Abstract
Supersymmetric Yang-Mills (SYM) theories in four dimensions exhibit many interesting non-perturbative phenomena that can be studied by means of Monte Carlo lattice simulations. However, the lattice regularization breaks supersymmetry explicitly, and in general a fine tuning of a large number of parameters is required to correctly extrapolate the theory to the continuum limit. From this perspective, it is important to preserve on the lattice as many symmetries of the original continuum action as possible. Chiral symmetry for instance prevents an additive renormalization of the fermion mass. A (modified) version of chiral symmetry can be preserved exactly if the Dirac operator fulfills the Ginsparg-Wilson relation. In this contribution, we present an exploratory non-perturbative study of N=1 supersymmetric Yang-Mills theory using the overlap formalism to preserve chiral symmetry at non-zero lattice spacings. N=1 SYM is an ideal benchmark toward the extension of our studies to more complex supersymmetric theories, as the only parameter to be tuned is the gluino mass. Overlap fermions allow therefore to simulate the theory without fine-tuning. We compare our approach to previous investigations of the same theory, and we present clear evidences for gluino condensation.
Highlights
Supersymmetric Yang-Mills (SYM) theories are promising extensions of the Standard Model to energies of the order and beyond the TeV scale
The main advantage of preserving exact chiral symmetry is that N 1⁄4 1 super Yang-Mills can be simulated on the lattice without the need of fine-tuning any parameter
The exploratory study of overlap gluino simulations presented in this contribution is promising, as the polynomial approximation of the sign function is able to regularize massless chiral fermions, while avoiding at the same time topological freezing and the sign problem
Summary
Supersymmetric Yang-Mills (SYM) theories are promising extensions of the Standard Model to energies of the order and beyond the TeV scale. The extension of the electromagnetic duality to more realistic models with less or no supersymmetry requires one, to control the behavior of the theory in the limit, where the mass of the scalar and gluino fields becomes large. In this limit SUSY is partially or softly broken and completely different confinement scenarios could be realized. If N 1⁄4 2 SYM arises as an effective four-dimensional theory, the scalar mass and the quartic scalar potential would be protected by gauge symmetry This is due to the fact that scalars emerge in the small compactification limit from the gauge fields living along the extra dimensions [4,5]. No further tunings are required if chiral symmetry is preserved exactly in the regularized theory, even at energy scales of the order of the ultraviolet cutoff
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
