arXiv subjects

Andreas Athenodorou

Publications and source records attributed to Andreas Athenodorou.

At least 19 recordsLinked to original sources

arXiv2026

A different kind of continuum limit for the three-dimensional U(1) gauge theory

In three-dimensional compact U(1) lattice gauge theory color confinement can be understood analytically through the dynamics of magnetic monopoles. However, its continuum limit is pathological, since the ratio of the glueball masses to the square root of the string tension vanishes as the continuum limit is approached. We investigate a simple extension of the Wilson action in which the total number of lattice monopoles is coupled to an additional parameter $\mu$. By tuning $\beta$ and $\mu$ simultaneously, we identify a line of constant physics along which the ratio of the lightest glueball mass to the square root of the string tension remains constant. We further show that the same scaling is satisfied, within numerical uncertainties, by the other low-lying glueball masses considered in this work. Along this trajectory, the string tension in lattice units decreases with increasing $\beta$, thus suggesting that the modified lattice action may provide a regularization of three-dimensional compact U(1) gauge theory with a physically well-behaved continuum limit.

hep-lat↗

arXiv2025

The spectrum of open confining strings in the large-Nc limit

In this study, we conduct a thorough examination of the spectrum of the open confining string in 3+1 dimensions, commonly referred to as the open flux-tube, across various gauge groups of $SU(N_c)$. Our primary objective is to explore its behaviour as we approach the large-$N_c$ limit and the identification of possible world-sheet axion states. Specifically, we undertake a detailed analysis of the associated spectrum for $N_c=3, 4, 5, 6$. This marks the first systematic investigation of the open flux-tube spectrum within the context of the large-$N_c$ limit. More specifically, we analyse the spectra of flux-tubes that form between a static quark-antiquark pair, considering a significant number of radial excitations and eight irreducible representations characterized by the quantum numbers of angular momentum $\Lambda$, charge conjugation and parity $\eta_{CP}$ and the reflection symmetry $\epsilon$ for $\Lambda=0$. To this purpose we employ a diverse set of suitable operators, an anisotropic action, smearing techniques, and solve the generalized eigenvalue problem. We compare our findings with predictions from the Nambu-Goto string model to assess potential tensions indicative of novel phenomena such as the existence of axion-like state along the flux-tube world-sheet. Notably, we provide undoubted evidence of the existence of a massive axion-like particle with the same mass as the corresponding axion extracted within the context of closed flux-tube. This strengthens the conjecture that the axion is a property of the world-sheet of the QCD string.

hep-lat↗

arXiv2025

Realizing string breaking dynamics in a $Z_2$ lattice gauge theory on quantum hardware

We investigate static and dynamical aspects of string breaking in a $Z_2$ lattice gauge theory coupled to Kogut-Susskind staggered fermions. Using Tensor Network simulations, we demonstrate that the static potential as well as the site-resolved configuration of the matter sites and gauge links allows us to identify the regimes in which string breaking occurs. Furthermore, we develop a variational quantum eigensolver that allows for reliably preparing the ground state of the theory in both the absence and presence of static charges and to capture the static aspects of the phenomenon. Carrying out state preparation on real quantum hardware for up to 19 qubits, we demonstrate its suitability for current quantum devices. In addition, we study the real-time dynamics of a flux tube between two static charges using both Tensor Networks and quantum hardware. Using a trotterization for the time-evolution operator, we are able to show that the breaking process starts with the creation of charges inside the string. These eventually redistribute towards the static charges and screen them, which leads to the breaking of the flux tube.

hep-lat↗

arXiv2025

Reproducibility and Open Science in Lattice Quantum Field Theory

Reproducibility and Open Science are increasingly discussed as essential aspects of the research process. While there are areas where the Lattice community has been ahead of the curve with respect to the broader research world in this space, including early adoption of open publications via the arXiv, and the introduction of the International Lattice Data Grid in the 2000s, there are other areas where lattice practitioners could benefit from practices already adopted in other disciplines. In this Contribution, we report the outcomes of a panel discussion on this topic at the Lattice 2024 conference; after a discussion on motivations for work in this space, and introductory discussions of the relevant experiences of the panelists, we provide summaries of answers to the questions posed by the audience in the panel.

