Nuc1ear Phy51c5 8262 (1985) 593-609 • N0rth-H011and Pu6115h1n9 C0mpany 57R1N65 1N 8ACK6R0UND F1ELD5 C.6. CALLAN J05eph Henry La60rat0r1e5, Pr1ncet0n Un1ver51ty, Pr1neet0n, NJ 08540, U5A D. FR1EDAN* Enr1c0 Ferm1 1n5t1tute and Dept. 0f Phy51c5, Un1ver51(v 0f Ch1ca90, Ch1ca90, 1L 60637, U5A E.J. MAR71NEC** and M.J. PERRY*** J05eph Henry La60rat0r1e5, Pr1ncet0n Un1t, er51(v, Pr1ncet0n, NJ 08544, U5A Rece1ved 19 June 1985 We f0rmu1ate the pr0pa9at10n 0f 5tr1n95 1n 6ack9r0und f1e1d5, 1nc1ud1n9 the effect5 0f metr1c, ant15ymmetr1c ten50r, and d11at0n expectat10n va1ue5, a5 we11 a5 9au9e f1e1d 6ack9r0und5 1n the ca5e 0f heter0t1c 5tr1n95. 7he 1nc1u510n 0f 6ack9r0und ferm10n f1e1d5 15 5ketched. 7he e4uat10n5 0f m0t10n 0f a11 the5e f1e1d5 are 5h0wn t0 6e the c0n5e4uence 0f (5uper) c0nf0rma1 1nvar1ance 0f the 5tr1n9. 1. 1ntr0duct10n 5uper5ymmetr1c 5tr1n9 the0r1e5 are pr0m151n9 cand1date5 f0r a un1f1ed the0ry 0f the phy51ca1 w0r1d. 7hey 0ffer the p05516111ty 0f exp1a1n1n9 the 10w-ener9y 5pectrum 0f ch1ra1 matter f1e1d5 1nteract1n9 thr0u9h 9au9e and 9rav1tat10na1 f0rce5 [1] 1n a framew0rk free 0f pertur6at1ve u1trav101et 1nf1n1t1e5 [2]. 7he h19h-ener9y 5pectrum 15 a1m05t un14ue1y determ1ned 6y re4u1r1n9 a c0n515tent 1nterp1ay 6etween 4uantum mechan1c5 and the reparametr12at10n 1nvar1ance 0f the 5tr1n9. Neverthe1e55, 0ur under5tand1n9 0f the 5tr1n9 the0ry 15 1nade4uate: at the m0ment we 0n1y kn0w h0w t0 ca1cu1ate 1n pertur6at10n the0ry, and pr0cedure5 f0r mu1t1100p ca1cu1at10n5 are 0n1y n0w 6e1n9 deve10ped. 51nce 10ca1 9au9e and c00rd1nate 5ymmetr1e5 are n0t man1fe5t 1n the Feynman ru1e5, the1r 0r191n and mean1n9 1n 5tr1n9 the0ry are 5t111 my5ter10u5. A fu11 under5tand1n9 w111 have t0 awa1t the d15c0very 0f the 9au9e- 1nvar1ant, 5ec0nd-4uant12ed 5tr1n9 act10n. 1n 0rder t0 he1p 6r1d9e th15 9ap 1n 0ur * 5upp0rted 1n part 6y D0E 9rant DE-F(102-84ER-45144 and the A1fred P. 510an F0undat10n. ** 5upp0rted 1n part 6y D0E 9rant DE-AC02-76ER-03072. *** 5upp0rted 1n part 6y N5F 9rant PHY-80-19754 and the A1fred P. 510an F0undat10n. 593