{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:24:06Z","timestamp":1760243046672,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2015,6,16]],"date-time":"2015-06-16T00:00:00Z","timestamp":1434412800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"U.S. National Science Foundation","award":["PHY-0354401"],"award-info":[{"award-number":["PHY-0354401"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper investigates the d = 4, N = 4 Abelian, global Super-Yang Mills system (SUSY-YM). It is shown how the N = 2 Fayet Hypermultiplet (FH) and N = 2 vector multiplet (VM) are embedded within. The central charges and internal symmetries provide a plethora of information as to further symmetries of the Lagrangian. Several of these symmetries are calculated to second order. It is hoped that investigations such as these may yield avenues to help solve the auxiliary field closure problem for d = 4, N = 4, SUSY-YM and the d = 4, N = 2 Fayet-Hypermultiplet, without using an infinite number of auxiliary fields.<\/jats:p>","DOI":"10.3390\/sym7021080","type":"journal-article","created":{"date-parts":[[2015,6,16]],"date-time":"2015-06-16T10:28:09Z","timestamp":1434450489000},"page":"1080-1121","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Extended Detailed Investigation of First and Second Order Supersymmetries for Off-Shell N = 2 and N = 4 Supermultiplets"],"prefix":"10.3390","volume":"7","author":[{"suffix":"Jr.","given":"Sylvester","family":"Gates","sequence":"first","affiliation":[{"name":"Center for String and Particle Theory, Department of Physics, University of Maryland, College Park, MD 20742-4111, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James","family":"Parker","sequence":"additional","affiliation":[{"name":"Center for String and Particle Theory, Department of Physics, University of Maryland, College Park, MD 20742-4111, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vincent","family":"Rodgers","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, The University of Iowa, Iowa City, IA 52242, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leo","family":"Rodriguez","sequence":"additional","affiliation":[{"name":"Department of Physics, Assumption College, Worcester, MA 01609, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kory","family":"Stiffler","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Physics, and Astronomy, Indiana University Northwest, Gary, IN 46408, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,6,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"231","DOI":"10.4310\/ATMP.1998.v2.n2.a1","article-title":"The large N limit of superconformal field theories and supergravity","volume":"2","author":"Maldacena","year":"1998","journal-title":"Adv. Theor. Math. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Klebanov, I.R., and Strassler, M.J. (2000). Supergravity and a confining gauge theory: Duality cascades and chiSB-resolution of naked singularities. JHEP, 8.","DOI":"10.1088\/1126-6708\/2000\/08\/052"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1103\/PhysRevLett.86.588","article-title":"Towards the large N limit of pure N = 1 super Yang Mills","volume":"86","author":"Maldacena","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/S0550-3213(01)00236-X","article-title":"Supersymmetric non-singular fractional D2-branes and NS-NS 2-branes","volume":"B606","author":"Cvetic","year":"2001","journal-title":"Nucl. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Maldacena, J.M., and Nastase, H.S. (2001). The supergravity dual of a theory with dynamical supersymmetry breaking. JHEP, 9.","DOI":"10.1088\/1126-6708\/2001\/09\/024"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Canoura, F., Edelstein, J.D., Zayas, L.A.P., Ramallo, A.V., and Vaman, D. (2006). Supersymmetric branes on AdS5 \u00d7 Y p,q and their field theory duals. JHEP, 3.","DOI":"10.1088\/1126-6708\/2006\/03\/101"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Herzog, C.P., and Klebanov, I.R. (2001). Gravity duals of fractional branes in various dimensions. Phys. Rev. D., 63.","DOI":"10.1103\/PhysRevD.63.126005"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Herzog, C.P. (2002). String tensions and three dimensional confining gauge theories. Phys. Rev. D., 66.","DOI":"10.1103\/PhysRevD.66.065009"},{"key":"ref_9","first-page":"3","article-title":"Regge trajectories revisited in the gauge\/string correspondence","volume":"B682","author":"Sonnenschein","year":"2004","journal-title":"Nucl. