Ian Affleck

A NEW MECHANISM FOR BARYOGENESIS

Abstract A new mechanism for baryogenesis is proposed. It is argued that, after inflation, the scalar quarks and leptons of a supersymmetric GUT may have large expectation values. The subsequent evolution of such a system is shown to generate a significant baryon density. For typical values of the parameters, n B / n γ may be as large as 10 3 .

Dynamical Supersymmetry Breaking in Supersymmetric QCD

The massless limit of supersymmetric QCD with Nƒ flavors and N colors is analyzed in detail. For Nƒ < N there is a unique superpotential which might be generated by non-perturbative effects. We show that it indeed appears, thus violating the non-renormalization theorems. For Nƒ = N − 1 instantons produce the superpotential. For Nƒ < N − 1 it is again generated, provided that a mild assumption about the dynamics of pure supersymmetric gauge theories is correct. For Nƒ ⩾ N no invariant superpotential exists; the classical vacuum degeneracy is a property of the full quantum theory. When a small quark mass term is added to the theory (for Nƒ < N), N supersymmetric ground states, identified with those found by Witten exist. As m → 0 these N vacua wander to infinity, leaving the massless theory without a ground state.

Valence bond ground states in isotropic quantum antiferromagnets

Haldane predicted that the isotropic quantum Heisenberg spin chain is in a “massive” phase if the spin is integral. The first rigorous example of an isotropic model in such a phase is presented. The Hamiltonian has an exactSO(3) symmetry and is translationally invariant, but we prove the model has a unique ground state, a gap in the spectrum of the Hamiltonian immediately above the ground state and exponential decay of the correlation functions in the ground state. Models in two and higher dimension which are expected to have the same properties are also presented. For these models we construct an exact ground state, and for some of them we prove that the two-point function decays exponentially in this ground state. In all these models exact ground states are constructed by using valence bonds.

Dynamical Supersymmetry Breaking in Four-Dimensions and Its Phenomenological Implications

It is now established that the non-renormalization theorems are violated by non-perturbative effects in many four-dimensional supersymmetric theories, and that dynamical supersymmetry-breaking (DSB) occurs in some chiral gauge theories. Here we presenr a set of general techniques which allow one to determine whether or not supersymmetry is broken in almost any theory, and permit a quite detailed analysis of the dynamics of many theories. These techniques are illustrated by analysis of a wide variety of instructive models, including one in which DSB occurs and in which we compute the spectrum and ground state energy. A careful discussion of the prospects for realistic model building is presented, including: an argument that additional gauge interactions are required to build realistic theories; dynamical supersymmetry-breaking in N = 1 supergravity theories; a detailed discussion of the problems and prospects for dynamical supersymmetry-breaking in the multi-TeV energy range.

Quantum spin chains and the Haldane gap

One-dimensional antiferromagnets have exotic disordered ground states. As was first argued by Haldane (1983), there is an excitation gap for integer, but not half-integer, spin. The authors review the arguments for this behaviour based on field-theory mappings, the Lieb-Schultz-Mattis theorem, exactly solvable models, finite-chain diagonalisation and real experiments.

INSTANTONS AND (SUPER-) SYMMETRY BREAKING IN (2+1) DIMENSIONS*

Abstract The connection between instantons and the breaking of supersymmetry and ordinary symmetries is studied in a variety of (2+1)-dimensional gauge theories.

Exact critical exponents for quantum spin chains, non-linear σ-models at θ=π and the quantum hall effect

Abstract We use non-abelian bosonization to predict critical exponents for quantum chains of arbitrary spin and arbitrary symmetry SU( n ). Passing to the large representation limit gives non-linear σ-models on the manifolds U(2 n )/U( n )×U( n ) at topological angle θ = π . For n =1 this is the familiar “O(3)” model; taking the replica limit n →0 given critical exponents for the localization transition in the quantum Hall effect. Given certain assumptions, these exponents should be exact.

On Constrained Instantons

Abstract A simple method is presented for doing systematic constrained instanton calculations in models such as φ4 or Higgs theories where the presence of a mass term prevents the existence of a classical solution. As an application, instanton estimates of the large-order behavior of the perturbation series in massive φ44 theory are derived. (These estimates agree with those of Frishman and Yankielowicz.)

DIMERIZATION AND INCOMMENSURATE SPIRAL SPIN CORRELATIONS IN THE ZIGZAG SPIN CHAIN : ANALOGIES TO THE KONDO LATTICE

Using the density matrix renormalization group and a bosonization approach, we study a spin-1/2 antiferromagnetic Heisenberg chain with near-neighbor coupling

Susceptibility of the spin 1/2 Heisenberg antiferromagnetic chain.

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