We extend our analysis of bound states in  $${\mathcal {N}}=1$$  <math> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </math>   supersymmetric Yang–Mills theory by the consideration of baryonic operators, which are composed of three gluino fields. The corresponding states are similar to the baryons in QCD, but due to the difference between gluino and quark fields, their properties and the fermion line contractions involved in their correlation functions are different from QCD. In this work, we first explain the derivation of these operators and the contractions needed in numerical calculations of their correlators. In contrast to QCD the correlators contain a spectacle piece, which requires methods for all-to-all propagators. We provide a first estimate of the two-point function and the mass of the lightest baryonic state in  $${\mathcal {N}}=1$$  <math> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </math>   supersymmetric Yang–Mills theory.

Pakistan

Germany

Sajid Ali

Georg Bergner

Camilo López

Istvan Montvay

Gernot Münster

Stefano Piemonte

Baryonic states in  $$\mathbf {{\mathcal {N}}=1}$$  <math> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </math>   supersymmetric SU(2) Yang–Mills theory on the lattice

In $${\mathcal {N}}=1$$ <math><mrow><mi>N</mi><mo>=</mo><mn>1</mn></mrow></math>  supersymmetric Yang–Mills theory, regularised on a space-time lattice, in addition to the breaking by the gluino mass term, supersymmetry is broken explicitly by the lattice regulator. In addition to the parameter tuning in the theory, the supersymmetric Ward identities can be used as a tool to investigate lattice artefacts as well as to check whether supersymmetry can be recovered in the chiral and continuum limits. In this paper we present the numerical results of an analysis of the supersymmetric Ward identities for our available gauge ensembles at different values of the inverse gauge coupling $$\beta $$ <math><mi>β</mi></math>  and of the hopping parameter $$\kappa $$ <math><mi>κ</mi></math> . The results clearly indicate that the lattice artefacts vanish in the continuum limit, confirming the restoration of supersymmetry.

Henning Gerber

Philipp Scior

Continuum extrapolation of Ward identities in $${{\mathcal {N}}=1}$$ <math><mrow><mi>N</mi><mo>=</mo><mn>1</mn></mrow></math>  supersymmetric SU(3) Yang–Mills theory

The physical particles in supersymmetric Yang-Mills (SYM) theory are bound states of gluons and gluinos. We have determined the masses of the lightest bound states in SU(3) <math><mi>N</mi><mo>=</mo><mn>1</mn></math> SYM theory. Our simulations cover a range of different lattice spacings, which for the first time allows an extrapolation to the continuum limit. Our results show the formation of a supermultiplet of bound states, which provides a clear evidence for unbroken supersymmetry.

Numerical Results for the Lightest Bound States in <math><mi>N</mi><mo>=</mo><mn>1</mn></math> Supersymmetric SU(3) Yang-Mills Theory

We have calculated the masses of bound states numerically in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supersymmetric Yang-Mills theory with gauge group SU(2). Using the suitably optimised variational method with an operator basis consisting of smeared Wilson loops and mesonic operators, we are able to obtain the masses of the ground states and first excited states in the scalar, pseudoscalar and spin-  <math> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math>  $$ \frac{1}{2} $$  sectors. Extrapolated to the continuum limit, the corresponding particles appear to be approximately mass degenerate and to fit into the predicted chiral supermultiplets. The extended operator basis including both glueball-like and mesonic operators leads to improved results compared to earlier studies, and moreover allows us to investigate the mixing content of the physical states, which we compare to predictions in the literature.

Simon Kuberski

Variational analysis of low-lying states in supersymmetric Yang-Mills theory

In numerical investigations of supersymmetric Yang–Mills theory on a lattice, the supersymmetric Ward identities are valuable for finding the critical value of the hopping parameter and for examining the size of supersymmetry breaking by the lattice discretisation. In this article we present an improved method for the numerical analysis of supersymmetric Ward identities, which takes into account the correlations between the various observables involved. We present the first complete analysis of supersymmetric Ward identities in $$\mathcal {N}=1$$ <math><mrow><mi>N</mi><mo>=</mo><mn>1</mn></mrow></math>  supersymmetric Yang–Mills theory with gauge group SU(3). The results indicate that lattice artefacts scale to zero as $$O(a^2)$$ <math><mrow><mi>O</mi><mo>(</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo></mrow></math>  towards the continuum limit in agreement with theoretical expectations.

Analysis of Ward identities in supersymmetric Yang–Mills theory

In this article we summarise our results from numerical simulations of  <math><mi>N</mi><mo>=</mo><mn>1</mn></math> $$ \mathcal{N}=1 $$ supersymmetric Yang-Mills theory with gauge group SU(3). We use the formulation of Curci and Veneziano with clover-improved Wilson fermions. The masses of various bound states have been obtained at different values of the gluino mass and gauge coupling. Extrapolations to the limit of vanishing gluino mass indicate that the bound states form mass-degenerate supermultiplets.

Pietro Giudice

The light bound states of  <math><mi>N</mi><mo>=</mo><mn>1</mn></math> $$ \mathcal{N}=1 $$ supersymmetric SU(3) Yang-Mills theory on the lattice

In this work we present the results of a numerical investigation of SU(2) gauge theory with N  f  = 3/2 flavours of fermions, corresponding to 3 Majorana fermions, which transform in the adjoint representation of the gauge group. At two values of the gauge coupling, the masses of bound states are considered as a function of the fundamental fermion mass, represented by the PCAC quark mass. The scaling of bound states masses indicates an infrared conformal behaviour of the theory. We obtain estimates for the fixed-point value of the mass anomalous dimension γ ∗ from the scaling of masses and from the scaling of the mode number of the Wilson-Dirac operator. The difference of the estimates at the two gauge couplings should be due to scaling violations and lattice spacing effects. The more reliable estimate at the smaller gauge coupling is γ ∗ ≈ 0.38(2).

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

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 $$ \mathcal{N}=1 $$ 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 super-multiplets 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.