical considerations point to the existence of such a...

We consider the role that gauge symmetry breaking terms play on the continuum limit of gauge theories in three dimensions.

As a paradigmatic example we consider scalar electrodynamics in which $N_f$ complex scalar fields interact with a U(1) gauge field. We discuss under which conditions a mass term destabilizes the critical behavior (continuum limit) of the gauge-invariant theory and the...

Universal features of second order phase phase transitions can be investigated by studying the phi-to-the-fourth field theory with the corresponding global symmetry breaking pattern. When gauge symmetries are present, the same technique is usually applied to a gauge invariant order parameter field, as in the Pisarski-Wilczek analysis of the QCD chiral phase transition. Gauge fields are thus...

We address the interplay between local and global symmetries by analyzing the continuum limit of two-dimensional multicomponent scalar lattice gauge theories, endowed by non-abelian local and global invariance. These theories are asymptotically free. By exploiting Monte Carlo simulations and Finite-Size Scaling techniques, we thus provide numerical results concerning the universal behavior of...

We use the two-dimensional Schwinger model to investigate how lattice fermion operators perceive the global topological charge $q\in\mathbf{Z}$ of the gauge background. After a warm-up part devoted to Wilson and staggered fermions, we consider Karsten-Wilczek and Borici-Creutz fermions, which are in the class of minimally doubled lattice fermion actions. The focus is on the eigenvalue spectrum...

The bosonization procedure for Majorana modes based on Clifford algebra-valued degrees of freedom, valid for arbitrary lattices, will be summarized. In the case of honeycomb geometry the Kitaev model emerges. The role of boundary effects and edge states will be discussed.

The euclidean representation of a newly proposed spin system, which is equivalent to a single Majorana fermion in 2+1 dimensions, is derived. The unconstrained euclidean system reveals a mild sign problem which is quantitatively studied. Implementing constraints without breaking positivity will be shortly outlined.

Scalar $\phi^4$ theory in three dimensions with fields in the adjoint of $SU(N)$ is of interest as holographically dual to a model for inflationary cosmology. The theory is perturbatively IR divergent but it was proposed in the past that its dimensionful coupling constant plays the role of the IR regulator nonperturbatively. Using a combination of Markov-Chain-Monte-Carlo simulations of the...

In holographic cosmology, the dual theory may be described by a family of super-renormalisable QFTs in 3 dimensions. In order to obtain cosmological observables, correlators in the massless regime of this QFT are obtained via lattice field theory. Previous work has focused on scalar $\phi^4$ matrix theories in the adjoint representation of SU(N). In this work we present a preliminary...

In the holographic approach to cosmology, cosmological observables are described in terms of correlators of a three-dimensional boundary quantum field theory. As a concrete model, we study the 3D massless SU(N) scalar matrix field theory with a $\phi^4$ interaction. On the lattice, the energy-momentum tensor (EMT) in this theory can mix with the operator $\phi^2$. We utilise the Wilson Flow to...

We study a recently proposed formulation of U(1) lattice field theory with electric and magnetic matter based on the Villain formulation. This discretization allows for a duality that gives rise to relations between weak and strong coupling. We use a worldline version of the model to overcome the complex action problem and discuss suitable algorithms for its simulation. We investigate the...

QED in the presence of strong external fields is relevant to Laser physics, Accelerator physics, Astrophysics and Condensed Matter physics. Standard methods of relativistic quantum mechanics and QED, including perturbation theory, have their limitations. To go beyond this, approximate non-perturbative methods such as the Schwinger-Dyson approach have been applied. We are simulating Lattice QED...

The gradient flow, which exponentially suppresses ultraviolet field fluctuations and removes ultraviolet divergences (up to a multiplicative fermionic wavefunction renormalization), can be used to describe real-space Wilsonian renormalization group transformations and determine the corresponding beta function. We propose a new nonperturbative renormalization scheme for local operators that...

When using deep inelastic scattering (DIS) to probe hadronic structure, we can use the operator product expansion to approximate the product of currents, using the operators' twist to suppress higher order effects. On the lattice, these operators experience power divergent mixing, which we aim to control by introducing the gradient flow. We study an example in perturbation theory.

I discuss symmetric mass generation (SMG) and its relevance to the problem of constructing lattice chiral fermions. A necessary condition for SMG is the

cancellation of certain discrete anomalies which constrain the number of

fermions to multiples of sixteen. I give some examples of models based on

reduced staggered fermions that are capable of SMG.

We construct a four dimensional lattice gauge theory in which fermions acquire mass without

breaking symmetries as a result of gauge interactions. We start from

a $SU(2)$ lattice Yang-Mills theory with staggered fermions transforming under an additional

global $SU(2)$ symmetry. The fermion representations are chosen

so that single site bilinear mass terms vanish identically. A symmetric...

We study a strongly interacting lattice field theory model with two massless flavors of staggered fermions in three space-time dimensions. We consider the phase diagram of the model as a function of two couplings: (1) a lattice current-current interaction $U$, and (2) an on-site four-fermion interaction $U^\prime$. While individually both these interactions drive second order phase transitions...

We present preliminary results for a lattice study of the chiral and continuum limit of pseudoscalar mass and decay constant for $SU(N_c)$ gauge theory with $N_c=3,4,5$ colors and $N_f=2$ degenerate fermions. Clover fermions are used. We fit these observables to predictions of Wilson chiral perturbation theory. Model-averaging is used to determine an appropriate range of quark masses for the...

Gauge anomaly in 4-dimensions can be viewed as a current inflow into an extra-dimension, where the total phase of the fermion partition function is given in a gauge invariant way by the Atiyah-Patodi-Singer(APS) eta-invariant of a 5-dimensional Dirac operator. However, this formalism requires a non-local boundary condition, which makes the physical roles of edge/bulk modes unclear and the...