18-24 June 2017
Palacio de Congresos
Europe/Madrid timezone
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Contribution Parallel

Andalucía I
Theoretical Developments

Loop equation in Lattice gauge theories and bootstrap-like methods

Speakers

  • Prof. Martin KRUCZENSKI

Primary authors

Content

In principle the loop equation provides a complete formulation of a gauge theory purely in terms of Wilson loops. In the case of lattice gauge theories the loop equation is a well defined equation for a discrete set of quantities and can be easily solved at strong coupling either numerically or by series expansion. At weak coupling, however, we argue that the equations are not well defined unless a certain set of positivity constraints is imposed. Using semi-definite programming we show numerically that, for a pure Yang Mills theory in two, three and four dimensions, these constraints lead to good results for the mean value of the energy at weak coupling. Further, the positivity constraints imply the existence of a positive definite matrix whose entries are expectation values of Wilson loops. This matrix allows us to define a certain entropy associated with the Wilson loops. We compute this entropy numerically and describe some of its properties. Finally we discuss some preliminary ideas for extending the results to supersymmetric N=4 SYM.

Preferred track (if multiple tracks have been selected)

Theoretical Developments