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A superfield formulation of gauge invariant σ-models, previously written in component form, is given. Both the N = 1 global supersymmetry case and the N = 1 supergravity case are treated. A superfield formulation of σ-models involving abelian and non-abelian N = 2 vector multiplets coupled to N = 2 supergravity is also presented. In the non-abelian case, this is a new class of models.

Integrals over anticommuting variables are use to rewrite partition functions as fermionic field theories. The method is used to solve the two‐dimensional Ising model, the planar close‐packed dimer problems, and the free‐fermion eight vertex model.

Two-dimensional chiral models are investigated from a strong coupling viewpoint, with the ultimate objective of understanding the phase structure of gauge theories. Predictions for the average link and beta function are obtained. The abelian case agrees well with previous work. Strong evidence for a phase transition in the U( N ) cases is found, in contrast to the SU(2) and SU(3) theories. Large N character expansion techniques are developed and give strong evidence for a large N phase transition. Our conclusions can be applied qualitatively to gauge theories, with one difference: instantons are necessary in QCD for connecting weak with strong coupling.

We analyze disorder operators in the chiral models in order to better understand the behavior of 't Hooft loops in four-dimensional gauge theories. We use both theoretical and numerical approaches.

Superconformal field theory is used to compute off-shell amplitudes for the superstring. Off-shell three- and four-point functions in Witten's superstring field theory are obtained. The problem of gauge invariance due to the associativity anomaly in the bosonic sector is resolved to order g 2 .

We analyze the large-N phase transition phenomenon in lattice gauge and chiral models. In particular, we prove the existence of a large-N phase transition in 4d lattice QCD without fermions and present a physical understanding of why it takes place. The phase transition occurs at g2N = 2.53.

The flat-space limit of a supergravity theory involving the Akulov-Volkov field as well as other matter multiplets is found to be an ordinary renormalizable globally supersymmetric theory with explicit soft-breaking mass terms. This allows one to easily construct realistic models of nature which are analyzable at the tree and one-loop level. This is carried out for QED-like and Weinberg-Salam-like models.

By using scalar quarks, we study the quark model on the lattice. Computer simulations are used to measure constituent masses and quark wave functions for a quark-heavy antiquark system. As a function of the quark mass, we compute the charge radius and the value of the wave function at the origin.

We develop large N character-like expansion techniques for vector and vector-like models. These are used to compute the mass gaps and beta functions in the d = 2 CP N −1 models. Surprisingly there is an intermediate region where neither strong coupling nor perturbation theory is applicable. This “unknown” region is a consequence of the non-commutativity of strong coupling and large N , an interesting mathematical effect not found in other models and due to an interesting physical phenomenon: superconfinement.

The subject of off-shell conformal field theory is developed and is used to produce the off-shell amplitudes of string field theory. The method is also applied to the reparametrization ghosts.

The Ising model in three dimensions is fermionized by using integrals over anticommuting variables. The result is generalized to the Ising model in arbitrary dimensions and in a magnetic field. Approximation methods are developed to attack unsolved statistical mechanics models. Perturbation theory and the Hartree approximation are applied to the unsolved monomer‐dimer problems. The result is a numerical solution to this unsolved class of problems. Anticommuting variables appear to be a powerful approach to unsolved problems.

A new model building technique is reviewed in which supersymmetry models do not necessarily have boson-fermion particle degeneracy. Possible low-energy phenomenological implications are discussed.

Quenched SU(3) gauge theory is simulated on a CDC CYBER 205. We describe how to deal with large data sets and discuss the performance of the machine for the two main tasks involved: Monte Carlo updating and Gauss-Seidel inversion.

A method of resumming perturbation theory is used to re-analyze previous Monte Carlo data of Bhanot and Dashen. We find no inconsistency with universality. There appears to be a relatively large region where Monte Carlo studies can reliably be done.

In an effort to understand whether the open bosonic string theory has a stable vacuum, the four-point contribution to the static tachyon potential is computed. This off-shell calculation is carried out using covariant string field theory.

When ghost coordinates are used in combination with the ∂ X μ and ψ μ degrees of freedom, an infinite set of operators of conformal dimension one can be constructed for the open superstring. These conservation laws aid in computing the string scattering amplitudes for bosons and fermions. Using them and an additional trick, N -point correlation functions can be reduced to ( N − 1)-point ones, so that any superstring tree-amplitude can be calculated in a manifestly Lorentz covariant form if the two-point correlation functions are known. The method is applicable to both closed and open strings and can be adapted to heterotic strings. Sample calculations are presented.

Rules are provided for the calculation of string amplitudes on all exotic topologies to one loop. These topologies include the real projective plane, the disk, the annulus, the Mobius strip, the torus and the Klein bottle. The rules are valid for bosonic strings, superstrings, and heterotic strings either in their critical dimensions or toroidally compactified, and they are applicable to amplitudes with arbitrary external bosonic and fermionic states, including mixed open- and closed-string transitions. The modular invariance of the torus amplitudes is discussed.

Covariant off-shell dual-resonance model amplitudes for four reggeons are computed in the open bosonic string using Witten's string field theory. The four-tachyon, the two-tachyon two-vector and the four-vector cases are explicitly worked out, although the formalism applies to higher mass states as well. Properties of the amplitudes are analyzed. Finally, a demonstration of associativity of the ∗ product is given for a certain set of Fock-space states.

Recently, Chen, Tan and Zheng have qualitatively obtained in the large-N limit the phase diagram of the lattice Yang-Mills theory with fundamental and adjoint action terms. In this letter, this model is solved exactly in terms of the N=∞ pure Wilson theory. This enables the author to obtain the phase diagram quantitatively. Finally, large but finite N is discussed.

