Deconfinement transition and string tensions in SU(4) Yang-Mills theory

We present results from numerical lattice calculations of SU(4) Yang-Mills theory. This work has two goals: to determine the order of the finite temperature deconfinement transition on an

N_t = 6

lattice and to study the string tensions between static charges in the irreducible representations of SU(4). Motivated by Pisarski and Tytgat's argument that a second-order SU(

\infty

) deconfinement transition would explain some features of the SU(3) and QCD transitions, we confirm older results on a coarser,

N_t = 4

, lattice. We see a clear two-phase coexistence signal, characteristic of a first-order transition, at

8/g^2 = 10.79

on a

6\times 20^3

lattice, on which we also compute a latent heat of

\Delta\epsilon\approx 0.6 \epsilon_{SB}

. Computing Polyakov loop correlation functions we calculate the string tension at finite temperature in the confined phase between fundamental charges,

\sigma_1

, between diquark charges,

\sigma_2

, and between adjoint charges

\sigma_4

. We find that

1 < \sigma_2/\sigma_1 < 2

, and our result for the adjoint string tension

\sigma_4

is consistent with string breaking.

gauge field theory: SU(4)
lattice field theory
string tension
critical phenomena: confinement
finite temperature
Polyakov loop: correlation function
numerical calculations: Monte Carlo

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