hep-lat↗

arXiv2024

Towards an Effective String Theory for the flux tube

The quest to develop an effective string theory capable of describing the confining flux tube has been a longstanding objective within the theoretical physics community. Recent lattice results indicate that the low-lying spectrum of the flux tube in both three and four dimensions can be partially described by the Nambu-Goto string with minor deviations. However, several excitation states exhibit significant corrections that have remained unexplained until recently. Recent advancements suggest that a Thermodynamic Bethe Ansatz (TBA) analysis, expanded in both $1/R \sqrt{\sigma}$ and the softness of phonons i.e. $p/\sqrt{\sigma}$, can lead to a robust effective string theory for the flux-tube with length $R$. Furthermore, lattice data points to the existence of an axion field on the world-sheet of the flux-tube, implying that an Axionic String Ansatz (ASA) should accompany the Nambu-Goto framework. We will provide compelling evidence in these proceedings that this approach can closely approximate the flux tube data. We will demonstrate this by comparing results obtained for the spectrum of the closed $SU(N_c)$ flux-tube extracted using lattice techniques in four dimensions.

hep-lat↗

arXiv2024

The spectrum of open confining strings in the large-$N_c$ limit

We compute the spectra of open flux tubes formed between a static quark-antiquark pair for various gauge groups in the large-$N_c$ limit, focusing on different symmetries manifested by the quantum numbers of angular momentum, parity, and charge conjugation. Specifically, we present spectra from $N_c=3$ up to $N_c=6$ and for eight different irreducible representations of the symmetry characterizing the flux tube. In this study, we employed an anisotropic Wilson action, a large number of suitable spacial operators, and solved the generalized eigenvalue problem (GEVP) to obtain a significant number of excitations for different combinations of flux tube quantum numbers. The spectra are compared with the Nambu-Goto string model, revealing novel phenomena such as the presence of massive axions in the flux tube spectrum. We find that the mass of the axion in the open flux tube spectra sector is consistent with the mass obtained in the closed flux tube sector.

hep-lat↗

arXiv2024

Confining Strings and the Worldsheet Axion from the Lattice

We present a major update on the spectrum of closed flux tubes in $D=3+1$ $SU(N)$ gauge theories. We measure the excitation spectrum of confining strings wound around a spatial dimension of a size $R$. We do so for the $SU(N)$ Yang-Mills theory with $N=3,5,6$ and for two different values of the lattice spacing. We employ the generalized eigenvalue problem in combination with an extended basis of operators; this enables us to project onto all possible irreducible representations characterised by spin $|J_{\rm modulo \ 4}|$, transverse parity $P_{\perp}$, longitudinal parity $P_{\parallel}$ as well as by longitudinal momentum $p_{\parallel}=\frac{2 \pi q}{R}$, and extract accurate results for approximately $35$ lightest states. Applying the Thermodynamic Bethe Ansatz (TBA) technique for calculating the finite volume spectrum, we confirm that the observed states are well described by the low energy effective theory of a long string consisting of two translational Goldstone bosons (``phonons"), along with a massive pseudoscalar (``the worldsheet axion") coupled to phonons through a $\theta$-term. Moreover, we find that the leading axion-axion and axion-phonon interactions are well approximated by the $T\bar{T}$ deformation of a free axion.

hep-th↗

arXiv2024

Towards the $\beta$ function of SU(2) with adjoint matter using Pauli-Villars fields

The family of SU(2) theories with matter transforming in the adjoint representation has attracted interest from many angles. The two-flavour theory, known as Minimal Walking Technicolor, has a body of evidence pointing to it being in the conformal window with anomalous dimension $\gamma_{*}\approx0.3$. Perturbative calculations would suggest that the one-flavour theory should be confining and chirally broken; however, lattice studies of the theory have been inconclusive. In this contribution we present a first look at efforts towards the computation of the beta function of these theories using the gradient flow methodology. Following an exploration of the phase diagram of the two theories with Wilson fermions and additional Pauli-Villars fields, we tune the bare fermion mass to near the chiral limit, and subsequently generate ensembles at five lattice volumes and a range of lattice spacings.

hep-lat↗

arXiv2024

SU(2) gauge theory with one and two adjoint fermions towards the continuum limit

We provide an extended lattice study of the SU(2) gauge theory coupled to one Dirac fermion flavour ($N_{\mathrm{f}} =1$) transforming in the adjoint representation as the continuum limit is approached. This investigation is supplemented by numerical results obtained for the SU(2) gauge theory with two Dirac fermion flavours ($N_{\mathrm{f}} =2$) transforming in the adjoint representation, for which we perform numerical investigations at three values of the lattice spacing. The purpose of our study is to advance the characterisation of the infrared properties of both theories, which previous investigations have concluded to be in the conformal window. For both, we determine the mass spectrum and the anomalous dimension of the fermion condensate using finite-size hyperscaling of the spectrum, mode number analysis of the Dirac operator (for which we improve on our previous proposal) and the ratio of masses of the lightest spin-2 particle over the lightest scalar. All methods provide a consistent picture, with the anomalous dimension of the condensate $\gamma_*$ decreasing significantly as one approaches the continuum limit for the $N_{\mathrm{f}} = 1$ theory towards a value consistent with $\gamma_* = 0.170(6)$, while for $N_{\mathrm{f}} = 2$ the anomalous dimension converges more rapidly with $\beta$ to a value of $\gamma_* = 0.291(9)$. A chiral perturbation theory analysis shows that the infrared behaviour of both theories is incompatible with the breaking of chiral symmetry.

