We provide a first-principles non-perturbative determination of the mass of the lightest gluino-gluon bound state (gluino-glue) in large- $$ \mathcal{N} $$ = 1 Supersymmetric Yang-Mills theory by means of numerical Monte Carlo simulations of the lattice-discretized theory, and exploiting large- twisted volume reduction. Our large- determination is consistent with naive extrapolation of previously-known SU(2) and SU(3) results.

Spain

Claudio Bonanno

Margarita Pérez

Antonio González-Arroyo

Japan

Ken-Ichi Ishikawa

Masanori Okawa

The mass of the gluino-glue bound state in large-

We present the first nonperturbative large <math><mi>N</mi></math> calculation of the <math><mi>N</mi><mo>=</mo><mn>1</mn></math> supersymmetric <math><mi>SU</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> Yang-Mills gluino condensate obtained by means of numerical simulations of the lattice-discretized theory, exploiting large-<math><mi>N</mi></math> twisted volume reduction. We present two different determinations based, respectively, on the Banks-Casher formula and on the Gell-Mann–Oakes–Renner relation, both giving perfectly consistent results. By expressing the lattice results in the Novikov-Shifman-Vainshtein-Zakharov (NSVZ) scheme, we are able for the first time to compare numerical and analytic computations. Our most accurate determination of the renormalization group invariant (RGI) gluino condensate gives <math><mrow><msub><mrow><mi>Σ</mi></mrow><mrow><mi>RGI</mi></mrow></msub><mo>/</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>NSVZ</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mo>=</mo><mo>[</mo><mn>1.18</mn><mo>(</mo><mn>08</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mn>12</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>syst</mi></mrow></msub><msup><mrow><mo>]</mo></mrow><mrow><mn>3</mn></mrow></msup><mo>=</mo><mn>1.64</mn><mo>(</mo><mn>33</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mn>50</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>syst</mi></mrow></msub><mo>=</mo><mn>1.64</mn><mo>(</mo><mn>60</mn><mo>)</mo></mrow></math>, in agreement with the <math><mi>N</mi></math> dependence and the value predicted by the weak coupling instanton-based approach <math><mrow><msub><mrow><mi>Σ</mi></mrow><mrow><mi>RGI</mi></mrow></msub><mo>/</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>NSVZ</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mo>=</mo><mn>1</mn></mrow></math>.

Pietro Butti

Margarita García Pérez

Nonperturbative determination of the <math><mi>N</mi><mo>=</mo><mn>1</mn></math> supersymmetric Yang-Mills gluino condensate at large <math><mi>N</mi></math>

We present new investigations on the Adjoint Filtering Method (AFM), a proposal for filtering gauge configurations by using adjoint zero modes. This method relies on the existence of the Supersymmetric Zero Mode (SZM), whose density follows the gauge action density for classical configurations. We review how a similar construction on the lattice is implemented based on the overlap operator and test the method against smooth configurations showing a remarkable agreement with the expected densities even when pairs of fractionals instanton/anti-instantons are present and noise is added. Then we explore the application of the method to Monte Carlo generated configurations based on SU(2) gauge group. The tuning of the parameters and quantitative results are explicitly shown for a T 3 × R lattice. We show explicit examples comparing the AFM to the density obtained from the Gradient Flow. The agreement is remarkable for some specific configurations containing fractional instantons with the advantage that the AFM does not modify the underlying structures.

Germany

Georg Bergner

Ivan Soler

Identifying topological structures with adjoint mode filtering

We compute the large-N limit of the QCD chiral condensate on the lattice using twisted reduced models, and performing controlled continuum and chiral extrapolations. We perform two different calculations: one consists in extracting the chiral condensate from the quark mass dependence of the pion mass, and the other consists in extracting the chiral condensate from the behaviour of the mode number of the Wilson-Dirac operator for small eigenvalues. We find consistency between the results of the two methods, giving a joint estimate of lim N→∞ Σ(N)/N = [184(13) MeV]3 (  <math> <mover> <mi>MS</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\textrm{MS}} $$ , μ = 2 GeV, taking the square root of the string tension   <math> <msqrt> <mi>σ</mi> </msqrt> </math>  $$ \sqrt{\sigma } $$  = 440 MeV to set the scale), in remarkable agreement with the SU(3) 2-flavor FLAG result.