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Pando Zayas, L.A., Rodgers, V.G.J., and Stiffler, K. (2008). Luscher term for k-string potential from holographic one loop corrections. JHEP, 12.","DOI":"10.1088\/1126-6708\/2008\/12\/036"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Doran, C.A., Pando Zayas, L.A., Rodgers, V.G.J., and Stiffler, K. (2009). Tensions and Luscher terms for (2+1)-dimensional k-strings from holographic models. JHEP, 11.","DOI":"10.1088\/1126-6708\/2009\/11\/064"},{"key":"ref_12","unstructured":"Stiffler, K. Mesons From string theory. arXiv:0909.5681. Available online: http:\/\/arxiv.org\/abs\/0909.5681."},{"key":"ref_13","unstructured":"Stiffler, K. (2010). A Walk through Superstring Theory with an Application to Yang-Mills Theory: K-Strings and D-branes as Gauge\/gravity Dual Objects. [Ph.D. Thesis, University of Iowa]."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/0370-2693(81)90887-X","article-title":"On off-shell supermultiplets","volume":"105","author":"Siegel","year":"1981","journal-title":"Phys. Lett. B."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Aharony, O., Bergman, O., Jafferis, D.L., and Maldacena, J. (2008). N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals. JHEP, 10.","DOI":"10.1088\/1126-6708\/2008\/10\/091"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/0370-2693(92)90277-B","article-title":"Remarks on the N = 2 supersymmetric Chern-Simons theories","volume":"281","author":"Gates","year":"1992","journal-title":"Phys. Lett. B."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3371","DOI":"10.1142\/S0217751X93001363","article-title":"Chern-Simons theories with supersymmetries in three-dimensions","volume":"A8","author":"Nishino","year":"1993","journal-title":"Int. J. Mod. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0550-3213(94)90600-9","article-title":"Extended supersymmetry and superBF gauge theories","volume":"B432","author":"Brooks","year":"1994","journal-title":"Nucl. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/0370-2693(95)00474-Y","article-title":"A Theory of spinning particles for large N extended supersymmetry","volume":"352","author":"Gates","year":"1995","journal-title":"Phys. Lett. B."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1088\/0264-9381\/1\/5\/004","article-title":"Unconstrained N = 2 Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace","volume":"1","author":"Galperin","year":"1984","journal-title":"Class. Quant. Grav."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Galperin, A., Ivanov, E., Ogievetsky, V., and Sokatchev, E. (1985). Harmonic Supergraphs. Feynman Rules and Examples. Class. Quant. Grav., 2.","DOI":"10.1088\/0264-9381\/2\/5\/005"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/0550-3213(84)90592-3","article-title":"Twisted Multiplets and New Supersymmetric Nonlinear Sigma Models","volume":"B248","author":"Gates","year":"1984","journal-title":"Nucl. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/0370-2693(84)90120-5","article-title":"Selfinteracting tensor multiplets in N = 2 superspace","volume":"147","author":"Karlhede","year":"1984","journal-title":"Phys. Lett. B."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/0550-3213(76)90458-2","article-title":"Fermi-Bose hypersymmetry","volume":"B113","author":"Fayet","year":"1976","journal-title":"Nucl. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Gates, S.J.J., Gonzales, J., MacGregor, B., Parker, J., Polo-Sherk, R., Rodgers, V.G.J., and Wassink, L. (2009). 4D, N = 1 Supersymmetry Genomics (I). JHEP, 12.","DOI":"10.1088\/1126-6708\/2009\/12\/008"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0370-2693(81)90743-7","article-title":"Quantum geometry of bosonic strings","volume":"103","author":"Polyakov","year":"1981","journal-title":"Phys. Lett. B."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0370-2693(81)90744-9","article-title":"Quantum geometry of fermionic strings","volume":"103","author":"Polyakov","year":"1981","journal-title":"Phys. Lett. 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