J.L. Petersen

A Supersymmetric Wess-Zumino Lagrangian in Two-Dimensions

Abstract We construct a supersymmetric version of the Wess-Zumino action in two dimensions. For a special value of the coupling constant γ 2 = 4 π / n it turns out that this theory consists of the original WZ action plus free fermions in the adjoint representation. By bosonization such a theory should be equivalent to a theory of two sets of free fermions. We study in some detail how supersymmetry is realized in these two theories. We further develop the general formalism for studying any two-dimensional quantum theory that is superconformal and super-Kac-Moody invariant, the SWZ theory and the particular free Fermi theory being examples. We generalize and apply this formalism to prove the equivalence of SWZ to a free Fermi theory.

Explicit Construction of Unitary Representations of the N=2 Superconformal Algebra

Abstract A representation based on free fermions has been found, realizing the unitary representations of N = 2 superconformal theory when the central charge, c2, is between 0 and 1. The results confirm previous conjectures for the list of discrete values of c2 and the superconformal dimensions, h, for highest-weight states with t = 0 in the Neveu-Schwarz sector (and t = ±1 4 in the Ramond sector). Here t is the eigenvalue of the U(1) Kac-Moody current in the theory. For t ≠ 0 ( ±1 4 ) new results are obtained, including a list of possible discrete t-values and a modified list of the possible discrete h-values.

N=2 extended superconformal theories in two dimensions

Abstract The general formalism for studying these theories is set up and some details are given concerning degenerate representations of the N=2 super Virasoro algebra in (generalized) Neveu-Schwarz and Ramond sectors. In particular the N=2 version of Kacs formula for conformal dimensions is derived.

The Wess-Zumino action in two dimensions and non-abelian bosonization

Abstract Using recent results on fermionic determinants in two-dimensional non-abelian background fields we give a very simple path integral demonstration of the equivalence between the free Fermi theory in this background and a corresponding chiral Bose theory with Wess-Zumino action. The result is compared to previously proposed bosonization rules and certain limitations to the general validity of these are found.

On the Unitary Representations of N=2 Superconformal Theory

Abstract The Kac formula for superconformal dimensions (generalized to N = 2) is further developed (compared to a previous article). A list of discrete values of the central charge for which unitary representations are expected to exist is proposed. For several of these, unitarity is checked by computer. For two values, unitarity is proven by providing explicit fermionic representations. For one of those values, the N = 2 theory coincides with a sub theory of one of the known unitary N = 1 theories, thus extending a similar situation between N = 0 and N = 1.

COVARIANT N STRING AMPLITUDE

The BRST-invariant N-reggeon vertex (for the bosonic string) previously given by us in the operator formulation is considered in more detail. In particular we present a direct derivation from the string path integral. Several crucial symmetry properties found a posteriori before, become a priori clearer in this formulation. A number of delicate points related to zero modes, cut off procedures and normal ordering prescriptions are treated in some detail. The old technique of letting the string field acquire a small dimension 12e → 0+ is found especially elegant.

BRST INVARIANT N REGGEON VERTEX

Abstract An N -reggeon vertex is constructed with the inclusion of the contribution of the ghost coordinates. It is shown that it is projective and BRST invariant.

Covariant loop-calculus for the closed bosonic string

Covariant N-string amplitudes for the closed bosonic string are analyzed with emphasis on the relation between ghost zero modes and integration measure over Koba-Nielsen like variables (here we find that a modification of the results of refs. [1,18] is needed). Factorization and correct BRST-cohomology properties are established. Multi-loop amplitudes for arbitrary external states are constructed by formulating sewing rules generalizing the old treatment of reggeons to include ghosts. In particular the ghost zero modes encode and generate the measure on moduli space in a way similar to ideas proposed by Martinec [2]. Explicit N-tachyon multi-loop results agree with results of ref. [30] obtained using similar, but technically quite different methods, and manifestly show Belavin-Knizhnik singularities when surfaces degenerate.

Polyakov's quantized string with boundary terms

Abstract We compute the boundary terms due to the conformal anomaly which are needed in Polyakovs method of calculating averages of functionals defined on surfaces. The method we use is due to Seeley, who found recursive relations yielding the boundary terms. We solve these relations for a general second-order elliptic differential operator. This solution is then applied to Polyakovs problem.

Properties of the three-reggeon vertex in string theories

Abstract We construct in a very simple way a three-reggeon vertex that includes also the contribution of the ghost coordinates, both for the bosonic and fermionic string. We show its connection with the vertex operators that are usually used to construct dual amplitudes and with the light-cone three-string vertex. Finally, we prove its invariance under BRST transformations.