Whether conformal supersymmetry is broken by quantum p-branes with exotic supersymmetry?
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Classical and quantum symmetries of super $p$-branes preserving exotic 3/4 fraction of $N=1 D=4$ global supersymmetry are studied. Classical realization of the algebra of global and world-volume symmetries is constructed and its quantum generalizations are analyzed. Established is that the status of the conformal supersymmetry $OSp(1|8)$ as a proper quantum symmetry of brane depends both on the choice of its vacuum state and the associated ordering of $\hat{\cal Q}$ and $\hat{\cal P}$ operators.
Latex, 18 pages, no figures. Talk given at the International Workshop "Supersymmetry and Quantum Symmetries SQS'03", July 2003, Dubna. V2: title corrected, added new material in Sec. 6 and Conclusion, new references included, typos corrected
Latex, 18 pages, no figures. Talk given at the International Workshop "Supersymmetry and Quantum Symmetries SQS'03", July 2003, Dubna. V2: title corrected, added new material in Sec. 6 and Conclusion, new references included, typos corrected