Recollections of My Work on Msugra with Pran Nath and Richard

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2 published in Trieste Lectures Series[10]) since there were some other weighty ideas we were after and these included the construction of a realistic model of particle interactions within the N = 1 supergravity framework where supersymmetry was broken by a super Higgs mechanism. The main aim was to obtain soft breaking including mass growth for the sparticles which overcame the pitfalls of models based on global supersymmetry where, for example, spontaneous breaking of supersymmetry leads to a squark having mass less than that of a quark. Thus beginning in early Spring of 1982, our efforts over the next few months were focused in this direction. There were several hurdles to be overcome. The first was to break supersymmetry and adjust the vacuum energy to zero. This could be done by breaking supersymmetry by a super Higgs mechanism, and utilizing the fact that the scalar potential of the model was not positive definite, to fix the vacuum energy to zero. The second was to protect the low energy theory below the Planck scale from mass growth of the size of the Planck mass. Such a mass growth would arise naturally if the super Higgs mechanism occurred in the same sector where the quarks, leptons and other matter fields reside in the superpotential. To overcome this hurdle the superpotential was split into two different sectors, a (visible) sector where visible matter, i.e., quarks, leptons, and Higgs, reside and a (hidden) sector where the super Higgs mechanism operates. The key idea here was to have no direct interaction between these two sectors. Because of a lack of this direct interaction soft masses in the physical sector of the size of the Planck scale are avoided. On the other hand, the two sectors are coupled by gravitational interactions because of the supergravity structure of the scalar potential. An interesting question then arises, what is the implication of breaking of supersymmetry in the hidden sector on the visible sector?. We addressed this issue by deducing the effective low energy theory in the visible sector. The result of the analysis was very interesting in that the scalar fields in the visible sector showed mass 2 growths of size O(m /MPlanck) where m is an effective intermediate scale that appears in the super Higgs effect. Thus with m ∼ 1010 GeV, soft masses of size O(102−3) GeV could be generated. Additionally we found that there were soft bilinear and trilinear couplings in the effective theory before the Planck scale. The nature of soft breaking depends on the nature of Kahler potential chosen and for the analysis we performed the Kahler potential was assumed to be flat. Consequently our analysis exhibited a universality of the soft parameters. There are two further phenomena which need to be commented on in

3 this initial work on supergravity model building. The first one is that the model we were working with was a grand unified supergravity model. And in this model the breaking of supersymmetry and of grand unification was accomplished in one step. Quite remarkably the soft breaking was found to be independent of not just the Planck scale but also of the grand unification scale MG. Second, in our analysis we showed that the soft breaking lead to the breaking of the electroweak symmetry from SU(2)L × U(1)Y to U(1)em. Thus together these phenomena produced a supergravity grand unification with soft breaking of electroweak size and provided also for an explanation for the breaking of the electroweak symmetry. All these results are contained in our first paper Ref.[11]. After the submission of our work to Physical Review Letters[11] we became aware of the work of Cremmer et al on the couplings of N = 1 supergravity[12]. However, this paper did not contain formulation of a SUGRA model with hidden sector breaking. Immediately after, we received the work of Ref[13] which also achieved soft breaking of supersymmetry through the hidden sector mechanism. However, this work did not contain a grand unification nor an exhibition of the phenomenon that the low energy theory was independent of MG. I spent the next three years working hard in a very fruitful collaboration with Dick and Pran on different applications of N = 1 supergravity pushing the idea to its limits which resulted in many interesting additional works[14, 15, 16, 17, 18, 19, 20, 21, 22]. I learned from them how to work as part of a team, spending endless hours in discussions. They served for me an excellent example of how to dedicate oneself to science. With Pran I found the friend who was eager to help long after I left Northeastern. I am glad for having his friendship all these years.

References

[1] Pran Nath and R. Arnowitt, Generalized Supergauge Symmetry as a New Framework for Uniﬁed Gauge Theories, Phys. Lett. B 56, 177 (1975).

[2] Ali H. Chamseddine, Supersymmetry and Higher Spin Fields, PH. D. Thesis, Chapters IV and V, Imperial College, London University (1976).

