arXiv subjects

Georg Bergner

Publications and source records attributed to Georg Bergner.

At least 37 records · Page 2Linked to original sources

arXiv2022

Supercurrent renormalization of $\mathcal{N}=1$ supersymmetric Yang-Mills theory on the lattice

Supersymmetry on the lattice is explicitly broken by the gluino mass and lattice artifacts. However, it can be restored in the continuum limit by fine tuning the parameters based on the renormalized Ward identities. On the renormalization step not only the mass but also the renormalization of the supercurrent needs to be addressed. Here we present a lattice investigation to obtain the renormalization factors of the supercurrent for $\mathcal{N}$=1 Super-Yang Mills theory in a gauge invariant renormalization scheme. We also provide the conversion factors which are necessary in order to translate our results to the more standard $\overline{\text{MS}}$ scheme.

hep-lat↗

arXiv2022

Exploring gauge theories with adjoint matter on the lattice

We review our efforts in investigating gauge theories with fermions in the adjoint representation of the gauge group by means of numerical simulations. These theories have applications in possible extensions of the Standard Model of particle physics, being a core part of supersymmetric gauge theories. They also play an important role in uncovering fundamental properties of strongly interacting theories due to distinct features, such as a substantially different phase diagram.

hep-lat↗

arXiv2022

Noether supercurrent operator mixing from lattice perturbation theory

In this work we present perturbative results for the renormalization of the supercurrent operator, $S_μ$, in ${\cal N} =1$ Supersymmetric Yang-Mills theory. At the quantum level, this operator mixes with both gauge invariant and noninvariant operators, which have the same global transformation properties. In total, there are 13 linearly independent mixing operators of the same and lower dimensionality. We determine, via lattice perturbation theory, the first two rows of the mixing matrix, which refer to the renormalization of $S_μ$, and of the gauge invariant mixing operator, $T_μ$. To extract these mixing coefficients in the ${\overline{\rm MS}}$ renormalization scheme and at one-loop order, we compute the relevant two-point and three-point Green's functions of $S_μ$ and $T_μ$ in two regularizations: dimensional and lattice. On the lattice, we employ the plaquette gluonic action and for the gluinos we use the fermionic Wilson action with clover improvement.

hep-lat↗

arXiv2022

Nonperturbative renormalization of the supercurrent in $\mathcal{N} = 1$ Supersymmetric Yang-Mills Theory

In this work, we study the nonperturbative renormalization of the supercurrent operator in $\mathcal{N} = 1$ Supersymmetric Yang-Mills (SYM) theory, using a gauge-invariant renormalization scheme (GIRS). The proposed prescription addresses successfully the unwanted mixing of the supercurrent with other operators of equal or lower dimension, which respect the same global symmetries. This mixing is introduced by the unavoidable breaking of supersymmetry on the lattice. In GIRS all gauge-noninvariant operators, which mix with the supercurrent, are excluded from the renormalization procedure. The one remaining mixing operator is accessible by numerical simulations. We present results for the renormalization of the supercurrent using a GIRS scheme. We also compute at one-loop order the conversion matrix which relates the nonperturbative renormalization factors in GIRS to the reference scheme $\bar{\rm MS}$.

hep-lat↗

arXiv2022

The spectrum and mass anomalous dimension of SU(2) adjoint QCD with two Dirac flavours

In this work we present the results of our investigation of \su{2} gauge theory with two Dirac fermions in the adjoint representation (aQCD2), which belongs to the class of strongly interacting gauge theories that are of basic interest for extensions of the Standard Model. We have done numerical lattice simulations of this theory at two different values of the gauge coupling and several fermion masses. Our results include the particle spectrum and the mass anomalous dimension. The spectrum contains new exotic fermion-gluon states and flavour-singlet mesons. The mass anomalous dimension is determined from the scaling of the masses and the mode number. The remnant dependence of the universal mass ratios and mass anomalous dimension on the gauge coupling indicates the relevance of scaling corrections, such that earlier estimations for the universal fixed point value of the mass anomalous dimension are incomplete without their inclusion.

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arXiv2022

Nonperturbative test of the Maldacena-Milekhin conjecture for the BMN matrix model

We test a conjecture by Maldacena and Milekhin for the ungauged version of the Berenstein-Maldacena-Nastase (BMN) matrix model by lattice Monte Carlo simulation. The numerical results reproduce the perturbative and gravity results in the limit of large and small flux parameter, respectively, and are consistent with the conjecture.

hep-th↗

arXiv2022

Confinement/deconfinement transition in the D0-brane matrix model -- A signature of M-theory?

