Ratio of flavour non-singlet and singlet scalar density renormalisation parameters in $$N_\mathrm {f}=3$$ QCD with Wilson quarks

We determine non-perturbatively the normalisation factor $$r_{\mathrm{m}}\equiv Z_{\mathrm{S}}/Z_{\mathrm{S}}^{0}$$ r m ≡ Z S / Z S 0 , where $$Z_{\mathrm{S}}$$ Z S and $$Z_{\mathrm{S}}^{0}$$ Z S 0 are the renormalisation parameters of the flavour non-singlet and singlet scalar densities, respectively. This quantity is required in the computation of quark masses with Wilson fermions and for instance the renormalisation of nucleon matrix elements of scalar densities. Our calculation involves simulations of finite-volume lattice QCD with the tree-level Symanzik-improved gauge action, $$N_{\mathrm{f}}= 3$$ N f = 3 mass-degenerate $${\mathrm{O}}(a)$$ O ( a ) improved Wilson fermions and Schrödinger functional boundary conditions. The slope of the current quark mass, as a function of the subtracted Wilson quark mass is extracted both in a unitary setup (where nearly chiral valence and sea quark masses are degenerate) and in a non-unitary setup (where all valence flavours are chiral and the sea quark masses are small). These slopes are then combined with $$Z \equiv Z_{\mathrm{P}}/(Z_{\mathrm{S}}Z_{\mathrm{A}})$$ Z ≡ Z P / ( Z S Z A ) in order to obtain $$r_{\mathrm{m}}$$ r m . A novel chiral Ward identity is employed for the calculation of the normalisation factor Z. Our results cover the range of gauge couplings corresponding to lattice spacings below $$0.1\,$$ 0.1 fm, for which $$N_{\mathrm{f}}= 2+1$$ N f = 2 + 1 QCD simulations in large volumes with the same lattice action are typically performed.

Determination of the charm quark mass in lattice QCD with 2 + 1 flavours on fine lattices

We present a determination of the charm quark mass in lattice QCD with three active quark flavours. The calculation is based on PCAC masses extracted from Nf = 2 + 1 flavour gauge field ensembles at five different lattice spacings in a range from 0.087 fm down to 0.039 fm. The lattice action consists of the O(a) improved Wilson-clover action and a tree-level improved Symanzik gauge action. Quark masses are non-perturbatively O(a) improved employing the Symanzik-counterterms available for this discretisation of QCD. To relate the bare mass at a specified low-energy scale with the renormalisation group invariant mass in the continuum limit, we use the non-pertubatively known factors that account for the running of the quark masses as well as for their renormalisation at hadronic scales. We obtain the renormalisation group invariant charm quark mass at the physical point of the three-flavour theory to be Mc = 1486(21) MeV. Combining this result with five-loop perturbation theory and the corresponding decoupling relations in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme, one arrives at a result for the renormalisation group invariant charm quark mass in the four-flavour theory of Mc(Nf = 4) = 1548(23) MeV, where effects associated with the absence of a charmed, sea quark in the non-perturbative evaluation of the QCD path integral are not accounted for. In the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme, and at finite energy scales conventional in phenomenology, we quote $$ {m}_{\mathrm{c}}^{\overline{\mathrm{MS}}} $$ m c MS ¯ ($$ {m}_{\mathrm{c}}^{\overline{\mathrm{MS}}} $$ m c MS ¯ ; Nf = 4) = 1296(19) MeV and $$ {m}_{\mathrm{c}}^{\overline{\mathrm{MS}}} $$ m c MS ¯ (3 GeV; Nf = 4) = 1007(16) MeV for the renormalised charm quark mass.

Lattice $$ \mathcal{N} $$ = 4 super Yang-Mills at strong coupling

In this paper we present results from numerical simulations of $$ \mathcal{N} $$ N = 4 super Yang-Mills for two color gauge theory over a wide range of ’t Hooft coupling 0 < λ ≤ 30 using a supersymmetric lattice action [1]. Numerical study of this lattice theory has been stymied until recently by both sign problems and the occurrence of lattice artifact phases at strong coupling. We have recently developed a new action that appears capable of solving both problems. The resulting action possesses just SU(2) rather than U(2) gauge symmetry. By explicit computations of the fermion Pfaffian we present evidence that the theory possesses no sign problem and exists in a single phase out to arbitrarily strong coupling. Furthermore, preliminary work shows that the logarithm of the supersymmetric Wilson loop varies as the square root of the ’t Hooft coupling λ for large λ in agreement with holographic predictions.

Wavelets and Lattice Field Theory.

When continuous fields are expanded in a wavelet basis, a D-dimensional continuum action becomes a (D+1)-dimensional lattice action on the naively discretized Poincare-patch coordinates of an Euclidean AdS(D+1). New possible criteria for acceptable actions open up.

Simulations of QCD and QED with C* boundary conditions

We present exploratory results from dynamical simulations of QCD in isolation, as well as QCD coupled to QED, with C* boundary conditions. In finite volume, the use of C* boundary conditions allows for a gauge invariant and local formulation of QED without zero modes. In particular we show that the simulations reproduce known results and that masses of charged mesons can be extracted in a completely gauge invariant way. For the simulations we use a modified version of the HiRep code. The primary features of the simulation code are presented and we discuss some details regarding the implementation of C* boundary conditions and the simulated lattice action. Preprint: CP3-Origins-2017-046 DNRF90, CERN-TH-2017-214

Two dimensional super QCD on a lattice

We construct a lattice theory with one exact supersymmetry which consists of fields transforming in both the adjoint and fundamental representations of a U(Nc) gauge group. In addition to gluons and gluinos, the theory contains Nf flavors of fermion in the fundamental representation along with their scalar partners and is invariant under a global U(Nf) flavor symmetry. The lattice action contains an additional Fayet-Iliopoulos term which can be used to generate a scalar potential. We perform numerical simulations that corroborate the theoretical expectation that supersymmetry is spontaneously broken for Nf<Nc.

Maximally supersymmetric Yang–Mills on the lattice

We summarize recent progress in lattice studies of four-dimensional [Formula: see text] supersymmetric Yang–Mills theory and present preliminary results from ongoing investigations. Our work is based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, and we review a new procedure to regulate flat directions by modifying the moduli equations in a manner compatible with this supersymmetry. This procedure defines an improved lattice action that we have begun to use in numerical calculations. We discuss some highlights of these investigations, including the static potential and an update on the question of a possible sign problem in the lattice theory.