Unless otherwise indicated, all of the following papers are authored jointly by Charles F. Doran, Michael G. Faux, S. James Gates, Jr., Tristan Hübsch, Kevin M. Iga, and Gregory D. Landweber.
DFGHIL (Peer-Reviewed, Journal-Intended) Papers
- math-ph/0512016
- On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields, Int. J. Mod. Phys. A22 (2007) 869-930.
Hanging Garden's Theorem; Main Sequence; Adinkra \to Superfield mapping (a superfield construct for every Adinkra of a family in terms of the superfield of any one Adinkra in that family). - math-ph/0603012
- Off-shell supersymmetry and filtered Clifford supermodules.
Clifford module = [Supersymmetry module]_{\partial_\tau\to1}; Supersymmetry modules recovered by deforming Clifford modules. - hep-th/0605269
- Adinkras and the Dynamics of Superspace Prepotentials, Adv. S. Th. Phys. 2 (3) (2008) 113-164.
Kinetic terms for all (1|N)-superfields; superfields for hook-shaped Adinkras; sums thereof = projectors. - hep-th/0611060
- A Counter-Example to a Putative Classification of 1-Dimensional, N-extended Supermultiplets, Adv. S. Th. Phys. 2 (3) (2008) 99-111.
N=5,6 counterexamples to Toppan's "complete classification"; response to their "refined complete classification"; counter-examples to their new claim. - 0710.5245
- On the Matter of \mathcal{N}=2 Matter, Phys. Lett. B659 (2008) 441-446.
The Hyperplet: a (24|72|72|24)-dimensional off-shell supermultiplet of center-less (4|8)-supersymmetry the on-shell reduction of which contains a Fayet Hypermultiplet; the relaxation mechanism. - 0803.3434
- Super-Zeeman Embedding Models on N-Supersymmetric World-Lines: Journal of Physics A: Mathematical and Theoretical, J. Phys. A 42 No. 6 (13 Feb. 2009) 065402 (12 pp.)
(N=1)-supersymmetric dipole, coupled to an external magnetic field, with the target space constrained either by Lagrange multipliers or a potential to an algebraic (sub)variety, has supersymmetry broken in the bulk of the parameter space but restored in the boundary. N>1 generalization of this using isoscalar and isospinor supermultiplets. - 0806.0050
- Topology Types of Adinkras and the Corresponding Representations of N-Extended Supersymmetry.
Demonstrates that the topology type of connected Adinkras is always a quotient of an N-dimensional cube with a doubly-even code. Describes our attempts to classify doubly-even codes. - 0809.5279
- Frames for supersymmetry, Accepted, Int. J. Mod. Phys. A (2009, in press).
Splitting Adinkras that are connected by one-way gray lines, as a model for a situation observed in N=2 matter multiplets, and N=1 vector multiplets. - 0811.3410
- Adinkras for Clifford Algebras, and Worldline Supermultiplets.
Adinkras are related to Clifford Algebras, which is used to produce a supermultiplet (with a Valise Adinkra) for every linear, doubly even binary block code. This classifies the chromotopologies of Adinkras, leaving open their "hanging" and edge-dashing. - 0901.4970
- A Superfield for Every Dash-Chromotopology.
We prove the first D.F.Ghil conjecture, by explicitly describing how to construct a constrained superfield for every doubly-even binary linear block code, together with an over-abundance of edge-dashing choices, which is guaranteed to include all inequivalent cases.
Conference Proceedings
- 0901.2136
- T. Hubsch, Superspace: a Comfortably Vast Algebraic Variety, in Geometric Analysis: Present and Future, eds. L. Ji et al., (International Press & Higher Education Press, 2009).
