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Michael Teper

Publications and source records attributed to Michael Teper.

At least 55 records · Page 3Linked to original sources
arXiv2008

On the running of the bare coupling in SU(N) lattice gauge theories

Interpreting the way that the SU(3) bare lattice coupling runs with the lattice spacing is complicated by the fact that there is a smooth cross-over region in which the strong coupling expansion transforms into a weak-coupling one. For N > 4, however, there is a first order bulk transition that cleanly separates the strong and weak coupling regimes. We find that in this case the calculated string tension can be readily fitted throughout the weak coupling region by a standard 3-loop expression modified by lattice spacing corrections of the expected form. While our fits demand the presence of the latter, they do not constrain the perturbative coupling scheme enough to enable us to extract a usefully accurate value of a(beta) in units of Lambda_MSbar. To resolve this ambiguity we turn to SU(3) where we use the Schrodinger Functional coupling scheme to extract a value of r_0 x Lambda_SF as a benchmark. We then find that the Parisi mean-field improved coupling scheme closely reproduces this result. We also develop a comparison between different schemes that does not rely on the calculation of any physical quantity and which can therefore be applied much further into weak coupling. Again the Parisi scheme is favoured over the others that we compare. Using the mean-field scheme we have fitted the values of the string tension that have been calculated for N=2 to N=8, to obtain Lambda_MSbar/sqrt(sigma) = 0.503(2)(40) + 0.33(3)(3)/N^2 for N > 2, where the first error is statistical and the second is our estimate of the systematic error from all sources.

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arXiv2008

Closed k-strings in SU(N) gauge theories : 2+1 dimensions

We calculate the ground state energies of closed k-strings in (2+1)-dimensional SU(N) gauge theories, for N=4,5,6,8 and k=2,3,4. From the dependence of the ground state energy on the string length, we infer that such k-strings are described by an effective string theory that is in the same bosonic universality class (Nambu-Goto) as the fundamental string. When we compare the continuum k-string tensions to the corresponding fundamental string tensions, we find that the ratios are close to, but typically 1-2 percent above, the Casimir scaling values favoured by some theoretical approaches. Fitting the N-dependence in a model-independent way favours an expansion in 1/N (as in Casimir scaling) rather than the 1/N^2 that is suggested by naive colour counting. We also observe that the low-lying spectrum of k-string states falls into sectors that belong to particular irreducible representations of SU(N), demonstrating that the dynamics of string binding knows about the full gauge group and not just about its centre.

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arXiv2007

Structure and properties of the vacuum of the Twisted Eguchi-Kawai model

We investigate numerically the phase structure of the Twisted Eguchi-Kawai (TEK) model in four dimensions. In the numerical simulations of the zero temperature TEK model (using a symmetric twist) we observe the existence of new phases that break its centre symmetry at intermediate lattice couplings and for large SU(N) gauge groups. This effect can be explained by the contribution of diagonal configurations with collapsed eigenvalues, which are particular cases of ``generalised fluxons''. We also investigate finite temperature versions of the TEK model using anisotropic lattice couplings, where in particular we find van Baal fluxons contributing at large anisotropies.

hep-lat↗
arXiv2007

The running of the bare coupling in SU(N) gauge theories

For N>4 there is a first order bulk transition that cleanly separates the strong and weak coupling regimes of SU(N) lattice gauge theories with the plaquette action. We find that in this case the calculated string tension can be readily fitted throughout the weak coupling region by a standard 3-loop perturbative expression modified by lattice spacing corrections of the expected form. While our fits demand the presence of the latter, they are not constraining enough to tell us which of the various bare coupling schemes is a `good' one, in the sense that terms in the beta-function beyond 3-loops are indeed negligible (in the relevant range of scales). To resolve this ambiguity we work in SU(3), using the Schrodinger Functional coupling scheme as a benchmark, and find that the Parisi mean-field improved coupling scheme matches it very well. Using the latter scheme, we have fitted the values of the string tension that have been calculated for SU(3) to SU(8), to obtain Lambda_MSbar/sqrt(sigma) = 0.503(2)(40) + 0.33(3)(3)/N**2, where the first error is statistical and the second is our estimate of the systematic error from all sources.

