Barak Bringoltz

We analyze the large-N behavior of SU(N) lattice gauge theories with adjoint fermions by studying volume-reduced models, as pioneered by Eguchi and Kawai. We perform simulations on a single-site lattice for N f = 1 and N f = 2 Wilson Dirac fermions with values of N ≤ 53. We show for both values of N f that in the large-N limit there is a finite region, containing both light and heavy fermions, of unbroken center symmetry where the theory exhibits volume independence. Using large-N reduction we attempt to calculate physical quantities such as the string tension and meson masses.

We analyze the large-N behavior of SU(N) lattice gauge theories with adjoint fermions by studying volume-reduced models, as pioneered by Eguchi and Kawai. We perform simulations on a single-site lattice for Nf = 1 and Nf = 2 Wilson Dirac fermions with values of N up to 53. We show for both values of Nf that in the large-N limit there is a finite region, containing both light and heavy fermions, of unbroken center symmetry where the theory exhibits volume independence. Using large-N reduction we attempt to calculate physical quantities such as the string tension and meson masses.

We study the single site SU(N) lattice gauge theory with N f = 2 adjoint Wilson fermions for values of N up to 53. We determine the phase diagram of the theory as a function of the hopping parameter κ and the inverse 't Hooft coupling b, searching for the region in which the Z 4 N center symmetry is unbroken. In this region the theory is equivalent to the infinite volume theory when N → ∞. We find a region of values of κ on both sides of κ c for which the symmetry is unbroken, including both light physical quarks and masses ∼ O(1/a). This is surrounded by a region with a complicated sequence of partially broken phases. We calculate Wilson loop expectation values and find that using N ≤ 53 it is possible to extract the heavy-quark potential at small distances (1-3 links) but not at longer distances. For this, larger values of N, or lattices with more sites, are needed.

We study the single site SU(N) lattice gauge theory with N_f=2 adjoint Wilson fermions for values of N up to 53. We determine the phase diagram of the theory as a function of the hopping parameter kappa and the inverse 't Hooft coupling b, searching for the region in which the Z_N^4 center symmetry is unbroken. In this region the theory is equivalent to the infinite volume theory when N goes to infinity. We find a region of values of kappa on both sides of kappa_c for which the symmetry is unbroken, including both light physical quarks and masses ~O(1/a). This is surrounded by a region with a complicated sequence of partially broken phases. We calculate Wilson loop expectation values and find that using N <= 53 it is possible to extract the heavy-quark potential at small distances (1-3 links) but not at longer distances. For this, larger values of N, or lattices with more sites, are needed.

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.