We study the confinement/deconfinement transition in the D0-brane matrix model (often called the BFSS matrix model) and its one-parameter deformation (the BMN matrix model) numerically by lattice Monte Carlo simulations. Our results confirm general expectations from the dual string/M-theory picture for strong coupling. In particular, we observe the confined phase in the BFSS matrix model, which is a nontrivial consequence of the M-theory picture. We suggest that these models provide us with an ideal framework to study the Schwarzschild black hole, M-theory, and furthermore, the parameter region of the phase transition between type IIA superstring theory and M-theory. A detailed study of M-theory via lattice Monte Carlo simulations of the D0-brane matrix model might be doable with much smaller computational resources than previously expected.

hep-th↗

arXiv2022

Perturbative renormalization of the supercurrent operator in lattice ${\cal N}{=}1$ supersymmetric Yang-Mills theory

In this work we perform a perturbative study of the Noether supercurrent operator in the context of Supersymmetric ${\cal N}{=}1$ Yang-Mills (SYM) theory on the lattice. The supercurrent mixes with several other operators, some of which are not gauge invariant, having the same quantum numbers. We determine, to one loop order, the renormalization and all corresponding mixing coefficients by computing relevant Green's functions of each one of the mixing operators with external elementary fields. Our calculations are performed both in dimensional and lattice regularization. From the first regularization we obtain the $\bar{MS}$-renormalized Green's functions; comparison of the latter with the corresponding Green's functions in the lattice regularization leads to the extraction of the lattice renormalization factors and mixing coefficients in the $\bar{MS}$ scheme. The lattice calculations are performed to lowest order in the lattice spacing, using Wilson gluons and clover improved gluinos. The lattice results can be used in nonperturbative studies of supersymmetric Ward identities.

hep-lat↗

arXiv2022

Lattice simulations of adjoint QCD with one Dirac overlap fermion

In this work we investigate the infrared behaviour of a Yang-Mills theory coupled to a massless fermion in the adjoint representation of the gauge group SU(2). This model has many interesting properties, corresponding to the $\mathcal{N}=2$ Super-Yang-Mills theory without scalars and in the recent years there has been an increasing interest toward understanding whether confinement and fermion condensation occur at low energy. We simulate the theory on the lattice close to the massless limit using the overlap discretization of the fermion action, allowing a precise and clean study of the chiral symmetry breaking pattern and of the fermion condensate. We present results for the scale setting, the condensate and the running of the coupling constant through the gradient flow -- all of them pointing to a theory without an infrared fixed point and remaining confined deep in the infrared regime.

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arXiv2022

Pion-pole contribution to HLbL from twisted mass lattice QCD at the physical point

We report on our computation of the pion transition form factor ${\cal F}_{P\rightarrow γ^*γ^*}$ from twisted mass lattice QCD in order to determine the numerically dominant light pseudoscalar pole contribution in the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon $a_μ=(g-2)_μ$. The pion transition form factor is computed directly at the physical point. We present first results for our estimate of the pion-pole contribution with kinematic setup for the pion at rest.

hep-lat↗

arXiv2022

Investigating the conformal behaviour of SU(2) with one adjoint Dirac flavor

We present a major update on our investigations of SU(2) gauge theory with one Dirac flavor in the adjoint representation on the lattice. In particular we consider larger volumes, as well as four different values of the gauge coupling. We provide results for the spectrum including gluonic, fermionic, and hybrid observables, Polyakov loops, and the anomalous dimension of the fermionic condensate from the Dirac mode number. These data confirm that the theory is close to the lower boundary of the conformal window for adjoint fermions. Our investigations provide important insights regarding the realization of different infrared scenarios that have been conjectured for this theory.

hep-lat↗

arXiv2021

Mixed adjoint-fundamental matter and applications towards SQCD and beyond

Gauge theories with fermions in adjoint and fundamental representations are relevant for many different applications including composite Higgs models and general aspects of the confinement problem. We present first results from simulations of SU(2) gauge theory with two Dirac fermions in the fundamental representation and one adjoint flavor. In this context, we also discuss applications towards simulations of supersymmetric QCD.

hep-lat↗

arXiv2021

Estimates for the lightest baryon masses in $\mathcal{N} = 1$ supersymmetric Yang-Mills theory

