EPJ Web Conf.
Volume 175, 201835th International Symposium on Lattice Field Theory (Lattice 2017)
|Number of page(s)||7|
|Section||11 Theoretical Developments|
|Published online||26 March 2018|
Loop equation in Lattice gauge theories and bootstrap methods
Department of Physics and Astronomy, Purdue U., 525 Northwestern Avenue, W. Lafayette, IN 47907-2036, USA.
2 Wigner Research Center for Physics of the HAS, 29–33 Konkoly–Thege Miklós Str. H-1121 Budapest, Hungary.
* Speaker, e-mail: firstname.lastname@example.org, partially supported by DOE under Grant DE-SC0007884.
Published online: 26 March 2018
In principle the loop equation provides a complete formulation of a gauge theory purely in terms ofWilson 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 theWilson 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.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
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