The canonical commutation relations (CCR), {[}H,\tau{]} = i\hbar, and the defining supersymmetry relations (DSR), \{Q_I,Q_J\}=2\delta_{IJ}H, imply via the Jacobi identity (Q_I,Q_J,\tau) that \tau':={[}Q,\tau{]}\neq0. In this way, supersymmetry extends (space)time to super(space)time, coordinatized by (\tau|\tau'|\tau''|\cdots|\tau^{[N]}). Since the consistency of CCR and DSR imply nothing of (anti)commutativity of \tau^{[k]}, super(space)time is seen to be fibered over the space of obstructions to its (anti)commutativity, coordinatized by \eta':={[}\tau,\tau'{]}, \eta^{(2)}:=\{\tau',\tau'\}, \eta^{[2]}:=\{\tau,\tau^{[2]}\}, etc. This fibration in turn itself is fibered over a space of obstructions to its (anti)commutativity, thus defining an indefinite hierarchical fibration, = the superspace indicated in the title. - Pre-arXive'd version, 0806.0051
- Relating doubly-even error-correcting codes, graphs, and irreducible representations of N-supersymmetry, in New Advances in Applied and Computational Mathematics, eds. F. Liu et al., Nova Science Publishers, Inc., Hauppauge, NY, 2007.
Every Adinkra topology is an iterated \mathbb{Z}_2-quotient of a cube; these iterated \mathbb{Z}_2-quotients are encoded, alternately, as 4k-gone graphs and as doubly even binary error-correcting codes; the classification of these through N=16; remark that: (1) direct sums, (2) kernels and (3) cokernels of supersymmetric maps define many more representations. - hep-th/0602259
- S. Bellucci, S. J. Gates Jr., E. Orazi, A Journey Through Garden Algebras, lectures delivered at the Winter School on Modern Trends in Supersymmetric Mechanics, 7-12 March 2005, Frascati, Italy.
- not arXive'd
- Off-shell supersymmetry via graph theory and superspace, BIRS Workshop 06frg313, 22-29 July 2006, final report.
Pre-DFGHIL Papers
- hep-th/0408004
- M. G. Faux, S. J. Gates, Jr., Adinkras: A Graphical Technology for Supersymmetric Representation Theory, Phys. Rev. D71 (2005) 065002.
- hep-th/0211034
- S. J. Gates, Jr., W. D. Linch, J. Phillips, When Superspace Is Not Enough.
Introduction of root superfields. - hep-th/0109109
- S. J. Gates, Jr., W. D. Linch, J. Phillips, L. Rana, The Fundamental Supersymmetry Challenge Remains, Grav. Cosmol. 8 (2002) 96-100.
- hep-th/9602072
- S. J. Gates, Jr., L. Rana, Tuning the RADIO to the off-shell 2-D Fayet hypermultiplet problem.
Introduction of the Klein flip on the arXiv. - not arXive'd
- S. J. Gates Jr., S. V. Ketov, 2D (4,4) Hypermultiplets (II): Field Theory Origins of Dualities, Phys. Lett. B418 (1998) 119-127.
Further discussion of the Klein flip. - hep-th/9510151
- S. J. Gates, Jr., L. Rana, A Theory of Spinning Particles for Large N-extended Supersymmetry (II), Phys. Lett. B369 (1996) 262-268.
Introduction of "Garden Algebras" - hep-th/9504025
- S. J. Gates, Jr., L. Rana, A Theory of Spinning Particles for Large N-extended Supersymmetry (I), Phys. Lett. B352 (1995) 50-58.
Introduction of "Garden Algebras" - hep-th/9410150
- S. J. Gates Jr., L. Rana, Ultra-Multiplets: A New Representation of Rigid 2D, N = 8 Supersymmetry, Phys. Lett. B342 (1995) 132-137.
Introduction of node-moving. - not arXive'd
- S. J. Gates, Jr., L. Rana, On Extended Supersymmetric Quantum Mechanics, UMDEPP 93-194 (1994).
Introduction of the Klein flip. - hep-th/9901038
- T. Hübsch, "Haploid (2,2)-Superfields in 2-Dimensional Spacetime”, Nucl. Phys. B555 (1999) 567-628.
Representations of (1,1|2,2)-supersymmetry: mostly off-shell, some on-shell, including the on-halfshell leftons and rightons; includes the "Adinkra" of the unconstrained (1|4|6|4|1) projection operators and component fields.