Nucl ear Physi cs B354 ( 1991) 141- 153 Nort h-Hol l and ELEMENTAR! ' FI VE- BRANE SOLUTI ONS OF D= 10 SUPERGRAVI TY M.J . DUFF' : AND J .X. LU* * Cent er f or Theor et i cal Pl t psi cs, Physi cs Depart ment , Texas A&A1 Uri her ci t y. Col l ege St at i on, TX 77843, USA Recei ved 22 Oct ober 1990 We f i nd exact sol ut i ons to t he f i el d equat i ons of t en-di mensi onal super gr avi t y cor r espondi ng to st abl e mul t i - f i ve- br ane conf i gur at i ons whi ch br eak hal f t he spacet i me supersymmet ri es . The sol ut i ons sat ur at e a Bogomol ' nyi bound bet ween t he mas s per uni t ar ea and t he conser ved Noet her char ge, whi ch al so guar ant ees t hei r st abi l i t y. We compar e and cont r ast t hi s el ement ary f i ve- br ane sol ut i on with St r om i nger s sol i t oni c f i ve- br ane sol ut i on, and di scuss t he i mpl i cat i ons f or st r i ng/ f i ve- br ane dual i t y. 1 . I nt r oduct i on N= 1, D= 10 super gr avi t y has t wo f ormul at i ons : one with a 7- f or m f i el d st r engt h [ 1] and one with a 3- f or m st r engt h [ 2] . Pr ovi ded we coupl e t hem to EK X E H or SO( 32) super - Yang- M i l l s, t hen bot h ar e anomal y f r ee [ 3, 4] . Si nce t he 3- f or m ver si on cor r esponds to t he l ow- ener gy lim it of t he het er ot i c st r i ng, it was conj ect ur ed t hat t her e exi st s a " het er ot i c f i ve- br ane" r el at ed to t he 7- f or mver si on [ 5] . The super f i ve- br ane is wel l known [ 6] but t he het er ot i c f i ve- br ane has yet to be const r uct ed expl i ci t l y. Its exi st ence has never t hel ess been demonst rat ed r ecent l y by St r om i nger [ 7] who f i nds t hat t he het er ot i c st r i ng adm its t he het er ot i c f i ve- br ane as a sol i t on sol ut i on . Act ual l y, he sol ves t he l ow- ener gy super gr avi t y equat i ons but he assumes, and so shal l we, t hat t he f ul l st r i ng equat i ons al so adm it such a sol i t on. Pr i or to t hi s, Dabhol kar et al . [ 8] demonst rat ed t hat t he el ement ary st r i ng emer ges as a cl assi cal sol ut i on of t he 3- f or m ver si on of t he D= 10 super gr avi t y equat i ons. Thi s sol ut i on may be shown to f ol l ow by si mul t aneous di mensi onal r educt i on of t he el ement ary super membr ane sol ut i on of D = 11 super gr avi t y [ 9] . However , nei t her of t hese sol ut i ons ar e " sol i t ons" , whi ch woul d be non- si ngul ar conf i gur at i ons st abi l i zed by an i dent i cal l y conser ved t opol ogi cal char ge. They i nst ead exhi bi t 5- f unct i on si ngul ar i t i es at t he l ocat i on of t he ext ended obj ect and ar e st abi l i zed by a conser ved Noet her char ge. They bot h sat ur at e a Bogomol ' nyi * Work suppor t ed in par t by NSF gr ant PHY- 9045132 . * Suppor t ed by a Worl d Labor at or y Schol ar shi p. 0550- 3213/ 91/ $03. 50©1991 - El sevi er Sci ence Publ i sher s B.V . ( Nor t h- Hol l and)