Luis Alvarez-Gaumé

Minimal low-energy supergravity☆

Abstract We discuss the motivation for considering models of particle physics based on 0=1 supergravity. Analysis of the scalar potential for such models suggests a minimal low energy sector. We use the renormalization group to relate parameters at the grand unification scale to their low energy (i.e. ∼100 GeV) values and show that renormalization effects drive spontaneous breakdown of SU(2)×U(1) to U(1) for a top quark mass between 55–200 GeV. The phenomenology of minimal low energy supergravity is discussed.

Low-energy supersymmetry☆

Abstract We discuss the problem of constructing a model in which supersymmetry is unbroken down to low energies. It is suggested that the scalar partners of quarks and leptons may get their masses through radiative corrections and that the breaking of the weak interactions also occurs through radiative corrections. A toy model is constructed which illustrates these ideas.

Theta functions, modular invariance, and strings

We use Quillens theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory. In particular, we show that the spin structure dependence of the chiral Dirac determinant on a Riemann surface is given by Riemanns theta function. We use this result to investigate the modular invariance of multiloop heterotic string amplitudes.

The structure of gauge and gravitational anomalies

It is shown how the form of the gauge and gravitational anomalies in quantum field theories may be derived from classical index theorems. The gravitational anomaly in both Einstein and Lorentz form is considered and their equivalence is exhibited. The formalism of gauge and gravitational theories is reviewed using the language of differential geometry, and notions from the theory of characteristic classes necessary for understanding the classical index theorems are introduced. The treatment of known topological results includes a pedagogical derivation of the Wess-Zumino effective Lagrangian in arbitrary even dimension. The relation between various forms of the anomaly present in the literature is also clarified.

The topological meaning of non-abelian anomalies

We show how the non-abelian anomaly for gauge fields coupled to Weyl fermions in 2n dimensions is related to the non-trivial topology of gauge orbit space. The form of the anomaly and its normalization are shown to follow from a familiar index theorem for a certain (2n + 2)-dimensional Dirac operator. We are thus able to recover and give topological meaning to a variety of results concerning anomalies in 4- and higher-dimensional theories.

An O(16) × O(16) heterotic string

By modifying the definition of the fermion number projection in the E 8 × E 8 heterotic superstring theory in a manner consistent with modular invariance and factorization, a tachyon-free string theory is obtained without spacetime supersymmetry. The low energy limit is a ten-dimensional anomaly-free chiral SO(16) × SO(16) gauge theory coupled to gravity.

Anomalies and odd dimensions

The parity-violating effective action for theories of fermions coupled to external gauge and gravitational fields in odd dimensions is computed exactly. This action is then used to compute gauge and gravitational anomalies in even dimensions. This derivation of the anomalies elucidates the relation of covariant to consistent anomalies as well as the relation between the Abelian anomaly and the non-Abelian anomaly in two lower dimensions.

Finiteness of Ricci Flat Supersymmetric Nonlinear Sigma Models

Combining the constraints of Kähler differential geometry with the universality of the normal coordinate expansion in the background field method, we study the ultraviolet behavior of 2-dimensional supersymmetric non-linear σ-models with target space an arbitrary riemannian manifoldM. We show that the constraint ofN=2 supersymmetry requires that all counterterms to the metric beyond one-loop order be cohomologically trivial. It follows that such supersymmetric non-linear σ-models defined on locally symmetric spaces are super-renormalizable and thatN=4 models are on-shell ultraviolet finite to all orders of perturbation theory.

Bosonization in Arbitrary Genus

Abstract The equivalence is proved between fermionic and scalar field theories on Riemann surfaces of arbitrary topology. The effects of global topology include a modification of the bosonic action.

The Two Quantum Symmetries Associated With a Classical Symmetry

Given a classical local symmetry, it is shown how to build two associated quantum symmetries s and s. These generalized BRS and anti-BRS symmetries interchange classical and ghost fields. A direct consequence of the closure and Jacobi identities of the classical algebra are the complete nilpotency relations s2 = ss+ss = s2 = 0. This nilpotency allows one to derive very simply the correct quantum lagrangian from the classical one without recourse to the Faddeev-Popov construction. A simple formal proof is given, showing that s and s are preserved by renormalization.