arXiv subjects

Michael Teper

Publications and source records attributed to Michael Teper.

At least 37 records · Page 2Linked to original sources

arXiv2016

SU(N) gauge theories in 2+1 dimensions: glueball spectra and k-string tensions

We calculate the low-lying glueball spectrum and various string tensions in SU(N) lattice gauge theories in 2+1 dimensions, and extrapolate the results to the continuum limit. We do so for for the range N=2 to N=16 so as to control the N-dependence with a useful precision. We observe a number of striking near-degeneracies in the various J^PC sectors of the glueball spectrum, in particular between C=+ and C=- states. We calculate the string tensions of flux tubes in a number of representations, and provide evidence that the leading correction to the N-dependence of the k-string tensions varies as 1/N rather than 1/N^2, and that the dominant binding of k fundamental flux tubes into a k-string is via pairwise interactions. We comment on the possible implications of our results for the dynamics of these gauge theories.

hep-lat↗

arXiv2016

The deconfining phase transition of SO(N) gauge theories in 2+1 dimensions

We calculate the deconfining temperature of SO(N) gauge theories in 2+1 dimensions, and determine the order of the phase transition as a function of N, for various values of N in the range [4,16]. We do so by extrapolating our lattice results to the infinite volume limit, and then to the continuum limit, for each value of N. We then extrapolate to the N=infinity limit and observe that the SO(N) and SU(N) deconfining temperatures agree in that limit. We find that the the deconfining temperatures of all the SO(N) gauge theories appear to follow a single smooth function of N, despite the lack of a non-trivial centre for odd N. We also compare the deconfining temperatures of SO(6) with SU(4), and of SO(4) with SU(2)xSU(2), motivated by the fact that these pairs of gauge theories share the same Lie algebras.

hep-lat↗

arXiv2016

On the weak N-dependence of SO(N) and SU(N) gauge theories in 2+1 dimensions

We consider (continuum) mass ratios of the lightest `glueballs' as a function of N for SO(N) and SU(N) lattice gauge theories in D=2+1. We observe that the leading large N correction is usually sufficient to describe the N-dependence of SO(N.geq.3) and SU(N.geq.2), within the errors of the numerical calculation. Just as interesting is the fact that the coefficient of this correction almost invariably turns out to be anomalously small, for both SO(N) and SU(N). We point out that this can follow naturally from the strong constraints that one naively expects from the Lie algebra equivalence between certain SO(N) and SU(N') theories and the equivalence of SO(infinity) and SU(infinity). The same argument for a weak N-dependence can in principle apply to SU(N) and SO(N) gauge theories in D=3+1.

hep-lat↗

arXiv2016

Closed flux tubes in D=2+1 SU(N) gauge theories: dynamics and effective string description

We extend our earlier calculations of the spectrum of closed flux tubes in SU(N) gauge theories in 2+1 dimensions, with a focus on questions raised by recent theoretical progress on the effective string action of long flux tubes and the world-sheet action for flux tubes of moderate lengths. Our new calculations in SU(4) and SU(8) provide evidence that the leading O(1/l^gamma) non-universal correction to the flux tube ground state energy does indeed have a power gamma greater than or equal to 7. We perform a study in SU(2), where we can traverse the length at which the Nambu-Goto ground state becomes tachyonic, to obtain an all-N view of the spectrum. Our comparison of the k=2 flux tube excitation energies in SU(4) and SU(6) suggests that the massive world sheet excitation associated with the k=2 binding has a scale that knows about the group and hence the theory in the bulk, and we comment on the potential implications of world sheet massive modes for the bulk spectrum. We provide a quantitative analysis of the surprising (near-)orthogonality of flux tubes carrying flux in different SU(N) representations, which implies that their screening by gluons is highly suppressed even at small N.

hep-lat↗

arXiv2015

Deconfining temperatures in SO(N) and SU(N) gauge theories

We present our current results for the deconfining temperatures in SO(N) gauge theories in 2+1 dimensions. SO(2N) theories may help us to understand QCD at finite chemical potential since there is a large-N orbifold equivalence between SO(2N) QCD-like theories and SU(N) QCD, and SO(2N) theories do not have the sign problem present in QCD. We show that the deconfining temperatures in these two theories match at the large-N limit. We also present results for SO(2N+1) gauge theories and compare results for SO(6) with SU(4) gauge theories, which have the same Lie algebras but different centres.

hep-lat↗

arXiv2013

Stable and quasi-stable confining SU(N) strings in D=2+1

We investigate the low-lying spectrum of closed confining flux-tubes that wind around a spatial torus in D=2+1 and carry flux in different representations of SU(N). We focus on our most recent calculations for N=6 and β=171, where the calculated low-energy physics is very close to the continuum and large-N limits. We investigate the adjoint, 84, 120, k = 2A, 2S and k = 3A, 3M, 3S representations and show that the corresponding flux-tubes do exist. Similarly to the results for the fundamental representation, the ground state of a flux-tube with momentum along its axis appears to be well described by Nambu-Goto all the way down to very short tubes. In contrast, excited states have much larger deviations from Nambu-Goto. We discuss whether these states are non-string-like and associated with excitations of massive flux-tube modes.

