Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-03-31
JHEP 0308 (2003) 021
Physics
High Energy Physics
High Energy Physics - Theory
27 pages, 2 figures; v2: minor corrections and clarifications; v3: published version
Scientific paper
10.1088/1126-6708/2003/08/021
We study the matrix model/gauge theory connection for three different N=1 models: U(N) x U(N) with matter in bifundamental representations, U(N) with matter in the symmetric representation, and U(N) with matter in the antisymmetric representation. Using Ward identities, we explicitly show that the loop equations of the matrix models lead to cubic algebraic curves. We then establish the equivalence of the matrix model and gauge theory descriptions in two ways. First, we derive generalized Konishi anomaly equations in the gauge theories, showing that they are identical to the matrix-model equations. Second, we use a perturbative superspace analysis to establish the relation between the gauge theories and the matrix models. We find that the gauge coupling matrix for U(N) with matter in the symmetric or antisymmetric representations is_not_ given by the second derivative of the matrix-model free energy. However, the matrix-model prescription can be modified to give the gauge coupling matrix.
Naculich Stephen G.
Schnitzer Howard J.
Wyllard Niclas
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