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arXiv2007

The spectrum of closed loops of fundamental flux in D=2+1 SU(N) gauge theories

We study the closed-string spectrum of SU(N) gauge theories in the fundamental representation in 2+1 dimensions. We calculate the energies of the lowest lying ~ 30 states using a large variety of operators characterised by the quantum numbers of parity and longitudinal momentum. We find that our results for the ground state are very well approximated by the Nambu-Goto (NG) predictions even for short strings. For the excited states, we observe significant deviations from the NG predictions only for very short strings and they decrease rapidly with increasing string length. Finally, we see that Nambu-Goto provides a much better description of our results than the effective string theoretical predictions. We discuss the continuum and large-N limits.

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arXiv2007

The closed string spectrum of SU(N) gauge theories in 2+1 dimensions

We use lattice techniques to study the closed-string spectrum of SU(N) gauge theories in 2+1 dimensions. We calculate the energies of the lowest lying ~30 states for strings with lengths between l ~ 0.45 fm and l ~ 3 fm, and compare to different theoretical predictions. We obtain unambiguous evidence that the closed-strings are in the universality class of the Nambu-Goto free bosonic string. Moreover, we clearly see that our data can be described by a covariant string theory with a small/moderate correction down to very short distance scales, and possibly on all distance scales at large-N.

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arXiv2007

Strings in SU(N) gauge theories in 2+1 dimensions: beyond the fundamental representation

We calculate energies and tensions of closed k-strings in (2+1)-dimensional SU(N) gauge theories with N=4,5,6,8. When we study the dependence of the ground state energy on the string length, we find that it is well described by a Nambu-Goto (NG) free bosonic string for large lengths. At shorter lengths we see deviations which we fit, and this allows us to control the systematic error involved in extracting the tension. We compare the resulting string tensions with Casimir scaling, which we find to be lower than our data by 1%-4%. Extrapolating our results to N=oo we see that our data fits more naturally to 1/N rather than 1/N^2 corrections. Finally, we see that the full spectrum of the k-string states falls into sectors that belong to particular irreducible representations of SU(N).

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arXiv2006

Symmetry Breaking In Twisted Eguchi-Kawai Models

We present numerical evidence for the spontaneous breaking of the centre symmetry of four-dimensional twisted Eguchi-Kawai models with SU(N) gauge group and symmetric twist, for sufficiently large N. We find that for N greater or equal than 100 this occurs for a wide range of bare couplings. Moreover for N less or equal than 144, where we have been able to perform detailed calculations, there is no window of couplings where the physically interesting confined and deconfined phases appear in the reduced model. We provide a possible interpretation for this in terms of generalised 'fluxon' configurations. We discuss the implications of our findings for the validity and utility of space-time reduced models as N goes to infinity.

hep-th↗
arXiv2006

A precise calculation of the fundamental string tension in SU(N) gauge theories in 2+1 dimensions

We use lattice techniques to calculate the continuum string tensions of SU(N) gauge theories in 2+1 dimensions. We attempt to control all systematic errors at a level that allows us to perform a precise test of the analytic prediction of Karabali, Kim and Nair. We find that their prediction is within 3% of our values for all N and that the discrepancy decreases with increasing N. When we extrapolate our results to N=oo we find that there remains a discrepancy of ~ 1%, which is a convincing ~6 sigma effect. Thus, while the Karabali-Nair analysis is remarkably accurate at N=oo, it is not exact.

hep-th↗
arXiv2006

String tensions of SU(N) gauge theories in 2+1 dimensions

We calculate the energy spectrum of closed strings in SU(N) gauge theories with N=2,3,4,6,8 in 2+1 dimensions to a high accuracy. We attempt to control all systematic errors, and this allows us to perform a precise comparison with different theoretical predictions. When we study the dependence of the string mass on its length L we find that the Nambu-Goto prediction is a very good approximation down to relatively short lengths, where the Luscher term alone is insufficient. We then isolate the corrections to the Luscher term, and compare them to recent theoretical predictions, which indeed seem to be mildly preferred by the data. When we take these corrections into account and extract string tensions from the string masses, we find that their continuum limit is lower by 2%-1% from the predictions of Karabli, Kim, and Nair. The discrepancy decreases with N, but when we extrapolate our results to N=oo we still find a discrepancy of 0.88% which is a 4.5 sigma effect.