hep-lat↗

arXiv2023

Confining Strings and Glueballs in $\mathbb{Z}_N$ Gauge Theories

Effective string theory has shown its universal power in the prediction of the spectrum of low-lying excited states of confining strings. Here we study confining flux tubes in $\mathbb{Z}_N$ gauge theories. For the $N=2$ theory, which corresponds to the 3d Ising gauge model, we compute the spectrum of low-lying excitations of confining strings and show that it agrees with the universal Nambu--Goto predictions except for an additional massive scalar resonance. This resonance, however, turns out to be a bulk glueball mixing with the flux tube excitations rather than a genuine string worldsheet state. In general $\mathbb{Z}_N$ gauge theories (dual to clock spin models), we observe a continuous phase transition for $N \geq 4$, while for $N > 5$ it is governed by the $O(2)$ universality class. The critical behavior of the string tension and mass gap is verified to be described by a dangerously irrelevant operator. At large $N$ the glueball spectrum is expected to approach the spectrum of U(1) gauge theory, which is confirmed by our lattice data.

hep-lat↗

arXiv2023

Glueballs in $N_f=1$ QCD

We present an evaluation of the glueball spectrum for configurations produced with $N_f=1$ dynamical fermions as a function of the $m_{\rm PCAC}$ mass. We obtained masses of states that fall into the irreducible representations of the octahedral group of rotations in combination with the quantum numbers of charge conjugation $C$ and parity $P$. Due to the low signal to noise ratio, practically, we can only extract masses for the irreducible representations $R^{PC}=$ $A_1^{++}$, $E^{++}$, $T_2^{++}$ as well as $A_1^{-+}$. We make use of the Generalized Eigenvalue Problem (GEVP) with an operator basis consisting only of gluonic operators. Throughout this work we are aiming towards the identification of the effects of light dynamical quarks on the glueball spectrum and how this compares to the statistically more precise spectrum of SU(3) pure gauge theory. We used large gauge ensembles which consist of ${\sim {~\cal O}}(10 {\rm K})$ configurations. Our findings demonstrate that the low-lying spectrum of the scalar, tensor as well as pseudo-scalar glueballs receive negligible contributions from the inclusion of $N_f=1$ dynamical fermions.

hep-lat↗

arXiv2023

Glueball Spectrum with four light dynamical fermions

We perform a calculation of the glueball spectrum for $N_f=4$ degenerate dynamical fermions with masses corresponding to light pions. We do so by making use of ensembles produced within the framework of maximally twisted fermions by the Extended Twisted Mass Collaboration (ETMC). We obtain masses of states that fall into the irreducible representations of the octahedral group of rotations in combination with the quantum numbers of charge conjugation $C$ and parity $P$; the above quantum numbers result in 20 distinct irreducible representations. We implement the Generalized Eigenvalue Problem (GEVP) using a basis that consists only of gluonic operators. The purpose of this work is to investigate the effect of light dynamical quarks on the glueball spectrum and how this compares to the statistically more accurate spectrum of $SU(3)$ pure gauge theory. Given that glueball states may have broad widths and thus need to be disentangled from all the relevant mixings, we use large ensembles of the order of ${\sim {~\cal O}}(20 {\rm K})$ configurations. Despite the large ensembles, the statistical uncertainties allow us to extract the masses for only a few irreducible representations; namely $A_1^{++}$, $A_1^{-+}$, $E^{++}$ as well as $T_2^{++}$. The results for the scalar $A_1^{++}$ representation show that an additional state appears as the lightest state in the scalar $A_1^{++}$ channel of the glueball spectrum, while the next two excited states are consistent with the lightest two states of the pure gauge theory. To further elucidate the nature of this additional state we perform a calculation using $N_f=2+1+1$ configurations and this demonstrates that it possesses a large quark content. Finally, the ground states of the $E^{++}$ and $T_2^{++}$ tensor channels and of the $A_1^{-+}$ pseudoscalar channel show, at most, minor effects due to the inclusion of dynamical quarks.

