D-Brane Probes in the Matrix Model

Abstract

Recently, a new approach to large N gauge theories, based on a generalization of the concept of D-brane probes to any gauge field theory, was proposed. In the present note, we compute the probe action in the one matrix model with a quartic potential. This allows to illustrate several non-trivial aspects of the construction in an exactly solvable set-up. One of our main goal is to test the bare bubble approximation. The approximate free energy found in this approximation, which can be derived from a back-of-an-envelope calculation, matches the exact result for all values of the 't Hooft coupling with a surprising accuracy. Another goal is to illustrate the remarkable properties of the equivariant partial gauge-fixing procedure, which is at the heart of the formalism. For this we use a general xi-gauge to compute the brane action. The action depends on xi in a very non-trivial way, yet we show explicitly that its critical value does not and coincide with twice the free energy, as required by general consistency. This is made possible by a phenomenon of ghost condensation and the spontaneous breaking of the equivariant BRST symmetry.

39 pages, including 12 figures and one appendix; v2: typos corrected

References in corpus (4)

• A Perturbative Window into Non-Perturbative Physics
• Insightful D-branes
• Extended N=1 super Yang-Mills theory
• Phase with no mass gap in non-perturbatively gauge-fixed Yang--Mills theory

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