An Effective Lagra!vgi for Supersymmetric Qcd*

I present a Lagrangian which describes the spontaneous breaking of chiral symmetries in strongly interacting supersymmetric Yang-Mills theory with matter fields. This Lagrangian predicts that supersymmetry is spontaneously broken if the matter fields have precisely zero mass. Lecture presented at the Workshop on “Problems in Unification and Supergravity” La Jolla Institute, La Jolla, California January 12-16, 1983 *Work supported by the Department of Energy under contract DEAC03-76SF00515. Over the past few years, as our understanding of weakly coupled supersymmetric theories has steadily increased, t,he dynamics of strongly coupled super_ symmetric Ya,ng-Mills theory has come to appear more and more mysterious. Initially, it was tempting t,o regard these theories as having qualitatively the same behavior as ordinary gauge theories of fermions. Using this hypothesis, Dine, Fischler, and Srednicki’ and Dimopoulos and Raby2 argued that these theories should show spontaneous supersymmetry brealking. This conclusion, however, was appa,rently contradicted when Witten derived a striking constraint on dynamical supersymmetry breaking. 3 This contradiction has left workers in this field more than a little puzzled and has led to a consensus that the pattern of chiral symmetry breaking in supersymmetric Yang-Mills theory must be an unusual one. However, it need not be so. In this lecture, I will demonstrate this by exhibiting an effective Lagrangian describing the spontaneous breaking of chiral symmetry in supersymmetric Yang-Mills theory which is consistent both with the physical picture of Dine, Fischler, Srednicki, Dimopoulos and Raby and with the constraints proved by \Titten. This conclusion differs from that of a ree4 cent paper by Taylor, Veneziano, and Yankielowicz, I will clarify the difference between my analysis and theirs as I proceed. I will restrict my attention in this lecture to theories in which a gauge supermultiplet (A,, X, Dj couples to matter fields which belong to a real representation of the gauge group. For most of the analysis of this paper, I will take this representation to comprise n copies each of a complex representation f and its complex conjugate P. The matter supermultiplets are, then, of the form: where i = I,. . . , n. $J denotes a left-handed fermion; the other fields are complex