Volume 200, number 3 PHYSICS LETTERS B 14 January 1988 A PATH-DEPENDENT SUPERSYMMETRIC FIELD THEORY OF ELECTRIC AND MAGNETIC CHARGES ~" B. SAZDOVIC Instuute of Physws, P 0 Box 57, 11001 Belgrade, Yugoslavm and Brown Umverstty, Department of Physws, ProvMence, RI 02912, USA Received 8 May 1987 We present a supersymmetnc field theory of electric and magnetic charges with a genmne string As a consequence of the convenUonal and representauon preserving constraints, the superstrmg variable has only a bosonic (space-Ume) part ~. We discuss the string°independence of the theory. Supersymmetric quantum electromagnetodynam- lCS (SUSY QEMD) is a supersymmetnc dual m- variant theory of electric and magnetic charges. Recently, a one-prepotentlal formulatmn [ 1 ] and a two-prepotential formulatmn [2,3] of this theory have been formulated. Both formulations are equiv- alent [ 1] and at the classical level they depend on the fixed four-vector n u. In th~s letter we present a path-dependent for- mulation of SUSY QEMD with a genuine string. If we freeze the string in the n ~' direction we come back to the one-prepotential formulauon of ref. [ 1 ]. This is also a supersymmetric generalizaUon of the QEMD formulation with a string [ 4 ]. In each formulation of SUSY QEMD at least one type of particle (a pole or a charge) has a string vari- able. Therefore, we will use gauge invanant and path- dependent SUSY QED [ 5 ] which already has a string as an unphyslcal variable, as a basis for SUSY QEMD. The action is [ 5 ] gt,=l fdxd20 m2-~-l fdxd20 ~/'2 , (1) ~ Work supported in part by the Department of Energy, contract DE-AC02-76ER03130 A021 - Task A Supported m part by the Serbian Soence Foundation, Yugoslawa t" ds = -2Jdx d20 d20~ exp(2o'2v) s, d,n=me(fdxd2OsVs+h.c.), (lcont'd) where s= , g=lgJ g21 are matter superfields and W,~, l~. are field strengths. Both are (anti)chiral and gauge mvanant. The superfields s, L W~, W~ are independent field vari- ables while the superfield -1 I v(z,P)= ~ dzl [T'~(z-z,)W~(Zl) + Tc~(Z-Z~)g"(z,)] (2) is the field strength dependent prepotential. The operators To,(z)=(a~,#,,)o,¢O"Da J d~ ~ 6(~) , (P) ~.(z)=(6~aJ.0"Dp ~ d¢~ ~(4) (3) (P) (for properties of T~, 7~ see re£ [3]) depend on the path P:~=¢~'(z,s)(-~<s~O), with endpomt z~={x ~, 0% 6,~}. In the derivaUon of eq. (2) we have used the con- 335