Gluino condensate and magnetic monopoles in supersymmetric gluodynamics

Abstract

We examine supersymmetric SU(N) gauge theories on R 3 × S 1 with a circle of circumference β. These theories interpolate between four-dimensional N = 1 pure gauge theory for β = ∞ and three-dimensional N = 2 gauge theory for β = 0. The dominant field configurations of the R 3 × S 1 SU(N) theories in the semi-classical regime arise from N varieties of monopole. Periodic instanton configurations correspond to mixed configurations of N single monopoles of the N different types. We semi-classically evaluate the non-perturbatively generated superpotential of the R 3 × S 1 theory and hence determine its vacuum structure. We then calculate monopole contributions to the gluino condensate in these theories and take the decompactification limit β = ∞. In this way we obtain a value for the gluino condensate in the four-dimensional N = 1 supersymmetric SU(N) Yang-Mills theory, which agrees with the previously known 'weak coupling' expression but not with the 'strong coupling' expression derived in the early literature solely from instanton considerations. Moreover, we discover that the superpotential gives a mass to the dual (magnetic) photon, which implies confinement of the original electric photon and disappearance of all the massless modes.

Instantons at work

“…The ratio, 56) seems to be more stable: it follows from phenomenological [5], variational [7,27] and lattice [21,36,37] studies. It means that the packing fraction, i.e.…”

“…An educated guess for the non-perturbative potential induced by dyons is therefore 8) to which the perturbative potential (3.5) must to be added. Let me note that in the supersymmetric theory there is a similar non-perturbative potential [56] (but in that case it is an exact result) and the perturbative potential is absent. The perturbative potential (3.5) has minima at φ = 0, 2πT corresponding to trivial holonomy P = ±1, while the non-perturbative potential (3.8) has the minimum just in the middle, at φ = πT corresponding to the non-trivial holonomy Tr P = 0, which is one of the requirements of confinement.…”

2d affine XY-spin model/4d gauge theory duality and deconfinement

“…This is in contrast with the n f = 0 case, where the theory on S 1 L is equivalent to a finite temperature pure Yang-Mills theory, where the theory deconfines at sufficiently high temperature [23]. In the supersymmetric n f = 1 case the one-loop potential vanishes and the center-symmetric vacuum is stabilized due to non-perturbative corrections [26][27][28].…”

“…Thus, for small y, the leading-order contribution to the vortex partition function is due to vortices with winding number vectors denoted by n A , A = 1, 2, 3: 28) and their corresponding anti-vortices. Note that the vortex with (n 1 , n 2 ) = (−1, −1) corresponds to the affine root α 3 = − α 1 − α 2 of the SU(3) algebra.…”

Microscopic structure of magnetic bions

“…The first studies of gauge dynamics in non-thermal circle compactifications were performed in supersymmetric theories and yielded many interesting results [3][4][5]. 1 More recently, it was shown that non-thermal circle compactifications offer a calculable window into the dynamics of general nonsupersymmetric gauge theories as well [7][8][9].…”