Physical State Conditions Research Articles

Modified superstring in the light-cone gauge

The covariant superstring theory proposed by Siegel is studied in the light-cone gauge. The physical states are the direct product of those of the Green-Schwarz superstring and the additional internal space spanned by light-cone spinors. The former is closed under super Poincaré transformations. The latter must be invariant under a set of gauge transformations remaining in the light-cone gauge. When the invariance is imposed as the physical state conditions, it is shown that no physical state exists for the modified superstring theory.

Nilpotent BRST invariance of the interacting Polyakov string

The BRST invariance currently popular in the construction of second-quantized string theories is only nilpotent on-shell. We show that the Faddeev-Popov representation of Polyakov's interacting bosonic string admits a BRST invariance that is also nilpotent off-shell. The invariant vertices are just the Weyl- and reparametrization-invariant vertices of the original model. We also show that failure of the physical state condition is intimately related to the divergences of the theory and suggest that its rehabilitation be a requirement of any scheme adopted to regularize and renormalize the model.

A detailed study of the physical state conditions in covariantly quantized string theories

We offer a detailed account of the Goddard-Thorn proof of the no-ghost theorem which incorporates simplifications presented earlier. We extend these methods to obtain a new calculation of the cohomology of the nilpotent operator Q occuring in BRST quantized strings. We further explain why the apparent doubling of transverse states in the cohomology of Q has no physical significance.

Physical state conditions and supersymmetry breaking in quantum mechanics

It is shown, by giving an explicit example, how the conditions imposed on physically admissible states can affect the pattern of supersymmetry breaking and, as a consequence, the values of physically interesting quantities such as the Witten index. As a by-product an unusual kind of explicit supersymmetry breaking is observed, where the supersymmetry algebra still holds formally, as well as a spontaneous breakdown of supersymmetry, which is not induced by instantons.

Comments on covariant formulations of string theories

We clarify the role of the critical dimension in some covariant formulations of string theory. The action for the free string proposed by Banks and Peskin is shown to be equivalent to the light-cone dynamics of Goddard, Goldstone, Rebbi, and Thorn if and only if the dimension of spacetime is critical and α 0=1. If these conditions are not satisfied, the action principle does not imply the physical state conditions in a class of completely fixed light-cone gauges.