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Volume 334 - The 36th Annual International Symposium on Lattice Field Theory (LATTICE2018) - Theoretical Developments
Towards a Dual Representation of Lattice QCD
G. Gagliardi,* W. Unger
*corresponding author
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Published on: 2019 May 29
Our knowledge about the QCD phase diagram at finite baryon chemical potential $\mu_{B}$ is limited by the well known sign problem. The path integral measure, in the standard determinantal approach, becomes complex at finite $\mu_{B}$ so that standard Monte Carlo techniques cannot be directly applied. As the sign problem is representation dependent, by a suitable choice of the fundamental degrees of freedom that parameterize the partition function, it can get mild enough so that reweighting techniques can be used. A successful formulation, capable to tame the sign problem, is known since decades in the limiting case $\beta\to 0$, where performing the gauge integration first, gives rise to a dual formulation in terms of color singlets (MDP formulation). Going beyond the strong coupling limit represents a serious challenge as the gauge integrals involved in the computation are only partially known analytically and become strongly coupled for $\beta>0$. We will present explict formulae for all the integral relevant for ${\rm SU}(N)$ gauge theories discretised a la Wilson, and will discuss how they can be used to obtain a positive dual formulation, valid for all $\beta$, for pure Yang Mills theory.
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