Neil Marcus

Three-Dimensional Supergravity Theories

Two three-dimensional supergravity theories are constructed. The first one has eight local supersymmetries as well as an SO(8, n) global symmetry, where n is an arbitrary positive integer. The physical spectrum consists of 8n scalars and 8n spinors. The second theory has sixteen local supersymmetries and an E8,8 global symmetry. The 128 bosons and 128 fermions transform as inequivalent spinors of the SO(16) subalgebra. The theories are formulated without auxiliary scalar fields, which requires that the non-compact symmetries act non-linearly.

Field theories that have no manifestly Lorentz-invariant formulation

Abstract A class of theories for which the Lorentz algebra closes only on the mass-shell, and which therefore cannot be written in a manifestly Lorentz-invariant form, is presented. Examples include certain supergravity theories in six and ten dimensions. These results make the corresponding phenomenon in the case of supersymmetry algebras less surprising. The also shed light on the problem of finding off-mass-shell dual string model amplitudes.

Ten-dimensional supersymmetric Yang-Mills theory in terms of four-dimensional superfields☆

Abstract We show that the usual formulation of the N = 4 supersymmetric Yang-Mills theory in terms of N = 1 superfields can be generalized to describe the full ten-dimensional theory.

Tree-level constraints on gauge groups for type I superstrings

A set of conditions expressing tree-level unitarity in the theory of open superstrings has recently been formulated by Schwarz. His conjecture that the Yang-Mills gauge group must be a classical group, with the massless particles in the adjoint representation, is proved in detail. It is also shown how the representations of the massive states are classified in each one.

The ultraviolet behavior of N=4 Yang-Mills and the power counting of extended superspace

Abstract A two-loop calculation in the N = 4 supersymmetric Yang-Mills theory is performed in various dimensions. The theory is found to be two-loop finite in six dimensions or less, but infinite in seven and nine dimensions. The six-dimensional result can be explained by a formulation of the theory in terms of N = 2 superfields. The divergence in seven dimensions is naively compatible with both N = 2 and N = 4 superfield power counting rules, but is of a form that cannot be written as an on-shell N = 4 superfield integral. The hypothesized N = 4 extended superfield formalism therefore either does not exist, or at least has weaker consequences than would have been expected. This leads one to expect that four-dimensional supergravity theories diverge at three loops. Some general issues about the meaning of finiteness in nonrenormalizable theories are discussed. In particular, we discuss the use of field redefinitions, the generalization of wave function renormalizations to nonrenormalizable theories, and whether counterterms should be used in calculations in finite theories.

A test of finiteness predictions for supersymmetric theories

Abstract We find that the N = 4 supersymmetric Yang-Mills theory is two-loop finite in six dimensions, despite the existence of a suitable supersymmetric counterterm. This supports the power-counting rules of extended superspace, suggesting that N = 8 supergravity in four dimensions is at least six-loop finite.

Infinite symmetry algebras of extended supergravity theories

Abstract When extended supergravity theories with noncompact symmetry groups are written in a physical gauge, the noncompact symmetries join with the supersymmetries to generate an infinite-dimensional algebra. The details are worked out explicitly for a two-dimensional theory with an SU(1, 1) internal symmetry. Our analysis confirms the observation of Ellis et al. that the infinite rigid superalgebra should be obtained from the finite-dimensional local superalgebra by replacing scalar fields with their asymptotic values at infinity. The infinite algebra is described by extending the super-Poincare generators to functions on the coset space defined by the scalar fields at infinity. While mathematically nontrivial, this result is, in a certain sense, trivial from a physical point of view.