Scalar lattice QCD methods are used to accurately predict the masses of hadrons with beauty, that is, states which contain a b quark. These states have not yet been seen in the laboratory. The accuracy of the predictions (≈ 25 MeV) make the calculation a good test of lattice methods as well as providing useful guidance for experimentalists.

Wave functions for mesons and baryons are computed from lattice QCD. They are used to obtain the electromagnetic properties of the low-lying mesons, including charge radii and electromagnetic form factors. Experimental data for the pion and proton electromagnetic form factor fall close to the theoretical lattice computation. Predictions are made for other states. The lepton width of the ϱ, θ and J/ψ are obtained. The wave functions are also used to obtain estimates for isospin splittings and proton decay.

The physical and ghost vertex operators in covariant superstring field theory are obtained. The integral and star operations are given in oscillator form and the free and interaction lagrangians are explicitly displayed for the massless fields.

The conformal equivalence of the Caneschi-Schwimmer-Veneziano vertex and the Witten vertex is established. This proves that, for all levels, the Witten vertex yields the same couplings as the Caneschi-Schwimmer-Veneziano vertex for on-shell physical string states.

A semi-perturbative improvement of the asymptotic-freedom formula is developed, to see scaling in the SU(3) lattice gauge theory. The method leads to a wider region over which one may extrapolate Monte Carlo results to their continuum limit.

Functional integrals over anticommuting variables are used to obtain a scattering formula for smooth localized potentials in one dimension. Via a calculational trick, the functional integral is evaluated to obtain the transition matrix coefficients as an expansion in [k′ (x)/k (x)] (k (x) ={ (2m/h/2)[E−V (x)]}1/2). This expansion is shown to have a simple physical interpretation.

An error in the construction of the two-parameter N = ∞ phase diagram is rectified and the correct diagram is presented.

We present an outline for a proof (the precise details of which will be presented in a follow-up paper) of a large-N phase transition in dimensions greater than two. The critical couplings are calculated in d=3 and d=4 and are found to be β=0.44 and β=0.40, respectively.

Conformal field theory is applied in the context of the o(16)×o(16) heterotic string. Branch cuts and unphysical operators are seen to appear in the operator-product expansions for certain physical fields. A four-fermion amplitude is calculated explicitly and found, nonetheless, to have correct physical behaviour.

Using covariant spin fields, the tree amplitude for six massless fermions in the open ten-dimensional superstring is calculated by superconformal field-theoretic methods. The amplitude is presented in a manifestly Lorentz-covariant form.

Calculational tools are provided allowing the determination of tree-level amplitudes for processes involving fermions and bosons in heterotic and superstring theories. A simple representation is given of the cocycle operators that are needed for bosonization of conformal operators, including spin fields and ghosts. This permits explicit computation of all correlation functions. The general m -boson, 2 n -fermion tree-level scattering amplitude in the open superstring is derived and a typical calculation of a four-point amplitude in the o(16) × o(16) heterotic string is presented in manifestly Lorentz-covariant form. An analysis of the branch-cut singularities in the o(16) × o(16) model is performed. In addition, the covariant form of the “new formalism” is developed. Particular attention is given to a lattice viewpoint of these results.

A new two-dimensional statistical mechanics model is solved. It is a general model with 32 free parameters. The solution uses integrals over anticommuting variables.

The manner by which topological symmetry breakdown leads to confinement in a non-Abelian gauge theory is discussed.

Low lying s-wave baryon states are analyzed in the context of scalar lattice QCD, that is, lattice QCD with scalar quarks replacing fermion quarks. Except for the proton where we disagree with experiment by 13%, results agree with experiment to better than 4% for the Δ, the Σ, the Σ ∗ , the Λ, the Ξ, the Ξ∗, the Ω, the Σc, and the Λc. In this calculation there were no adjustable parameters, the quark masses and ΛQCD having been already fixed in a previous meson calculation. We also make predictions accurate to 35 MeV for the masses of the Σ c ∗ , the Ωc,, and the Ω c ∗ .

We analyze Hamber's quenched QCD data using a recenty developed semiperturbative reformulation of asymptotic freedom. Scaling is seen quite well. We recompute ${f}_{\ensuremath{\pi}}$, ${m}_{\ensuremath{\rho}}$, and the sum of the current masses ${({m}_{u}+{m}_{d})}_{\stackrel{-}{\mathrm{MS}}}$ ($\stackrel{-}{\mathrm{MS}}$ denotes the modified minimal-subtraction scheme), and find agreement with experiment to within 5%.

The possibility of spontaneous breakdown of Lorentz symmetry in string theory is explored via covariant string field theory. A potential mechanism is suggested for the Lorentz breaking that may be generic in many string theories.

We investigate gravitational phenomenology in compactified higher-dimensional theories, with particular emphasis on the consequences in string theory of tensor-induced spontaneous Lorentz-symmetry breaking. The role played by this mechanism in causing a gravitational version of the Higgs effect and in compactification is explored. The experimental viability of compactified theories with zero modes is considered by examining nonleading but observable gravitational effects. Additional constraints from the observed cosmological properties of the Universe are uncovered. Our investigations significantly constrain many theories involving extra dimensions in their perturbative regime. To resolve the phenomenological difficulties one must generate masses for the higher-dimensional components of the metric while leaving massless the physical spacetime components. Some possibilities for overcoming this metric-mass problem are suggested. An open issue is whether the metric-mass problem is resolved in string theory.

Athletes that participate in contact sport are at risk of suffering Sports-Related Concussion (SRC). A traditional approach of SRC testing relies on the 5th version of the pen-and-paper based sports concussion assessment tool (SCAT5). An open, digital equivalent may facilitate more efficient and transparent assessment. We describe a co-created developed iOS SCAT5 app to enable an Internet of Things (IoT) assessment.