hep-lat↗

arXiv2023

Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics

Phase transitions in a non-perturbative regime can be studied by ab initio Lattice Field Theory methods. The status and future research directions for LFT investigations of Quantum Chromo-Dynamics under extreme conditions are reviewed, including properties of hadrons and of the hypothesized QCD axion as inferred from QCD topology in different phases. We discuss phase transitions in strong interactions in an extended parameter space, and the possibility of model building for Dark Matter and Electro-Weak Symmetry Breaking. Methodological challenges are addressed as well, including new developments in Artificial Intelligence geared towards the identification of different phases and transitions.

hep-lat↗

arXiv2023

Excitations of Ising Strings on a Lattice

The 3d Ising model in the low temperature (ferromagnetic) phase describes dynamics of two-dimensional surfaces -- domain walls between clusters of parallel spins. The Kramers--Wannier duality maps these surfaces into worldsheets of confining strings in the Wegner's ${\mathbb Z}_2$ gauge theory. We study the excitation spectrum of long Ising strings by simulating the ${\mathbb Z}_2$ gauge theory on a lattice. We observe a strong mixing between string excitations and the lightest glueball state and do not find indications for light massive resonances on the string worldsheet.

hep-lat↗

arXiv2023

Update on $SU(2)$ with one adjoint Dirac flavor

We present an update of our ongoing study of the SU(2) gauge theory with one flavor of Dirac fermion in the adjoint representation. Compared to our previous results we now have data at larger lattice volumes, smaller values of the fermion mass, and also larger values of $β$. We present data for the spectrum of mesons, baryons, glueballs, and the hybrid fermion-glue state, as well as new estimates of the mass anomalous dimension from both finite-size hyperscaling and the Dirac mode number, and discuss the implications of these data for the presence or otherwise of chiral symmetry breaking in this theory.

hep-lat↗

arXiv2022

Open Science in Lattice Gauge Theory community

Open science aims to make scientific research processes, tools and results accessible to all scientific communities, creating trust in science and enabling digital competences to be realized in research, leading to increased innovation. It provides standard and transparent pathways to conducting research and fosters best practices for collecting, analysing, preserving, sharing and reusing data, software, workflows and other outputs through collaborative networks. Open Science appears to be becoming the norm with its applications spanning throughout the whole research cycle of a project. The importance of making Open Science a reality is nowadays reflected in funding policies, research infrastructure and politics. In these proceedings we present the basic Open Science principles explaining briefly best practices for materialising Open Science. Subsequently, we present the results of the landscaping survey of Open Science in the Lattice Gauge Theories community. Finally, we provide directions in which the Lattice Gauge Theory community could move in order to enhance Openness and FAIRness (Findability, Accessibility, Interoperability, Reusability) in Science.

hep-lat↗

arXiv2022

The glueball spectrum with $N_f=4$ light fermions

We investigate the glueball spectrum for $N_f=4$ fermions corresponding to low pion masses of $m_π\sim 250$MeV. We do so by making use of configurations produced with maximally twisted fermions within the framework of the Extended Twisted Mass Collaboration (ETMC). We extract states that belong to irreducible representations of the octahedral group of rotations $R$ in combination with the quantum numbers of charge conjugation $C$ and parity $P$, i.e. $R^{PC}$. We implement the Generalized Eigenvalue Problem (GEVP) using a basis consisting only of gluonic operators. The purpose of this work is to investigate the effect of light dynamical quarks on the glueball spectrum and how this compares to the statistically more accurate spectrum of the pure gauge theory. We employed large ensembles of the order of ${\sim {~\cal O}}(10 {\rm K})$ configurations for each of three different lattice spacings. Our results demonstrate that in the scalar channel $A_1^{++}$ we obtain an additional, lightest state due to the inclusion of light dynamical quarks while the next two states are consistent with the lightest two states in the pure gauge theory. By contrast the mass of the lightest tensor glueball $J^{PC}=2^{++}$ appears to be insensitive to the inclusion of sea quarks, as is the mass of the lightest pseudoscalar. In addition we perform an investigation of the low lying spectrum of the representation $A_1^{++}$ for $N_f=2+1+1$ twisted mass quarks with low masses and demonstrate that the extra lowest state depends strongly on the pion mass. This suggests that the ground state of the scalar glueball has a large quark content, possibly representing the decay of a glueball to two pions.

hep-lat↗

arXiv2022

The QCD topological susceptibility at high temperatures via staggered fermions spectral projectors

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 focus on the topological susceptibility, related to the axion mass. We present lattice results for the topological susceptibility in QCD at high temperatures obtained by discretizing this observable via spectral projectors on eigenmodes of the staggered Dirac operator, and we compare them with those obtained with the standard gluonic definition. The adoption of the spectral discretization is motivated by the large lattice artifacts affecting the standard gluonic susceptibility, related to the choice of non-chiral fermions in the lattice action.

hep-lat↗