arXiv subjects

Michael Teper

Publications and source records attributed to Michael Teper.

At least 19 recordsLinked to original sources

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

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↗

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↗

arXiv2022

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↗

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 $m_\pi \sim 250$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

More methods for calculating the topological charge (density) of SU(N) lattice gauge fields in 3+1 dimensions

We revisit old ideas that smearing or blocking an SU(N) lattice gauge field, or averaging over an ensemble of fields created in the neighbourhood of that field, can reduce the high frequency fluctuations sufficiently that the naive lattice operator for the topological charge density is able to provide a reliable measure of the topological charge of the field. We show that these three methods do indeed provide additional simple methods for calculating the total topological charge, with smearing particularly economical at current couplings. More interestingly, the ensemble average method can also be used to expose the distribution in space-time of the topological charge and this conceptually transparent, albeit computationally expensive, method provides a useful benchmark against which to compare other methods. Using this benchmark we find that a few smearing steps are also reliable in exposing the distribution in space-time of the topological charge, thus providing a very economical and simple method for doing so. We also use the same benchmark to determine what is the number of `cooling' sweeps one needs to perform in order to expose the charge density reliably.

hep-lat↗

arXiv2021

The torelon spectrum and the world-sheet axion

We present a major update on the spectrum of the closed flux-tube (torelon) in $D=3+1$ $SU(N)$ gauge theories. Namely, we calculate the excitation spectrum of a confining flux-tube which winds around a spatial torus as a function of its length $l$, for short as well as long tubes. We do so for $N=3,5,6$ and two different values of the lattice spacing. Our states are characterised by the quantum numbers of spin $J$, transverse parity $P_{\perp}$, longitudinal parity $P_{\parallel}$ as well as by the longitudinal momentum $p_{\parallel}$. Our extended basis of operators used in combination with the generalized eigenvalue method enables us to extract masses for all irreducible representations characterised by $\{ |J|,P_{\perp},P_{\parallel} \}$. We confirm that most of the low-lying states are well described by the spectrum of the Goddard-Goldstone-Rebbi-Thorn string. In addition we provide strong evidence, that in addition to string like states, massive modes exist on the world-sheet. More precisely the ground state with quantum numbers ${|J|}^{P_{\perp}, P_{\parallel}}=0^{--}$ exhibits a behaviour which is in agreement with the interpretation of being an axion on the world-sheet of the flux-tube. This state arises from a topological interaction term included in the effective world-sheet action. In addition we observe that the second excited state with ${|J|}^{P_{\perp}, P_{\parallel}}=0^{++}$ behaves as a massive mode with mass twice that of the axion.

hep-lat↗

arXiv2021

SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology

We calculate the low-lying glueball spectrum, some string tensions and some properties of topology and the running coupling for SU(N) lattice gauge theories in 3+1 dimensions. We do so for N = 2,3,...12, using lattice simulations with the Wilson plaquette action, and for glueball states in all the representations of the cubic rotation group, for both values of parity and charge conjugation. We extrapolate these results to the continuum limit of each theory and then to N=infinity. For a number of these states we are able to identify their continuum spins with very little ambiguity. We calculate the fundamental string tension and k=2 string tension and investigate the N dependence of the ratio. Using the string tension as the scale, we calculate the running of a lattice coupling and confirm that g(a)**2 varies as 1/N for constant physics as N->oo. We fit our calculated values of the string tension with the 3-loop beta-function, and extract a value for Lambda-MSbar, in units of the string tension, for all our values of N, including SU(3). We calculate the topological charge Q for N=2,..,6 where it fluctuates sufficiently for a plausible estimate of the continuum topological susceptibility. We also calculate the renormalisation of the lattice topological charge, ZQ(beta), for all our SU(N) gauge theories, using a standard definition of the charge, and we provide interpolating formulae, which may be useful in estimating the renormalisation of the lattice theta parameter. We provide quantitative results for how the topological charge `freezes' with decreasing lattice spacing and with increasing N, and show how we cicumvent this issue in our calculations.

hep-lat↗

arXiv2020

The glueball spectrum of SU(3) gauge theory in 3+1 dimension

We calculate the low-lying glueball spectrum of the SU(3) lattice gauge theory in 3+1 dimensions for the range of beta up to beta=6.50 using the standard plaquette action. We do so for states in all the representations R of the cubic rotation group, and for both values of parity P and charge conjugation C. We extrapolate these results to the continuum limit of the theory using the confining string tension as our energy scale. We also present our results in units of the r0 scale and, from that, in terms of physical `GeV' units. For a number of these states we are able to identify their continuum spins J with very little ambiguity. We also calculate the topological charge Q of the lattice gauge fields so as to show that we have sufficient ergodicity throughout our range of beta, and we calculate the multiplicative renormalisation of Q as a function of beta. We also obtain the continuum limit of the SU(3) topological susceptibility.

hep-lat↗

arXiv2019

Glueball Spins in $ D=3$ Yang-Mills

We determine spins of more than 100 low lying glueball states in $D=2+1$ dimensional $SU(4)$ gluodynamics by a lattice calculation. We go up to $J=8$ in the spin value. We compare the resulting spectrum with predictions of the Axionic String Ansatz (ASA). We find a perfect match for 39 lightest states, corresponding to the first four string levels. In particular, this resolves tensions between the ASA predictions and earlier spin determinations. The observed spins of heavier glueballs are also in a good agreement with the ASA. We did not identify any sharp tension between lattice data and the ASA, but more work is needed to fully test the ASA predictions for the spins of 64 states at the fifth string level.

