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Matrix models and gravitational corrections. (English) Zbl 1061.81070
Summary: We provide evidence of the relation between supersymmetric gauge theories and matrix models beyond the planar limit. We compute gravitational $$R^2$$ couplings in gauge theories perturbatively, by summing genus one matrix model diagrams. These diagrams give the leading $$1/N^2$$ corrections in the large $$N$$ limit of the matrix model and can be related to twist field correlators in a collective conformal field theory.
In the case of softly broken $$\text{SU}(N)\,{\mathcal N}= 2$$ super Yang-Mills theories, we find that these exact solutions of the matrix models agree with results obtained by topological field theory methods.

##### MSC:
 81T60 Supersymmetric field theories in quantum mechanics 81T13 Yang-Mills and other gauge theories in quantum field theory 83E30 String and superstring theories in gravitational theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81V17 Gravitational interaction in quantum theory 81T45 Topological field theories in quantum mechanics
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