hep-lat↗

arXiv2013

SO(2N) and SU(N) gauge theories

We present our preliminary results of SO(2N) gauge theories, approaching the large-N limit. SO(2N) theories may help us to understand QCD at finite chemical potential since there is an orbifold equivalence between SO(2N) and SU(N) gauge theories at large-N and SO(2N) theories do not have the sign problem present in QCD. We consider the string tensions, mass spectra, and deconfinement temperatures in the SO(2N) pure gauge theories in 2+1 dimensions, comparing them to their corresponding SU(N) theories.

hep-lat↗

arXiv2013

Closed flux tubes in higher representations and their string description in D=2+1 SU(N) gauge theories

We calculate, numerically, the low-lying spectrum of closed confining flux tubes that carry flux in different representations of SU(N). We do so for SU(6) at beta=171, where the calculated low-energy physics is very close to the continuum limit and, in many respects, also close to N=infinity. We focus on the adjoint, 84, 120, k=2A,2S and k=3A,3M,3S representations and provide evidence that the corresponding flux tubes, albeit mostly unstable, do in fact exist. We observe that the ground state of a flux tube with momentum along its axis appears to be well defined in all cases and is well described by the Nambu-Goto free string spectrum, all the way down to very small lengths, just as it is for flux tubes carrying fundamental flux. Excited states, however, typically show very much larger deviations from Nambu-Goto than the corresponding excitations of fundamental flux tubes and, indeed, cannot be extracted in many cases. We discuss whether what we are seeing here are separate stringy and massive modes or simply large corrections to energy levels that will become string-like at larger lengths.

hep-lat↗

arXiv2012

SO(2N) and SU(N) gauge theories in 2+1 dimensions

We perform an exploratory investigation of how rapidly the physics of SO(2N) gauge theories approaches its N=oo limit. This question has recently become topical because SO(2N) gauge theories are orbifold equivalent to SU(N) gauge theories, but do not have a finite chemical potential sign problem. We consider only the pure gauge theory and, because of the inconvenient location of the lattice strong-to-weak coupling 'bulk' transition in 3+1 dimensions, we largely confine our numerical calculations to 2+1 dimensions. We discuss analytic expectations in both D=2+1 and D=3+1, show that the SO(6) and SU(4) spectra do indeed appear to be the same, and show that a number of mass ratios do indeed appear to agree in the large-N limit. In particular SO(6) and SU(3) gauge theories are quite similar except for the values of the string tension and coupling, both of which differences can be readily understood.

hep-lat↗

arXiv2011

Closed flux tubes and their string description in D=2+1 SU(N) gauge theories

We carry out lattice calculations of the spectrum of confining flux tubes that wind around a spatial torus of variable length l, in 2+1 dimensions. We compare the energies of the lowest c.30 states to the free string Nambu-Goto model and to recent results on the universal properties of effective string actions. Our most useful calculations are in SU(6) at a small lattice spacing, which we check is very close to the large-N continuum limit. We find that the energies, En(l), are remarkably close to the predictions of the free string Nambu-Goto model, even well below the critical length at which the expansion of the Nambu-Goto energy in powers of 1/l diverges and the series needs to be resummed. Our analysis of the ground state supports the universality of the O(1/l) and the O(1/l^3) corrections to l.sigma, and we find that the deviations from Nambu-Goto at small l prefer a leading correction that is O(1/l^7), consistent with theoretical expectations. We find that the low-lying states that contain a single phonon excitation are also consistent with the leading O(1/l^7) correction dominating down to the smallest values of l. By contrast our analysis of the other light excited states clearly shows that for these states the corrections at smaller l resum to a much smaller effective power. Finally, and in contrast to our recent calculations in D=3+1, we find no evidence for the presence of any non-stringy states that could indicate the excitation of massive flux tube modes.

hep-lat↗

arXiv2010

Closed flux tubes and their string description in D=3+1 SU(N) gauge theories

We calculate the energy spectrum of a confining flux tube that is closed around a spatial torus, as a function of its length l. We do so for various SU(N) gauge theories in 3+1 dimensions, and for various values of spin, parity and longitudinal momentum. We are able to present usefully accurate results for about 20 of the lightest such states, for a range of l that begins close to the (finite volume) deconfining phase transition, and extends up to l.sqrt(K)~6 (where K is the string tension). We find that most of these low-lying states are well described by the spectrum of the Nambu-Goto free string theory in flat space-time. Remarkably, this is so not only at the larger values of l, where the gap between the ground state energy and the low-lying excitations becomes small compared to the mass gap, but also down to much shorter lengths where these excitation energies become large compared to sqrt(K), the flux-tube no longer `looks' anything like a thin string, and an expansion of the effective string action in powers of 1/l no longer converges. All this is for flux in the fundamental representation. We also calculate the k=2 (anti)symmetric ground states and these show larger corrections at small l. So far all this closely resembles our earlier findings in 2+1 dimensions. However, and in contrast to the situation in D=2+1, we also find that there are some states, with J,P=0,- quantum numbers, that show large deviations from the Nambu-Goto spectrum. We investigate the possibility that (some of) these states may encode the massive modes associated with the internal structure of the flux tube, and we discuss how the precocious free string behaviour of most states constrains the effective string action, on which much interesting theoretical progress has recently been made.

