Worldsheet matter superfields on half-shell

Abstract

In this paper we discuss some of the effects of using "unidexterous" worldsheet superfields, which satisfy worldsheet differential constraints ∂ = Λ = 0 = ∂ = | Υ and so are partly on-shell, i.e., on half-shell. Most notably, this results in a stratification of the field space that reminds of "brane-world" geometries. Linear dependence on such superfields provides a worldsheet generalization of the super-Zeeman effect. In turn, non-linear dependence yields additional left-right asymmetric dynamical constraints on the propagating fields, again in a stratified fashion. PACS: 11.30.Pb, 12.60.Jv Introduction, Results and SynopsisSupersymmetry has been studied for almost four decades [1,2,3,4], but still seems to harbor novel features. In particular, worldsheet supersymmetry is unique among supersymmetric field theories in that the Lorentz group is abelian Spin(1, 1) U(1). This permits the definition of the twistedchiral superfields [5], and a whole host of supersymmetry representations not possible in higherdimensional spacetimes [6]; see Eqs. (1.2b)-(1.2c) for two that we will need herein: the lefton and rightons superfields, denoted Λ and Υ, respectively.In superfield formulations of supersymmetry it is not uncommon that some of the component fields, called auxiliary, end up having algebraic equations of motion. It is routinely assumed that such algebraic equations may be solved for, and their solutions substituted back into the Lagrangians, thereby obtaining an equivalent but simpler description of the model.It is our main purpose to point out that this is not as straightforward as it may seem, that it may well impose rather non-standard dynamical constraints on the model, and may well result in stratifying the field space of the model into regions (strata) of varying dimensions and dynamics. As worldsheet models are most often used in superstring theory and suitable subsets of the field space are identified as the effective, "real" spacetime, worldsheet models with such stratified field space would seem to provide a natural Lagrangian framework for "brane-world"-like geometries.The remainder of this section offers a basic review of (1, 1|2, 2)-superspace notation, with a few technical details deferred to Appendix A. Section 2 employs this to derive some simple consequences of using lefton superfields Λ, and section 3 showcases these results in a few simple but nontrivial examples. Section 4 collects our conclusions.

On dimensional extension of supersymmetry: from worldlines to worldsheets

“…Worldsheet dimensional extension is thus a stepping stone towards dimensional extension to higher-dimensional spacetimes. Of course, worldsheet supersymmetry is also important in its own right [23][24][25][26] and affords comparison with numerous known results; see [2,5,[27][28][29][30][31][32][33][34][35], to name but a few.…”

“…In addition to spin, all objects also have an engineering (mass-) dimension, defined by α− ). If it is subject to only unidextrous worldsheet differential equations [29,32] (involving either ∂ = | or ∂ = but not both), it is said to be on the half-shell [35]; such superfields are not off-shell in the standard field-theoretic sense on the worldsheet, but are off-shell on a continuum of unidextrously embedded worldlines and can provide for dynamics not describable otherwise [39]. Calling a superfield, operator, expression, equation or another construct thereof ambidextrous emphasizes that it is not unidextrous.…”

“…α− -transformations, but these superderivatives -and then also ∂ = -must annihilate the supermultiplet: α− and consequently also by ∂ = , so that they are on-the-half-shell [35]. The analogous holds for parity-mirrored extension to worldsheet (p, N )-supersymmetry, for arbitrary p.…”

Weaving worldsheet supermultiplets from the worldlines within

“…Worldsheet supersymmetry is essential in string theory [31,32,33,34], and is very rich in structure [35,36]. Worldsheet theories include worldlines and worldline-restricted (unidextrous) fields in several inequivalent ways [37,38,39,40,41,42,43,44], which provides for exceptional constructions on the worldsheet not possible in spacetimes of any other dimension and which provides for much of the richness and complexity of string theory and its M -and F -theoretic extensions. In addition, extending worldline supersymmetry to a worldsheet is a stepping stone in the realization of the original proposal [7,8] of studying higher-dimensional supersymmetry via dimensional extension of worldline results.…”

Final Year Project Report

“…These works rely on previous publications under this grant [7,8,9,10,6,11,12,13,14,15,16,17,18,19,20,21,22,23,24].…”