$\mathcal{N} = 1$ supersymmetric Yang-Mills theory describes gluons interacting with gluinos, which are spin-$\frac{1}{2}$ Majorana particles in the adjoint representation of the gauge group. In addition to glueballs and mesonic bound states, the theory contains color neutral bound states of three gluinos, which are analogous to baryons in QCD. We calculate their correlation functions, involving ``sunset diagrams'' and ``spectacle diagrams'', numerically for gauge group SU(2) and present an update on the estimates for the lowest masses.

hep-lat↗

arXiv2021

Gradient flow scale-setting with $N_f=2+1+1$ Wilson-clover twisted-mass fermions

We present a determination of the gradient flow scales $w_0$, $\sqrt{t_0}$ and $t_0/w_0$ in isosymmetric QCD, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f=2+1+1$ flavours of Wilson-clover twisted-mass quarks including configurations close to the physical point for all dynamical flavours. The simulations are carried out at three values of the lattice spacing and the scale is set through the PDG value of the pion decay constant, yielding $w_0=0.17383(63)$ fm, $\sqrt{t_0}=0.14436(61)$ fm and $t_0/w_0=0.11969(62)$ fm. Finally, fixing the kaon mass to its isosymmetric value, we determine the ratio of the kaon and pion leptonic decay constants to be $f_K/f_π=1.1995(44)$.

hep-lat↗

arXiv2021

New lattice results for SU(2) gauge theory with one adjoint Dirac flavor

Motivated by recent scenarios of exotic infrared behaviour and by earlier lattice findings, we present results for the SU(2) gauge theory with one Dirac flavor in the adjoint representation. This provides a major update on our previous investigation of this theory, including data for four values of the gauge coupling $β$, and for smaller masses and larger volumes than previously considered. Results for the particle spectrum, topological observables, and the anomalous dimension from both hyperscaling and the Dirac mode number are presented. At the finest coupling, we observe a mass anomalous dimension of $γ_* \gtrsim 0.6$. Our findings are analysed in relation to possible infrared behaviours of the model. In particular, we show that our results are not compatible with a confining scenario in which chiral symmetry is broken.

hep-lat↗

arXiv2021

Supercurrent Renormalization in $\mathcal{N}=1$ Supersymmetric Yang-Mills Theory

In this work we study the renormalization of the SUSY Noether current in Supersymmetric $\mathcal{N}$ = 1 Yang-Mills (SYM) theory on the lattice. In particular, we study the mixing of the current with all other compatible operators of dimension 7/2 and 5/2, leading from the lattice-regularized to the $\overline{\rm MS}$-renormalized operator basis. We perform our task in two ways: (a) We compute, in dimensional regularization, the conversion factors relating the $\overline{\rm MS}$ scheme to an intermediate gauge-invariant coordinate-space scheme. In this second scheme, renormalization can be performed via lattice simulations. This could help to investigate the breaking of SUSY on the lattice and strategies towards simulations of supersymmetric QCD. Here we present some preliminary numerical results. (b) We use lattice perturbation theory and compute, to one loop, various two- and three-point functions. We consider mixing with all relevant gauge-noninvariant operators, which contain also ghost fields.

hep-lat↗

arXiv2021

Quark and gluon momentum fractions in the pion from $N_f=2+1+1$ lattice QCD

We perform the first full decomposition of the pion momentum into its gluon and quark contributions. We employ an ensemble generated by the Extended Twisted Mass Collaboration with $N_f=2 + 1 +1$ Wilson twisted mass clover fermions at maximal twist tuned to reproduce the physical pion mass. We present our results in the $\overline{\mathrm{MS}}$ scheme at $2\gev$. We find $\avgx_{u+d}=0.601(28)$, $\avgx_s=0.059(13)$, $\avgx_c=0.019(05)$, and $\avgx_g=0.52(11)$ for the separate contributions, respectively, whose sum saturates the momentum sum rule.

hep-lat↗

arXiv2021

Eigenvalue spectrum and scaling dimension of lattice $\mathcal{N} = 4$ supersymmetric Yang-Mills

We investigate the lattice regularization of $\mathcal{N} = 4$ supersymmetric Yang-Mills theory, by stochastically computing the eigenvalue mode number of the fermion operator. This provides important insight into the non-perturbative renormalization group flow of the lattice theory, through the definition of a scale-dependent effective mass anomalous dimension. While this anomalous dimension is expected to vanish in the conformal continuum theory, the finite lattice volume and lattice spacing generically lead to non-zero values, which we use to study the approach to the continuum limit. Our numerical results, comparing multiple lattice volumes, 't Hooft couplings, and numbers of colors, confirm convergence towards the expected continuum result, while quantifying the increasing significance of lattice artifacts at larger couplings.

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