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arXiv2006

Strong to weak coupling transitions of SU(N) gauge theories in 2+1 dimensions

We find a strong-to-weak coupling cross-over in D=2+1 SU(N) lattice gauge theories that appears to become a third-order phase transition at N=\infty, in a similar way to the Gross-Witten transition in the D=1+1 SU(N\to\infty) lattice gauge theory. There is, in addition, a peak in the specific heat at approximately the same coupling that increases with N, which is connected to Z_N monopoles (instantons), reminiscent of the first order bulk transition that occurs in D=3+1 for N > 4. Our calculations are not precise enough to determine whether this peak is due to a second-order phase transition at N=\infty or to a third-order phase transition with different critical behaviour to that of the Gross-Witten transition. We investigate whether the trace of the Wilson loop has a non-analyticity in the coupling at some critical area, but find no evidence for this. However we do find that, just as one can prove occurs in D=1+1, the eigenvalue density of a Wilson loop forms a gap at N=\infty at a critical value of its trace. We show that this gap formation is in fact a corollary of a remarkable similarity between the eigenvalue spectra of Wilson loops in D=1+1 and D=2+1 (and indeed D=3+1): for the same value of the trace, the eigenvalue spectra are nearly identical. This holds for finite as well as infinite N; irrespective of the Wilson loop size in lattice units; and for Polyakov as well as Wilson loops.

hep-th↗
arXiv2006

Strong to weak coupling transitions of SU(N) gauge theories in 2+1 dimensions

We investigate strong-to-weak coupling transitions in D=2+1 SU(N->oo) gauge theories, by simulating lattice theories with a Wilson plaquette action. We find that there is a strong-to-weak coupling cross-over in the lattice theory that appears to become a third-order phase transition at N=oo, in a manner that is essentially identical to the Gross-Witten transition in the D=1+1 SU(oo) lattice gauge theory. There is also evidence for a second order transition at N=oo at approximately the same coupling, which is connected with centre monopoles (instantons) and so analogues to the first order bulk transition that occurs in D=3+1 lattice gauge theories for N>4. We show that as the lattice spacing is reduced, the N=oo gauge theory on a finite 3-torus suffers a sequence of (apparently) first-order ZN symmetry breaking transitions associated with each of the tori (ordered by size). We discuss how these transitions can be understood in terms of a sequence of deconfining transitions on ever-more dimensionally reduced gauge theories.We investigate whether the trace of the Wilson loop has a non-analyticity in the coupling at some critical area, but find no evidence for this although, just as in D=1+1,the eigenvalue density of a Wilson loop forms a gap at N=oo for a critical trace. The physical implications of this are unclear.The gap formation is a special case of a remarkable similarity between the eigenvalue spectra of Wilson loops in D=1+1 and D=2+1 (and indeed D=3+1): for the same value of the trace, the eigenvalue spectra are nearly identical.This holds for finite as well as infinite N; irrespective of the Wilson loop size in lattice units; and for Polyakov as well as Wilson loops.

