S. Solomon

Covariant canonical quantization of the green-schwarz superstring

Introducing a new type of D = 10 harmonic superspace with two generations of harmonic coordinates, we reduce the Green-Schwarz (GS) superstring to a system whose constraints are Lorentz covariant and functionally independent. These features allow us to impose Lorentz-covariant gauge fixing conditions for the reparametrization and the fermionic κ-invariances. The resulting QBRST corresponds to the finite-dimensional Lie algebra of the remaining purely harmonic constraints. The super-Poincare symmetry acts in a manifestly Lorentz-covariant form and is apparently anomaly free.

Covariant first and second quantization of the N = 2, D = 10 Brink-Schwarz superparticle

Using a new type of harmonic superspace variables, we reduce the N = 2, D = 10 Brink-Schwarz (BS) superparticle to a system whose constraints are (i) first class, (ii) functionally independent and (iii) Lorentz covariant. We show that these features are essential for a correct covariant quantization. QBRST is first rank. By using it to second quantize the system, we obtain a covariant off-shell unconstrained superfield action of the linearized D = 10 type IIB supergravity. A corresponding procedure for the Green Schwarz (GS) superstring is conjectured.

The twistor geometry of the covariantly quantized Brink-Schwarz superparticle

Abstract We perform the Lorentz-covariant BFV-BRST quantization of the Brink-Schwarz (BS) superparticle by reducing it to a system whose constraints are all covariant, first class and independent (CFI). This procedure requires the presence of certain auxiliary pure gauge variables which are then recognized as (super-)twistors. In a particular covariant gauge, the system reduces to a purely (super-)twistor one. We present several extensions of this 4-dimensional construction to higher dimensions.

Covariant unconstrained superfield action for the linearized D = 10 super-Yang-Mills theory

A new type of D = 10 harmonic superspace with two generations of harmonics allows us to reduce the D = 10, N = 1 Brink-Schwarz (BS) superpaticle to a system whose constraints are all first class, functionally independent and Lorentz-covariant. Given these properties, the covariant BFV-BRST quantization of the system is straightforward. By second quantizing this system, we circumvent the no-go theorem which forbids the existence of a covariant off-shell unconstrained superfield action for the linearized D = 10 super-Yang-Mills theory.

The fermionic matrix, instantons, zero modes and multigrid

Abstract We apply multigrid (MG) concepts to the problem of estimating the fermionic determinant. MG is used both as an analysis guide and as calculational tool. The MG analysis emphasizes the role of the “approximate zero modes” (AZM) in the slowing down of the process. We demonstrate that in the case of a single AZM the MG allows the estimation of the inverse matrix for K-S fermions with no slowing down . The connection between the total topological charge Q tot and the convergence rate is striking. While the convergence rate in a straightforward two-level “experiment” is poor for one smooth instanton ( Q tot = 1), it is good for an instanton-anti-instanton ( Q tot = 0), irrespective of their relative distance.

(Super-) field theories from (super-) twistors

Abstract We obtain higher spin linearized field theories through the BRST second quantization of the classical D =4 massless point particle. By applying the same procedure to the classical supersymmetric particles, one obtains linearized N -extended off-shell unconstrained superfield actions. By extending the procedure to D =10, one is led to a new spacetime geometry which reduces in some limit to the usual D =10 Minkowski geometry.

Off-shell superspace D = 10 super-Yang-Mills from a covariantly quantized Green-Schwarz superstring

Abstract We construct a gauge-invariant superspace action in terms of unconstrained off-shell superfields for the D = 10 supersymmetric Yang-Mills (SYM) theory. We use to this effect: 1. (i) the point particle limit of the BRST charge of the covariantly quantized harmonic Green-Schwarz superstring, 2. (ii) a general covariant action principle for overdetermined systems of nonlinear field equations of motion. One obtains gauge and super-Poincare invariant equations of motion equivalent to the Nilssons constraints for D = 10 SYM. In the previous approaches (light-cone-gauge, component-fields) one would have to sacrifice either explicit Lorentz invariance or explicit supersymmetry while in the present approach they are both manifest. Unfortunately the action we find is nonlocal in space-time. To restore locality one may have to introduce additional degrees of freedom.

Vortices and phase transitions in two-dimensional non-abelian spin models

Abstract We modify O(n) models (n>2) in two dimensions so as to comparedifferent thoeries with identical local properties and different global ones. Our O′ (3) model with a particular interaction has vortex-like configuration (π1(P2) = Z2) though it is locally equivalent to an O (3) model (π1(S2) = 0). Our results have been obtained by means of strong coupling methods. The Pade extrapolants show a critical value xc = 11.8.

The hadronic spectrum with dynamical fermions

Abstract Results are presented of a numerical calculation of the hadronic spectrum on a 12 3 ×24 lattice, which incorporates the effects due to virtual quark-antiquark pairs.

New canonical covariant formalism for then N=2, D=10 superparticle

Abstract Using a harmonic superspace with new geometry one reduces the N =2, D =10 Brink-Schwarz (BS) superparticle to a covariant system with first-class independent constraints only.