7-11 July 2014
Africa/Johannesburg timezone
<a href="http://events.saip.org.za/internalPage.py?pageId=16&confId=34"><font color=#0000ff>SAIP2014 Proceedings published on 17 April 2015</font></a>

The Large-N Limit Of Matrix Models And AdS/CFT

8 Jul 2014, 14:20
D Les 104

D Les 104

Oral Presentation Track G - Theoretical and Computational Physics Theoretical


Mr Mbavhalelo Mulokwe (University of the Witwatersrand)

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Abstract content <br> &nbsp; (Max 300 words)<br><a href="http://events.saip.org.za/getFile.py/access?resId=0&materialId=0&confId=34" target="_blank">Formatting &<br>Special chars</a>

Random matrix models have found numerous applications in both Theoretical Physics and Mathematics. In the AdS/CFT correspondence, for example, the dynamics of the half-BPS states can be fully described in terms of the holormorphic sector of a single complex matrix model which is related to (1+1)-dimensional free fermions in a harmonic potential.

In this work, we consider the strong-coupling limit of multi-matrix models coupled via Yang-Mills interactions. In particular, we consider the significance of rescaling the matrix fields. In order to investigate the role played by such a rescaling, we consider the matrix quantum mechanics of a simple Hermitian system. The system is compactified on a circle, and using the Das-Jevicki-Sakita Collective Field Theory approach we obtain the exact ground-state energy of the system.

We then fully compactify N=4 SYM on the four-sphere. A radial sub-sector is readily identified and the eigenvalue spectrum obtained for an arbitrary number of matrices. For two matrices we parametrize the system using matrix valued polar coordinates. A closed form (using the Harish-Chandra-Itzykson-Zuber formula) for the saddle point equations at strong-coupling is derived. A complementary approach to the saddle point equations technique - based on the Dyson-Schwinger equations - is given. The system is then regulated with a Penner-type potential and the density of eigenvalues is obtained.

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Main supervisor (name and email)<br>and his / her institution

Prof. JP Rodrigues.
University of the Witwatersrand, Johannesburg.

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Primary author

Mr Mbavhalelo Mulokwe (University of the Witwatersrand)

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