As far back as the industrial revolution, significant development in technical innovation has succeeded in transforming numerous manual tasks and processes that had been in existence for decades where humans had reached the limits of physical capacity. Artificial Intelligence (AI) offers this same transformative potential for the augmentation and potential replacement of human tasks and activities within a wide range of industrial, intellectual and social applications. The pace of change for this new AI technological age is staggering, with new breakthroughs in algorithmic machine learning and autonomous decision-making, engendering new opportunities for continued innovation. The impact of AI could be significant, with industries ranging from: finance, healthcare, manufacturing, retail, supply chain, logistics and utilities, all potentially disrupted by the onset of AI technologies. The study brings together the collective insight from a number of leading expert contributors to highlight the significant opportunities, realistic assessment of impact, challenges and potential research agenda posed by the rapid emergence of AI within a number of domains: business and management, government, public sector, and science and technology. This research offers significant and timely insight to AI technology and its impact on the future of industry and society in general, whilst recognising the societal and industrial influence on pace and direction of AI development.

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We test a variety of blocking and smearing algorithms for constructing glueball and string wave-functionals, and find some with much improved overlaps onto the lightest states. We use these algorithms to obtain improved results on the tensions of k-strings in SU(4), SU(6), and SU(8) gauge theories. We emphasise the major systematic errors that still need to be controlled in calculations of heavier k-strings, and perform calculations in SU(4) on an anisotropic lattice in a bid to minimise one of these. All these results point to the k-string tensions lying partway between the 'MQCD' and 'Casimir Scaling' conjectures, with the power in 1/N of the leading correction lying ∈ [1, 2]. We also obtain some evidence for the presence of quasi-stable strings in calculations that do not use sources, and observe some near-degeneracies between (excited) strings in different representations. We also calculate the lightest glueball masses for N = 2, ..., 8, and extrapolate to N = ∞, obtaining results compatible with earlier work. We show that the N = ∞ factorisation of the Euclidean correlators that are used in such mass calculations does not make the masses any less calculable at large N.

We extend our earlier investigation of the finite temperature deconfinement transition in SU(N) gauge theories, with the emphasis on what happens as N → ∞. We calculate the latent heat, L h , in the continuum limit, and find the expected behaviour, L h ∝ N 2 , at large N. We confirm that the phase transition, which is second order for SU(2) and weakly first order for SU(3), becomes robustly first order for N ≥ 4 and strengthens as N increases. As an aside, we explain why the SU(2) specific heat shows no sign of any peak as T is varied across what is supposedly a second order phase transition. We calculate the effective string tension and electric gluon masses at T ≃ T c confirming the discontinuous nature of the transition for N ≥ 3. We explicitly show that the large-N 'spatial' string tension does not vary with T for T ≤ T c and that it is discontinuous at T = T c . For T ≥ T c it increases ∝ T 2 to a good approximation, and the k-string tension ratios closely satisfy Casimir Scaling. Within very small errors, we find a single T c at which all the k-strings deconfine, i.e. a step-by-step breaking of the relevant centre symmetry does not occur. We calculate the interface tension but are unable to distinguish between the ∝ N or ∝ N 2 variations, each of which can lead to a striking but different N = ∞ deconfinement scenario. We remark on the location of the bulk phase transition, which bounds the range of our large-N calculations on the strong coupling side, and within whose hysteresis some of our larger-N calculations are performed.

We calculate the continuum value of the deconfining temperature in units of the string tension for SU(4), SU(6) and SU(8) gauge theories, and we recalculate its value for SU(2) and SU(3). We find that the N-dependence for 2 ≤ N ≤ 8 is well fitted by T c / √ σ = 0.596(4) + 0.453(30)/N 2 , showing a rapid convergence to the large-N limit. We confirm our earlier result that the phase transition is first order for N ≥ 3 and that it becomes stronger with increasing N. We also confirm that as N increases the finite volume corrections become rapidly smaller and the phase transition becomes visible on ever smaller volumes. We interpret the latter as being due to the fact that the tension of the domain wall that separates the confining and deconfining phases increases rapidly with N. We speculate on the connection to Eguchi-Kawai reduction and to the idea of a Master Field.

We study the gauge sector of Minimal Walking Technicolor, which is an SU(2) gauge theory with n f = 2 flavors of Wilson fermions in the adjoint representation. Numerical simulations are performed on lattices Nt × N 3 s , with Ns ranging from 8 to 16 and Nt = 2Ns, at fixed β = 2.25, and varying the fermion bare mass m0, so that our numerical results cover the full range of fermion masses from the quenched region to the chiral limit. We present results for the string tension and the glueball spectrum. A comparison of mesonic and gluonic observables leads to the conclusion that the infrared dynamics is given by an SU(2) pure Yang-Mills theory with a typical energy scale for the spectrum sliding to zero with the fermion mass. The typical mesonic mass scale is proportional to, and much larger than this gluonic scale. Our findings are compatible with a scenario in which the massless theory is conformal in the infrared. An analysis of the scaling of the string tension with the fermion mass towards the massless limit allows us to extract the chiral condensate anomalous dimension γ * , which is found to be γ * = 0.22 ± 0.06.

We calculate the string tensions of k-strings in SU(N) gauge theories in both 3 and 4 dimensions. We do so for SU(4) and SU(5) in D=3+1, and for SU(4) and SU(6) in D=2+1. In D=3+1, we find that the ratio of the k = 2 string tension to the k = 1 fundamental string tension is consistent, at the 2σ level, with both the M(-theory)QCDinspired conjecture that σ k ∝ sin(πk/N) and with 'Casimir scaling', σ k ∝ k(N − k). In D=2+1, where our results are very precise, we see a definite deviation from the MQCD formula, as well as a much smaller but still significant deviation from Casimir scaling. We find that in both D=2+1 and D=3+1 the high temperature spatial k-string tensions also satisfy approximate Casimir scaling. We point out that approximate Casimir scaling arises naturally if the cross-section of the flux tube is nearly independent of the flux carried, and that this will occur in an effective dual superconducting description, if we are in the deep-London limit. We estimate, numerically, the intrinsic width of k-strings in D=2+1 and indeed find little variation with k. In addition to the stable k-strings we investigate some of the unstable strings, which show up as resonant states in the string mass spectrum. While in D=3+1 our results are not accurate enough to extract the string tensions of unstable strings, our more precise calculations in D=2+1 show that there the ratios between the tensions of unstable strings and the tension of the fundamental string are in reasonably good agreement with (approximate) Casimir scaling. We also investigate the basic assumption that confining flux tubes are described by an effective string theory at large distances, and attempt to determine the corresponding universality class. We estimate the coefficient of the universal Lüscher correction from periodic strings that are longer than 1 fermi, and find c L = 0.98(4) in the D=3+1 SU(2) gauge theory and c L = 0.558(19) in D=2+1. These values are within 2σ of the simple bosonic string values, c L = π/3 and c L = π/6 respectively, and are inconsistent with other simple effective string theories such as fermionic, supersymmetric or Neveu-Schwartz.

We study the dual superconductivity of the ground state of SU͑2͒ gauge theory in connection with confinement. We do this measuring on the lattice a disorder parameter describing condensation of monopoles. Confinement appears as a transition to the dual superconductor, independent of the Abelian projection defining monopoles. Some speculation is made on the existence of a more appropriate disorder parameter. A similar study for SU͑3͒ is presented in a companion paper.