hep-lat↗

arXiv2018

On the spectrum and string tension of U(1) lattice gauge theory in 2+1 dimensions

We calculate the low-lying spectra of glueballs and confining flux tubes in the U(1) lattice gauge theory in 2+1 dimensions. We see that up to modest lattice spacing corrections, the glueball states are consistent with being multiparticle states composed of non-interacting massive JPC=0-- particles. We observe that the ag^2 -> 0 limit is, as expected, unconventional, and follows the well-known saddle-point analysis of Polyakov to a good approximation. The spectrum of closed (winding) flux tubes exhibits the presence of a massive world-sheet excitation whose mass is consistent with that of the bulk screening mass. These U(1) calculations are intended to complement existing lattice calculations of the properties of SU(N) and SO(N) gauge theories in D=2+1.

hep-lat↗

arXiv2018

Pfaffian particles and strings in SO(2N) gauge theories

We introduce (generalised) Pfaffian operators into our lattice calculations of the mass spectra and confining string tensions of SO(2N) gauge theories, complementing the conventional trace operators used in previous lattice calculations. In SO(6) the corresponding `Pfaffian' particles match the negative charge conjugation particles of SU(4), thus resolving a puzzle arising from the observation that SO(6) and SU(4) have the same Lie algebra. The same holds true (but much more trivially) for SO(2) and U(1). For SO(4) the Pfaffian particles are degenerate with, but orthogonal to, those obtained with the usual single trace operators. That is to say, there is a doubling of the spectrum, as one might expect given that the Lie algebra of SO(4) is the same as that of SU(2)xSU(2). Additional SO(8) and SO(10) calculations of the Pfaffian spectrum confirm the naive expectation that these masses increase with N, so that they cease to play a role in the physics of SO(N) gauge theories as N-->oo. We also calculate the energies of Pfaffian `strings' in these gauge theories. Although all our lattice calculations are for gauge theories in D=2+1, similar conclusions should hold for D=3+1.

hep-lat↗

arXiv2018

SO(4), SO(3) and SU(2) gauge theories in 2+1 dimensions: comparing glueball spectra and string tensions

We improve upon recent calculations of the low-lying `glueball' spectra of SO(3) and SO(4) lattice gauge theories in 2+1 dimensions, and compare the resulting continuum extrapolations with SU(2). We find that these are reasonably consistent, as are the SU(2) and SO(4) string tensions when these are corrected for the differing representations of the flux. All this indicates that the different global properties of these groups do not play a significant role in the low-lying physics.

hep-lat↗

arXiv2017

Spinorial flux tubes in SO(N) gauge theories in 2+1 dimensions

We investigate whether one can observe in SO(3) and SO(4) (lattice) gauge theories the presence of spinorial flux tubes, i.e. ones that correspond to the fundamental representation of SU(2); and similarly for SO(6) and SU(4). We do so by calculating the finite volume dependence of the JP=2+ glueball in 2+1 dimensions, using lattice simulations. We show how this provides strong evidence that these SO(N) gauge theories contain states that are composed of pairs of (conjugate) winding spinorial flux tubes, i.e. ones that are in the (anti)fundamental of the corresponding SU(N') gauge theories. Moreover, these two flux tubes can be arbitrarily far apart. This is so despite the fact that the fields that are available in the SO(N) lattice field theories do not appear to allow us to construct operators that project onto single spinorial flux tubes.

hep-lat↗

arXiv2017

On the mass of the world-sheet `axion' in SU(N) gauge theories in 3+1 dimensions

There is numerical evidence that the world sheet action of the confining flux tube in D=3+1 SU(N) gauge theories contains a massive excitation with 0- quantum numbers whose mass shows some decrease as one goes from SU(3) to SU(5). It has furthermore been shown that this particle is naturally described as arising from a topological interaction term in the world-sheet action, so that one can describe it as being `axion'-like. Recently it has been pointed out that if the mass of this `axion' vanishes as N -> oo then it becomes possible for the world sheet theory to be integrable in the planar limit. In this paper we perform lattice calculations of this `axion' mass from SU(2) to SU(12), which allows us to make a controlled extrapolation to N=oo and so test this interesting possibility. We find that the `axion' does not in fact become massless as N -> oo. So if the theory is to possess planar integrability then it must be some other world sheet excitation that becomes massless in the planar limit.

hep-lat↗

arXiv2017

SO(N) gauge theories in 2+1 dimensions: glueball spectra and confinement

We calculate the spectrum of light glueballs and the string tension in a number of SO(N) lattice gauge theories in 2+1 dimensions, with N in the range from N=3 to N=16. After extrapolating to the continuum limit and then to N=oo we compare to the spectrum and string tension of the SU(N=oo) gauge theory and find that the most reliably and precisely calculated physical quantities are consistent in that limit. We also compare the glueball spectra of those pairs of SO(N) and SU(N') theories that possess the same Lie algebra, i.e. SO(3) and SU(2), SO(4) and SU(2)xSU(2), SO(6) and SU(4), and find that for the very lightest glueballs the spectra are consistent within each such pair, as are the string tensions and the couplings. Where there are apparent discrepancies they are typically for heavier glueballs, where the systematic errors are much harder to control. We calculate the SO(N) string tensions with a particular focus on the confining properties of SO(2N+1) theories which, unlike SO(2N) theories, possess a trivial centre. We find that for both the light glueballs and for the string tension SO(2N) and SO(2N+1) gauge theories appear to form a single smooth sequence.

hep-lat↗