Margarita Peréz

The large-N limit of the chiral condensate from twisted reduced models

In this paper we study the large N limit of four-dimensional Supersymmetric Yang-Mills on the lattice using twisted reduced models. We have generated configurations with dynamical massive gluinos and various lattice ’t Hooft couplings, and verified that the Pfaffian remains positive. We have determined the lattice spacing in terms of various observables obtaining compatible results. Extrapolating to the massless gluino limit we obtain the lattice spacing dependence on the bare couplings for the supersymmetric theory. The observed dependence goes along the expected behaviour predicted by perturbation theory.

Scale setting for large-N SUSY Yang-Mills on the lattice

We present the result of our computation of the lowest lying meson masses for SU(N) gauge theory in the large N limit (with N  f  /N → 0). The final values are given in units of the square root of the string tension, and with errors which account for both statistical and systematic errors. By using 4 different values of the lattice spacing we have seen that our results scale properly. We have studied various values of N (169, 289 and 361) to monitor the N-dependence of the most sensitive quantities. Our methodology is based upon a first principles approach (lattice gauge theory) combined with large N volume independence. We employed both Wilson fermions and twisted mass fermions with maximal twist. In addition to masses in the pseudoscalar, vector, scalar and axial vector channels, we also give results on the pseudoscalar decay constant and various remormalization factors.

Meson spectrum in the large N limit

We study self-dual SU(N) gauge field configurations on the 4 torus with twisted boundary conditions, known as fractional instantons. Focusing on the minimum non-zero action case, we generalize the constant field strength solutions discovered by ‘t Hooft and valid for certain geometries. For the general case, we construct the vector potential and field strength in a power series expansion in a deformation parameter of the metric. The next to leading term is explicitly computed. The methodology is an extension of that used by the author for SU(2) fractional instantons and for vortices in two-dimensional Abelian Higgs models. Obviously, these solutions can also be seen as self-dual configurations in ℝ4 having a crystal structure, where each node of the crystal carries a topological charge of 1/N .

Constructing SU(N) fractional instantons

We present the results of an exploratory study of the numerical stochastic perturbation theory (NSPT) applied to the four dimensional twisted Eguchi-Kawai (TEK) model. We employ a Kramers type algorithm based on the Generalized Hybrid Molecular Dynamics (GHMD) algorithm. We have computed the perturbative expansion of square Wilson loops up to O(g 8). The results of the first two coefficients (up to O(g 4)) have a high precision and match well with the exact values. The next two coefficients can be determined and even extrapolated to large N, where they should coincide with the corresponding coefficients for ordinary Yang-Mills theory on an infinite lattice. Our analysis shows the behaviour of the probability distribution for each coefficient tending to Gaussian for larger N. The results allow us to establish the requirements to extend this analysis to much higher order.

Issaku Kanamori

Kanata Miyahana

Ryoichiro Ueno

Numerical stochastic perturbation theory applied to the twisted Eguchi-Kawai model

We compute and analyse the low-lying spectrum of 2+1 dimensional SU(N) Yang-Mills theory on a spatial torus of size l × l with twisted boundary conditions. This paper extends our previous work [1]. In that paper we studied the sector with non-vanishing electric flux and concluded that the energies only depend on the parameters through two combinations: x = λN l/(4π) (with λ the ’t Hooft coupling) and the twist angle  <math><mover><mi>θ</mi><mo>˜</mo></mover></math> $$ \tilde{\theta} $$ defined in terms of the magnetic flux piercing the two-dimensional box. Here we made a more complete study and we are able to condense our results, obtained by non-perturbative lattice methods, into a simple expression which has important implications for the absence of tachyonic instabilities, volume independence and non-commutative field theory. Then we extend our study to the sector of vanishing electric flux. We conclude that the onset of the would-be large-volume glueball states occurs at an approximately fixed value of x, much before the stringy torelon states have become very massive.

Mateusz Koren

The spectrum of 2+1 dimensional Yang-Mills theory on a twisted spatial torus

Motivated by our previous study of the Twisted Eguchi-Kawai model for non minimal twists, we re-examined the behaviour of the reduced version of the two dimensional principal chiral model. We show that this single matrix model reproduces the same features as the standard lattice model. In particular, scaling towards the continuum limit, the correct value of the internal energy, the magnetic susceptibility and the mass gap. Given our capacity to reach larger values of N, we use the reduced model to study the nature and properties of its large N phase transition existing at intermediate coupling. We conclude that the transition is of first order.