hep-th↗
arXiv2006

In search of a Hagedorn transition in SU(N) lattice gauge theories at large-N

We investigate on the lattice the metastable confined phase above Tc in SU(N) gauge theories, for N=8,10, and 12. In particular we focus on the decrease with the temperature of the mass of the lightest state that couples to Polyakov loops. We find that at T=Tc the corresponding effective string tension σ_{eff}(T) is approximately half its value at T=0, and that as we increase T beyond Tc, while remaining in the confined phase, σ_{eff}(T) continues to decrease. We extrapolate σ_{eff}(T) to even higher temperatures, and interpret the temperature where it vanishes as the Hagedorn temperature T_H. For SU(12) we find that T_H/Tc=1.116(9), when we use the exponent of the three-dimensional XY model for the extrapolation, which seems to be slightly preferred over a mean-field exponent by our data.

hep-lat↗
arXiv2005

The pressure of the SU(N) lattice gauge theory at large-N

We calculate bulk thermodynamic properties, such as the pressure, energy density, and entropy, in SU(4) and SU(8) lattice gauge theories, for the range of temperatures T <= 2.0Tc and T <= 1.6Tc respectively. We find that the N=4,8 results are very close to each other, and to what one finds in SU(3), and are far from the asymptotic free-gas value. We conclude that any explanation of the high-T pressure (or entropy) deficit must be such as to survive the N-->oo limit. We give some examples of this constraint in action and comment on what this implies for the relevance of gravity duals.

hep-lat↗
arXiv2005

The pressure and a possible hidden Hagedorn transition at large-N

In the first part of this contribution we present a numerical study motivated by recent attempts to understand the nonperturbative aspects of QCD at temperatures T~ a few times the deconfinement temperature Tc. We focus on the pure gauge theory, and ask whether the deficit in pressure and entropy, with respect to their free-gas values, is particular to SU(3). We find that the deficit in SU(4),SU(8) for T>= 2Tc,1.6 Tc, respectively, is remarkably close to that of SU(3). This suggests a similar deficit for SU(oo), which is fortunate since this theory is simpler, and can serve to constrain the possible dynamics underlying the deficits. In the second part we seek for signs of a Hagedorn temperature T_H in pure lattice SU(N) gauge theories with N=8,10,12. Since one expects T_H>Tc, we measure masses of strings in the metastable confined phase above Tc, and extrapolatethem to zero to estimate T_H. For SU(12) we find that T_H/Tc=1.116(9), when we extrapolate with a critical exponentof the three dimensional XY model, which seems to be preferred over a mean field exponent by our data.

hep-lat↗
arXiv2005

Casimir Scaling of domain wall tensions in the deconfined phase of D=3+1 SU(N) gauge theories

We perform lattice calculations of the spatial 't Hooft k-string tensions in the deconfined phase of SU(N) gauge theories for N=2,3,4,6. These equal (up to a factor of T) the surface tensions of the domain walls between the corresponding (Euclidean) deconfined phases. For T much larger than T_c our results match on to the known perturbative result, which exhibits Casimir Scaling, being proportional to k(N-k). At lower T the coupling becomes stronger and, not surprisingly, our calculations show large deviations from the perturbative T-dependence. Despite this we find that the behaviour proportional to k(N-k) persists very accurately down to temperatures very close to T_c. Thus the Casimir Scaling of the 't Hooft tension appears to be a `universal' feature that is more general than its origin in the low order high-T perturbative calculation. We observe the `wetting' of these k-walls at T around T_c and the (almost inevitable) `perfect wetting' of the k=N/2 domain wall. Our calculations show that as T tends to T_c the magnitude of the spatial `t Hooft string tension decreases rapidly.

hep-lat↗
arXiv2005

Large N

Some mysterious features of the strong interactions become easily understood if our usual QCD with N=3 is `close to' SU(oo) and if the latter theory is confining. N=oo theories are theoretically simpler; in particular there has been much progress in constructing weak-coupling duals in string theory. In this poster I will describe some of the things that recent lattice calculations tell us about the large-N limit of SU(N) gauge theories in 3+1 dimensions. The focus is on confinement, how close SU(oo) is to SU(3), new stable strings at larger N, the Pomeron, deconfinement, topology, 't Hooft string tensions. I also allude to other topics, such as the high-T pressure deficit, chiral physics and the phases of the theory.

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