Michael Teper

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 ℤ₂ gauge theory. We study the excitation spectrum of long Ising strings by simulating the ℤ₂ 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.

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.

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.

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.

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.

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.