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Register a new userDynamical simulation of lattice 4d N=1 SYM
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The lattice provides a powerful tool to non-perturbatively investigate strongly coupled supersymmetric Yang-Mills (SYM) theories. The pure SU(2) SYM theory with one supercharge is simulated on large lattices with small Majorana gluino masses down to about $am_{tilde g}=0.068$ with lattice spacing $asimeq 0.125$ fm. The gluino dynamics is simulated by the Two-Step Multi-Boson (TSMB) and the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) algorithms. Supersymmetry (SUSY) is broken explicitly by the lattice and the Wilson term and softly by the presence of a non-vanishing gluino mass. However, the recovery of SUSY is expected in the infinite volume continuum limit by tuning the bare parameters to the SUSY point in the parameter space. This scenario is studied by the determination of the low-energy mass spectrum and by means of lattice SUSY Ward-Identities (WIs).
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We perform Monte Carlo investigations of the 4d ${cal N}=1$ supersymmetric Yang-Mills (SYM) theory on the lattice with dynamical gluinos in the adjoint representation of the SU(2) gauge group. Our aim is to determine the mass spectrum of the low-lying bound states which is expected to be organised in supermultiplets in the infinite volume continuum limit. For this purpose we perform simulations on large lattices, up to an extension $L/r_0 simeq 6$ where $r_0 simeq 0.5 rm fm$ is the Sommer scale parameter. We apply improved lattice actions: tree-level improved Symanzik (tlSym) gauge action and in the later runs a Stout-smeared Wilson fermion action. The gauge configuration samples are prepared by the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) update algorithm.
We report on a lattice simulation result for four-dimensional {cal N}=1 SU(2) super Yang-Mills theory with the dynamical overlap gluino. We study the spectrum of the overlap Dirac operator at three different gluino masses m=0.2, 0.1 and 0.05 with the Iwasaki action on a 8^3 times 16 lattice. We find that the lowest eigenvalue distributions are in good agreement with the prediction from the random matrix theory. Moreover the mass dependence of the condensate is almost constant, which gives a clean chiral limit. Our results for the gluino condensate in the chiral limit is < bar{psi} psi > r_0^3 = 0.63(12), where r_0 is the Sommer scale.
In order to check the validity and the range of applicability of the 1/N expansion, we performed numerical simulations of the two-dimensional lattice CP(N-1) models at large N, in particular we considered the CP(20) and the CP(40) models. Quantitative agreement with the large-N predictions is found for the correlation length defined by the second moment of the correlation function, the topological susceptibility and the string tension. On the other hand, quantities involving the mass gap are still far from the large-$N$ results showing a very slow approach to the asymptotic regime. To overcome the problems coming from the severe form of critical slowing down observed at large N in the measurement of the topological susceptibility by using standard local algorithms, we performed our simulations implementing the Simulated Tempering method.
We find a family of complex saddle-points at large N of the matrix model for the superconformal index of SU(N) N=4 super Yang-Mills theory on $S^3 times S^1$ with one chemical potential $tau$. The saddle-point configurations are labelled by points $(m,n)$ on the lattice $Lambda_tau= mathbb{Z} tau +mathbb{Z}$ with $text{gcd}(m,n)=1$. The eigenvalues at a given saddle are uniformly distributed along a string winding $(m,n)$ times along the $(A,B)$ cycles of the torus $mathbb{C}/Lambda_tau$. The action of the matrix model extended to the torus is closely related to the Bloch-Wigner elliptic dilogarithm, and the related Bloch formula allows us to calculate the action at the saddle-points in terms of real-analytic Eisenstein series. The actions of $(0,1)$ and $(1,0)$ agree with that of pure AdS$_5$ and the supersymmetric AdS$_5$ black hole, respectively. The black hole saddle dominates the canonical ensemble when $tau$ is close to the origin, and there are new saddles that dominate when $tau$ approaches rational points. The extension of the action in terms of modular forms leads to a simple treatment of the Cardy-like limit $tauto 0$.
We report on the results of a numerical simulation concerning the low-lying spectrum of four-dimensional N=1 SU(2) Supersymmetric Yang-Mills (SYM) theory on the lattice with light dynamical gluinos. In the gauge sector the tree-level Symanzik improved gauge action is used, while we use the Wilson formulation in the fermion sector with stout smearing of the gauge links in the Wilson-Dirac operator. The ensembles of gauge configurations were produced with the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) updating algorithm. We performed simulations on large lattices up to a size of 24^3 x 48 at $beta=1.6$. Using QCD units with the Sommer scale being set to r_0 = 0.5 fm, the lattice spacing is about a ~ 0.09 fm, and the spatial extent of the lattice corresponds to 2.1 fm. At the lightest simulated gluino mass the spin-1/2 gluino-glue bound state appeared to be considerably heavier than its expected super-partner, the pseudoscalar bound state. Whether supermultiplets are formed remains to be studied in upcoming simulations.
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