$U(N)$ Gauge Theory and Lattice Strings

I.K. Kostov (1)

1 SPhT - Service de Physique Théorique

The $1/N$ expansion of pure $ U(N) $ gauge theory on a two-dimensional manifold $ {\cal M} $ is reformulated as the topological expansion of a special model of random surfaces defined on a lattice $ {\cal L} $ covering $ {\cal M}. $ The random surfaces represent branched coverings of $ {\cal L}. $ The Boltzmann weight of each surface is $ {\rm exp}[- {\rm area}] $ times a product of local factors associated with the branch points. The $ 1/N $ corrections are produced by surfaces with higher topology as well as by contact interactions due to microscopic tubes, trousers, handles, etc. The continuum limit of this model is the limit of infinitely dense covering lattice $ {\cal L}. $ The construction generalizes trivially to $ D > 2 $ where it describes the strong coupling phase of the lattice gauge theory. The weak coupling phase can be achieved by taking a larger configuration space of surfaces. A possible integration measure in the space of continuous surfaces is suggested.

Domaines: Physique Générale [physics.gen-ph]

I.K. Kostov. $U(N)$ Gauge Theory and Lattice Strings. Nuclear Physics B, 1994, 415, pp.29-70. ⟨10.1016/0550-3213(94)90066-3⟩. ⟨hal-00163192⟩