33 research outputs found
Adinkra ‘color’ confinement in exemplary off-shell constructions of 4D, N = 2 supersymmetry representations
Evidence is presented in some examples that an adinkra quantum number,
(arXiv:\ 0902.3830 [hep-th]), seems to play a role with regard
to off-shell 4D, = 2 SUSY similar to the role of color in QCD. The
vanishing of this adinkra quantum number appears to be a condition required for
when two off-shell 4D, = 1 supermultiplets form an off-shell 4D, = 2 supermultiplet. We also explicitly comment on a deformation of the Lie
bracket and anti-commutator operators that has been extensively and implicitly
used in our work on "Garden Algebras" adinkras, and codes.Comment: 37 page
Luscher Term for k-string Potential from Holographic One Loop Corrections
We perform a systematic analysis of k-strings in the framework of the
gauge/gravity correspondence. We discuss the Klebanov-Strassler supergravity
background which is known to be dual to a confining supersymmetric gauge theory
with chiral symmetry breaking. We obtain the k-string tension in agreement with
expectations of field theory. Our main new result is the study of one-loop
corrections on the string theoretic side. We explicitly find the frequency
spectrum for both the bosons and the fermions for quadratic fluctuations about
the classical supergravity solution. Further we use the massless modes to
compute 1/L contributions to the one loop corrections to the k-string energy.
This corresponds to the Luscher term contribution to the k-string potential on
the gauge theoretic side of the correspondence.Comment: 39 pages, 3 figures. New Calculation showing explicit k -> M - k
symmetry of Energy utilizing the new figure. Discussion of non-k-dependence
of Luscher term at end of last section right before Conclusion. Same version
to be published in JHE
Exploring the Abelian 4D, = 4 Vector-Tensor Supermultiplet and Its Off-Shell Central Charge Structure
An abelian 4D, = 4 vector supermultiplet allows for a duality
transformation to be applied to one of its spin-0 states. The resulting theory
can be described as an abelian 4D, = 4 vector-tensor
supermultiplet. It is seen to decompose into a direct sum of an off-shell 4D,
= 2 vector supermultiplet and an off-shell 4D, = 2
tensor supermultiplet. The commutator algebra of the other two supersymmetries
are still found to be on-shell. However, the central charge structure in the
resulting 4D, = 4 vector-tensor supermultiplet is considerably
simpler that that of the parent abelian 4D, = 4 vector
supermultiplet. This appears to be due to the replacement of the usual SO(4)
symmetry associated with the abelian 4D, = 4 vector
supermultiplet being replaced by a
GL(2,)GL(2,) symmetry in the 4D,
= 4 vector-tensor supermultiplet. The code detailing the
calculations is available open-source at the HEPTHools Data Repository on
GitHub.Comment: HEPTHools Data Repository available open-source at
https://hepthools.github.io/Data/, added references and related content,
corrected group from SU(2) to GL(2,R
4D, Matter Gravitino Genomics
Adinkras are graphs that encode a supersymmetric representation's
transformation laws that have been reduced to one dimension, that of time. A
goal of the supersymmetry ``genomics'' project is to classify all 4D,
off-shell supermultiplets in terms of their adinkras.
In~previous works, the genomics project uncovered two fundamental isomer
adinkras, the cis- and trans-adinkras, into which all multiplets investigated
to date can be decomposed. The number of cis- and trans-adinkras describing a
given multiplet define the isomer-equivalence class to which the multiplet
belongs. A further refining classification is that of a supersymmetric
multiplet's holoraumy: the commutator of the supercharges acting on the
representation. The one-dimensionally reduced, matrix representation of a
multiplet's holoraumy defines the multiplet's holoraumy-equivalence class.
Together, a multiplet's isomer-equivalence and holoraumy-equivalence classes
are two of the main characteristics used to distinguish the adinkras associated
with different supersymmetry multiplets in higher dimensions. This paper
focuses on two matter gravitino formulations, each with 20 bosonic and 20
fermionic off-shell degrees of freedom, analyzes them in terms of their isomer-
and holoraumy-equivalence classes, and compares with non-minimal supergravity
which is also a 20x20 multiplet. This analysis fills a missing piece in the
supersymmetry genomics project, as now the isomer-equivalence and
holoraumy-equivalence for representations up to spin two in component fields
have been analyzed for 4D, supersymmetry. To handle the
calculations of this research effort, we have used the Mathematica software
package called Adinkra.m. This package is open-source and available for
download at a GitHub Repository. Data files associated with this paper are also
published open-source at a Data Repository also on GitHub.Comment: version 3, added self-gadget analysis, edited some text and
references, data available at the GitHub Repository
https://hepthools.github.io/Data/ that uses the Adinkra.m package available
at https://hepthools.github.io/Adinkra