Wilson loops, confinement, and phase transitions in large N gauge theories from supergravity

Abstract

We use the recently proposed supergravity approach to large N gauge theories to calculate ordinary and spatial Wilson loops of gauge theories in various dimensions. In this framework we observe an area law for spatial Wilson loops in four and five dimensional supersymmetric Yang-Mills at finite temperature. This can be interpreted as the area law of ordinary Wilson loops in three and four dimensional non-supersymmetric gauge theories at zero temperature which indicates confinement in these theories. Furthermore, we show that super Yang Mills theories with 16 supersymmetries at finite temperature do not admit phase transitions between the weakly coupled super Yang Mills and supergravity regimes. This result is derived by analyzing the entropy and specific heat of those systems as well as by computing ordinary Wilson loops at finite temperature. The calculation of the entropy was carried out in all different regimes and indicates that there is no first order phase transition in these systems. For the same theories at zero temperature we also compute the dependence of the quark anti-quark potential on the separating distance.

Wilson Loops for a quark anti-quark pair in D3-brane space

“…For this space the energy has a non-confining Coulomb like behaviour, as expected for a conformal field theory. This approach was applied to multicentre and rotating branes [4,5] and many other spaces and models [6,7,8,9]. More recently this approach to Wilson loops has been used in the search for confining geometries [10,11,12,13] and their related properties [14,15,16,17,18,19].…”

Wilson-loop formalism for Reggeon exchange in soft high-energy scattering

“…Moreover, the area-law prescription Eq. (6.5) carries over to the confining case, substituting the AdS metric with an appropriate confining background [38,39,40] and replacing 1/(2πα ′ ) with an effective string tension 1/(2πα ′ eff ). At this point, one has to substitute the area-law expression Eq.…”

A note on the Coulomb branch of susy Yang–Mills

“…The restrictions on L are practically the same as in the U f → ∞ limit studied in [6]. For p < 3 one can always go to larger L by using either an S-dual description or an M-theory lift.…”

“…The behavior of this system as U f → ∞ was analyzed in [6]; for a treatment of the U f → ∞ limit of breaking to SU(N) × SU(N) see [7]. The U-shaped fundamental string is dual to a pair of W bosons, oppositely charged under the unbroken gauge group, and F 0 1 is related to the U(1) electric field one has to turn on for the configuration to be static (it counterbalances the attraction from SU(N) interactions).…”

“…This system was studied in the limit U f → ∞ in [6]. In this limit the force diverges unless L is fixed.…”