[3] Ali H. Chamseddine, N=4 Supergravity Coupled to N=4 Matter, Nucl. Phys. B 185, 403 (1981).

4 [4] Ali H. Chamseddine, Interacting Supergravity in Ten-Dimensions: The Role of the Six-Index Gauge Field, Phys. Rev. D24, 3065 (1981).

[5] P. Candelas, G. Horowitz, A. Strominger and E. Witten, Vacuum Con- ﬁgurations for Superstrings, Nucl. Phys. B 258, 46 (1985).

[6] S. Dimpoulos and H. Georgi, Softly Broken Supersymmetry and SU(5), Nucl. Phys. B 193, 150 (1981) and references therein.

[7] R. Arnowitt and Pran Nath, Comment on Eﬀective Lagrangian Formu- lations of the U(1) Axial Anomaly, Phys. Rev. D25, 595 (1982).

[8] E. Cremmer, B. Julia, J. Scherk, P. van Nieuwenhuizen, S. Ferrara and L. Giradello, Superhiggs Eﬀect in Supergravity with General Scalar Cou- plings Nucl. Phys. B 147, 105 (1979).

[9] For a review see P. van Nieuwenhuizen, Supergravtiy Phys. Rep. 68, 189 (1981).

[10] P. Nath, R. Arnowitt and A. H. Chamseddine, Applied N=1 Supergrav- ity, World Scientiﬁc, 1984.

[11] A. H. Chamseddine, R. Arnowitt and Pran Nath, Locally Supersymmet- ric Grand Uniﬁcation, Phys. Rev. Lett. 49, 970 (1982).

[12] E. Cremmer, S. Ferrara, L. Giradello and A. Van Proeyen, Yang-Mills Theories with Local Supersymmetry : Lagrangian, Transformation Laws and Superhiggs Eﬀect, Nucl. Phys. B 212, 413 (1983).

[13] R. Barbieri, S. Ferrara and C. A. Savoy, Gauge Models with Sponta- neously Broken Local Supersymmetry, Phys. Lett. B 119, 343 (1982).

[14] R. Arnowitt, A. H. Chamseddine and P. Nath, Quantum Loops and Dynamical Breaking of Supersymmetry in Locally Supersymmetric Guts, Phys. Lett. B 120, 145 (1983).

[15] P. Nath, R. Arnowitt and A. H. Chamseddine, Gravity Induced Sym- metry Breaking and Ground State of Local Supersymmetric Guts, Phys. Lett. B 121, 33 (1983).

[16] P. Nath, R. Arnowitt and A. H. Chamseddine, Gauge Hierarchy in Su- pergravity Guts, Nucl. Phys. B 227, 121 (1983).

5 [17] R. Arnowitt, A. H. Chamseddine and P. Nath, Masses of Superpartners of Quarks, Leptons, and Gauge Mesons in Supergravity Grand Uniﬁed Theories, Phys. Rev. Lett. 50, 232 (1983).

[18] T. C. Yuan, R. Arnowitt, A. H. Chamseddine and P. Nath, Supersym- metric Electroweak Eﬀects On g-2 (Mu), Z. Phys. C 26, 407 (1984).

[19] R. Arnowitt, A. H. Chamseddine and P. Nath, Nucleon Decay Branching Ratios in Supergravity SU(5) Guts, Phys. Lett. B 156, 215 (1985).

[20] P. Nath, A. H. Chamseddine and R. Arnowitt, Nucleon Decay in Super- gravity Uniﬁed Theories, Phys. Rev. D32, 2348 (1985).

[21] A. H. Chamseddine, P. Nath and R. Arnowitt, Experimental Signals for Supersymmetric Decays of the W and Z Bosons, Phys. Lett. B 129, 445 (1983)

[22] For a previous brief review of early history of the development of SUGRA models see, A. H. Chamseddine, R. Arnowitt and P. Nath, Supergravity Uniﬁca- tion, In Proceedings of 30 Years of Supersymmetry, Minneapolis, Minnesota, 13-27 Oct 2000, Nucl. Phys. Proc. Suppl. 101, 145 (2001) [arXiv:hep-ph/0102286].