hep-lat↗

arXiv2010

Delineating the conformal window

We identify and characterise the conformal window in gauge theories relevant for beyond the standard model building, e.g. Technicolour, using the criteria of metric confinement and causal analytic couplings, which are known to be consistent with the phase diagram of supersymmetric QCD from Seiberg duality. Using these criteria we find perturbation theory to be consistent throughout the predicted conformal window for several of these gauge theories and we discuss recent lattice results in the light of our findings.

hep-ph↗

arXiv2009

Large N and confining flux tubes as strings - a view from the lattice

I begin these three lectures by describing some of the useful things that we have learned about large-N gauge theories using lattice simulations. For example that the theory is confining in that limit, that for many quantities SU(3) is close to SU(oo), and that this includes the strongly coupled gluon plasma just above Tc, thus providing some of the justification needed to make use of gauge-gravity duality in analysing QCD at RHIC/LHC temperatures. I then turn, in a more detailed discussion, to recent progress on the problem of what effective string theory describes confining flux tubes. I describe lattice calculations of the energy spectrum of closed loops of confining flux, and some dramatic analytic progress in extending the `universal Luscher correction' to terms that are of higher order in 1/l, where l is the length of the string. Both approaches point increasingly to the Nambu-Goto free string theory as being the appropriate starting point for describing string-like degrees of freedom in SU(N) gauge theories.

hep-lat↗

arXiv2009

The spectrum of closed loops of fundamental flux in D = 3+1 SU(N) gauge theories

We study the spectrum of closed flux tubes in four dimensional SU(N) gauge theories. We do so by calculating the energies of the low lying states with the variational technique (whose basis consists of about ~700 operators). We study states of different values of angular momentum, transversal parity, longitudinal parity, and longitudinal momentum, and compare the results with effective string theories (ESTs) such as the Nambu-Goto (NG) model. Most of our states agree very well with the Nambu-Goto predictions and since most of our flux-tubes' lengths are outside the radius of convergence of the ESTs, then for some states it is only the NG that predicts the spectrum well. This strongly suggests that the ESTs can be re-summed. Nonetheless, there are a few states (all with negative parity and in the same representation of the lattice rotation group) that exhibit large deviations from the NG predictions; these deviations might provide clues to the nature of the effective string theory describing the large-N QCD string.

hep-lat↗

arXiv2009

On the spectrum of closed k=2 flux tubes in D=2+1 SU(N) gauge theories

We calculate the energy spectrum of a k=2 flux tube that is closed around a spatial torus, as a function of its length l. We do so for SU(4) and SU(5) gauge theories in 2 space dimensions. We find that to a very good approximation the eigenstates belong to the irreducible representations of the SU(N) group rather than just to its center, Z_N. We obtain convincing evidence that the low-lying states are, for l not too small, very close to those of the Nambu-Goto free string theory (in flat space-time). The correction terms appear to be typically of O(1) in appropriate units, much as one would expect if the bosonic string model were an effective string theory for the dynamics of these flux tubes. This is in marked contrast to the case of fundamental flux tubes where such corrections have been found to be unnaturally small. Moreover we find that these corrections appear to be particularly small when the `phonons' along the string have the same momentum, and large when their momentum is opposite. This provides information about the detailed nature of the interactions in the effective string theory. We have searched for, but not found, extra states that would arise from the excitation of the massive modes presumably associated with the non-trivial structure of the flux tube.

hep-lat↗

arXiv2008

Large N

I review some of the things we have learned about large N gauge theories (and QCD at N=oo) from lattice calculations in recent years. I point to some open problems.

hep-lat↗

arXiv2008

Spectrum of closed k-strings in D=2+1

We calculate the excitation spectrumof closed k-strings in 2+1 dimensional SU(N) gauge theories for N = 4, 5 and k = 2. Our results demonstrate that the low-lying spectrum of the k = 2 string falls into sectors that belong to nearly pure antisymmetric and symmetric representations, showing that k-strings know not only about the centre of the group, but also about the full group. We also observe that the lightest states in each irreducible representation are consistent with what one would expect from an effective string theory that belongs to the same bosonic universality class (Nambu-Goto) as the fundamental string. We find that the corrections compared to the free string theory are of O(1), in striking contrast to the very small correction observed for the fundamental string. We also observe unbound w = 2 states.

hep-lat↗

arXiv2008

The deconfining phase transition in D=2+1 SU(N) gauge theories

We study the deconfining transition of SU(N) gauge theories in 2+1 dimensions for N ranging between N=2 and N=8. We confirm that the transition is second order for N<4 and first order for N>4. For the more delicate case of SU(4) all our evidence points to the transition being weakly first order. After extrapolating to the continuum limit, we obtain a deconfining temperature that can be well fitted by Tc/sqrt(sigma) = 0.9026(23) + 0.880(43)/N^2 for all N.

hep-lat↗