Abstract
Supersymmetry (SUSY) has been proposed to be a central concept for the physics beyond the standard model and for a description of the strong interactions in the context of the AdS/CFT correspondence. A deeper understanding of these developments requires the knowledge of the properties of supersymmetric models at finite temperatures. We present a Monte Carlo investigation of the finite temperature phase diagram of the N=1 supersymmetric Yang-Mills theory (SYM) regularised on a space-time lattice. The model is in many aspects similar to QCD: quark confinement and fermion condensation occur in the low temperature regime of both theories. A comparison to QCD is therefore possible. The simulations show that for N=1 SYM the deconfinement temperature has a mild dependence on the fermion mass. The analysis of the chiral condensate susceptibility supports the possibility that chiral symmetry is restored near the deconfinement phase transition.
Highlights
Supersymmetric Yang-Mills theoryThe theory contains gluons as bosonic particles, and gluinos as their fermionic superpartners
Theory in ten dimensions and strong coupling N = 4 supersymmetric Yang-Mills theory (SYM) in four dimensions [9]
At zero temperature the theory is in a confined phase and chiral symmetry is spontaneously broken by a non-vanishing expectation value of the gluino condensate
Summary
The theory contains gluons as bosonic particles, and gluinos as their fermionic superpartners. The gluino is a spin-1/2 Majorana fermion in the adjoint representation of the gauge group. A Majorana fermion obeys the “reality” condition λ(x) = (λ(x))T C. The operator μνρσF μνF ρσ is topologically invariant and the theory is periodic in the parameter Θ, i. The additional parameter m introduces a bare mass for the gluino. This mass in the fermionic sector breaks supersymmetry softly, i. Gluons and gluinos can be found only in colourless bound states. Those bound states are expected to form supermultiplets of equal masses if exact supersymmetry is realised. A low-energy effective Lagrangian has been formulated [18, 19], predicting a bound spectrum of mesons, glueballs and gluino-glueballs, which has been subject of many numerical lattice investigations [20, 21]
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