The existence of maximally supersymmetric solutions to heterotic string theory that are not toroidal compactifications of the ten-dimensional superstring is established. We construct an exact fermionic realization of an % = 1 supersymmetric string theory in D = 8 with non-simply-laced gauge group Sp(20). Toroidal compactification to six and four dimensions gives maximally extended supersymmetric theories with reduced rank (4, 12) and (6, 14), respectively. PACS numbers: 11.25.Mj, 11. 25.Hf Finiteness is a robust property of the perturbative amplitudes of the known superstring theories. N = 4 supersymmetric Yang-Mills theory is known to be finite in four dimensions [1], and there is growing evidence that the theory exhibits an extension of Olive-Montonen strong-weak coupling duality known as 5 duality [2,3]. A generalization of the Olive-Montonen duality of N = 4 theories has also been identified in N = 1 supersymmetric Yang-Mills theory [4]. In string theory, conjectures for 5 duality have mostly been explored in the context of toroidal compactifications of the ten-dimensional heterotic string to spacetime dimensions D ( 10 [5].It would be helpful to have insight into the generic moduli space, and the generic duality group, of such maximally supersymmetric string theories. We will therefore consider the possibility of exact solutions to string theory beyond those obtained by dimensional reduction from a ten-dimensional superstring.These solutions are exact in the sigma model (n') expansion but are perturbative in the string coupling constant. To be specific, we will construct solutions to heterotic string theory, i.e. , with (NR, Nt ) = (2, 0) superconformal invariance on the world sheet. Our construction is, however, quite general, and the conclusions can be adapted to solutions of any closed string theory in any spacetime dimension.Toroidal compactification of the ten-dimensional N = I heterotic string to six (four) dimensions results in a lowenergy effective N = 2 (N = 4) supergravity coupled to 20 (22) Abelian vector multiplets, giving a total of 24 (28) Abelian vector gauge fields with gauge group (U(1)) ((U(1)) ), respectively. Four (six) of these Abelian multiplets are contained within the N = 2 (N = 4) supergravity multiplets. At enhanced symmetry points in the moduli space the Abelian group (U(1))zo ((U(1))z2) is enlarged to a simply laced group of rank 20 (22). The lowenergy field theory limit of such a solution has maximally extended spacetime supersymmetry.Since all of the elementary scalars appear in the adjoint representation of the gauge group, symmetry breaking via the Higgs mecha-nism is adequate in describing the moduli space of vacua with a fixed number of Abelian multiplets.In this Letter we show that there exist maximally supersymmetric vacua with four-, six-, and eight-dimensional Lorentz invariance that are not obtained by toroidal compactification of a ten-dimensional heterotic string. The total number of Abelian vector multiplets in the fourdimensional theory can be reduced to just six, n...

Lattice gauge theory techniques have recently achieved sufficient accuracy to permit a determination of the strong coupling constant from the \P-\S splitting in the charmonium system, with all systematic errors estimated quantitatively. The present result is 0^(5 GeV) =0.174 ±0.012, or, equivalently, A^= 160^37 MeV (MS denotes the modified minimal subtraction scheme).PACS numbers: 12.38. Gc, 12.38.Aw, 14.40.Gx A central task in understanding quantum chromodynamics (QCD) is the determination of its coupling constant, g 2 . The Particle Data Group quotes values for a s (5 Ge\)=g 2 /4n in the range 0.18-0.22 [l]. Recent measurements at the CERN e *e ~ collider LEP yield values in the range 0.20-0.24 [2]. Most perturbative determinations of g 2 contain nonperturbative contaminations which become small only at high energies. On the other hand, high-energy determinations yield g 2 at lower energies only imprecisely. Lattice gauge theory calculations provide a nonperturbative means of determining the strong coupling constant from low-energy quantities.In principle, any lattice calculation of a mass or energy E allows a determination of the strong coupling constant. The lattice calculation yields the dimensionless quantity aE, where a is the lattice spacing which is determined by comparing aE with the experimentally measured value for E. The bare lattice coupling constant g § at scale a may then be converted into one of the more familiar definitions of the coupling constant using known perturbative results [3,4]. In practice, most existing lattice calculations contain systematic errors which are difficult to analyze quantitatively. Consider, for example, the obvious case of the proton mass. Lattice calculations have not yet been done with quark masses as light as their physical values. Chiral perturbation theory calculations [5] indicate that at pion masses of around 400 MeV, where lattice calculations are often done, the proton mass is reduced by a term (of order ml) of around 100% of its physical, light pion value. Similarly, the most accurate lattice calculations to date have been done ignoring the effects of sea quarks. Some chiral quark model calculations [6] estimate that the proton mass may be altered as much as 30% by the effects of the strange quarks in the sea, let alone the light quarks. Whether or not these calculations are quantitatively reliable, the point is that the approximation of ignoring the sea quarks (the "quenched" approximation) introduces potentially large systematic errors for the light hadrons which are difficult to analyze and control.Heavy quark systems offer the best opportunity for determining the strong coupling constant with present day lattice calculations [7]. For these systems no extrapolation to light valence quark masses is necessary, and er-rors arising from the omission of sea quarks and also from the finiteness of the lattice spacing may be systematically analyzed and quantitatively estimated with some input from phenomenology, as we discuss below. As lattice calculations impro...

to be published in Physics Letters B FERMILAB-Pub 95/199-T hep-lat/9507010Abstract We demonstrate that lattice QCD calculations can be made 10 3 -10 6 times faster by using very coarse lattices. To obtain accurate results, we replace the standard lattice actions by perturbativelyimproved actions with tadpole-improved correction terms that remove the leading errors due to the lattice. To illustrate the power of this approach, we calculate the static-quark potential, and the charmonium spectrum and wavefunctions using a desktop computer. We obtain accurate results that are independent of the lattice spacing and agree well with experiment.

No abstract

We obtain three generation SU (3) c ×SU (2) L ×U (1) Y string models in all of the exactly solvable (0, 2) constructions sampled by fermionization. None of these examples, including those that are symmetric abelian orbifolds, rely on the Z 2 ×Z 2 orbifold underlying the NAHE basis. We present the first known three generation models for which the hypercharge normalization, k 1 , takes values smaller than that obtained from an SU (5) embedding, thus lowering the effective gauge coupling unification scale. All of the models contain fractional electrically charged and vectorlike exotic matter that could survive in the light spectrum.10/95 †