The light bound states of supersymmetric SU(2) Yang-Mills theory

Abstract

Supersymmetry provides a well-established theoretical framework for extensions of the standard model of particle physics and the general understanding of quantum field theories. We summarise here our investigations of N = 1 supersymmetric Yang-Mills theory with SU(2) gauge symmetry using the non-perturbative first-principles method of numerical lattice simulations. The strong interactions of gluons and their superpartners, the gluinos, lead to confinement, and a spectrum of bound states including glueballs, mesons, and gluino-glueballs emerges at low energies. For unbroken supersymmetry these particles have to be arranged in supermultiplets of equal masses. In lattice simulations supersymmetry can only be recovered in the continuum limit since it is explicitly broken by the discretisation. We present the first continuum extrapolation of the mass spectrum of supersymmetric Yang-Mills theory. The results are consistent with the formation of supermultiplets and the absence of non-perturbative sources of supersymmetry breaking. Our investigations also indicate that numerical lattice simulations can be applied to non-trivial supersymmetric theories.

Low energy properties of SU(2) gauge theory with Nf = 3/2 flavours of adjoint fermions

“…For β = 1.5 this gives k = 0.675(24). The corresponding number for β = 1.7, ensembles M, O, P, is k = 0.751 (8). For comparison, we get k = 0.817(36) from N, O, P, Q, and k = 0.817(24) from L -P. Figure 6 shows the averaged logarithmic masses for β = 1.7 and the fit with k = 0.751.…”

“…A study of SU (2) with N f = 1 fermion flavours [7] gives indications for IRconformal behaviour, too. The case of N f = 1/2 describes one flavour of Majorana fermions and corresponds to N = 1 supersymmetric Yang-Mills theory, which has been studied by our collaboration, see [8] and references therein. This theory is QCD-like concerning its scaling behaviour.…”

The light bound states of $$ \mathcal{N}=1 $$ supersymmetric SU(3) Yang-Mills theory on the lattice

“…We have investigated the particle spectrum of the theory and observed the expected degeneracy of the states in the lightest supermultiplet [6]. We have now extended our studies to the multiplet of excited states, and first results have been reported in a contribution to the Lattice2017 conference [7].…”

“…Alternative tunings of the coefficient are possible. In the SU(2) case we have tested a tadpole resummation [6], that leads to a considerable improvement of the mass degeneracy for finite lattice spacings. At our current parameter range the value of c sw obtained with the proposed tadpole formula is not much different from the one-loop prediction.…”

“…The results in units of r 0 can be converted to QCD units fm or MeV using the QCD scale setting r 0 = 0.5 fm. The methods for the determination of r 0 /a from a fit of the static quark-antiquark potential are explained in our earlier work on SU(2) SYM [6]. At each β the final values of the scales w 0 /a and r 0 /a are obtained by linearly extrapolating them as a function of the square of the adjoint pion mass to the chiral limit.…”