Mastering the master field

Gopakumar, Rajesh ; Gross, David J. (1995) Mastering the master field Nuclear Physics - Section B: Particle Physics, Field Theory and Statistical Systems, Physical Mathematics, 451 (1-2). pp. 379-415. ISSN 0550-3213

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The basic concepts of non-commutative probability theory are reviewed and applied to the large-N limit of matrix models. We argue that this is the appropriate framework for constructing the master field in terms of which large-N theories can be written. We explicitly construct the master field in a number of cases including QCD2. There we both give an explicit construction of the master gauge field and construct master loop operators as well. Most important we extend these techniques to deal with the general matrix model, in which the matrices do not have independent distributions and are coupled. We can thus construct the master field for any matrix model, in a well defined Hilbert space, generated by a collection of creation and annihilation operators-one for each matrix variable-satisfying the Cuntz algebra. We also discuss the equations of motion obeyed by the master field.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:22371
Deposited On:23 Nov 2010 12:57
Last Modified:23 Nov 2010 12:57

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