Talk presented by Nayasinganahalli Hari Dass

Parallel Session: Theoretical Developments II

Friday July 2nd, 14.30 - 14.50, Room 8

Numerical Simulations of d=3 SU(2) Lattice Gauge Theory in the Dual Formulation

Abstract: The d=3 SU(2) Lattice gauge theory has been formulated in the dual formulation by Anishetty et al [1]. There are many attractive features of this approach the chief among them being ; i) the disordered operators are diagonal in this representation, and hence it may be easier to study their role in confinement than the conventional Lattice Gauge Theories.ii) there is an immediate connection to the Regge-Ponzano formulation of d=3 gravity.iii) it is a completely new approach to Lattice Gauge Theories. In this work we have laid the foundations for numerical simulations in this approach. SU(2) angular momenta live on the edges as well as the diagonals of the plaquettes of the dual lattice and the action consists of a product of a product of 5 SU(2) 6-j symbols for each elementary cube of the dual lattice. Two types of updates have been constructed. In the "Local" method, every angular momentum is updated to a new value in a range allowed by the various triangle inequalities.But this does not allow half-integral values to be changed to integral values and is hence not ergodic. The other method which is "Quasi-local",all the variables in the interrior of a 8-cube volume are changed and this allows half-integral values to be changed to integral values. It is possible to study the role of Z(2)-fluctuations by switching on/off the quasi-local updates.The t'Hooft disordered variables can be directly measured. On the other hand, objects which are simple to study in the conventional LGT's like Wilson loops are more complicated in this approach. The Kagome-lattice construction given by [2] has been used to construct really efficient updating algorithms for both the local and quasi-local cases. Some preliminary results obtained with small lattices will be presented. Also, the generalisation of the original construction of [1] to d=4 given by [3] is currently being studied to carry out our program for d=4. References: [1] R. Anishetty, Srinath Cheluvaraja, H.S. Sharatchandra and Manu Mathur, Phys. Letts. B314(1993) 387,hep-lat/9210024. [2] G.H. Gadiyar, Ph.D Thesis (1995),Institute of Mathematical Sciences,Chennai. [3] I. Halliday and P. Suranyi, Phys. Letts. B350(1995)189, hep-lat/9412110.

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