Abstract
We present a new dual representation for lattice QCD in terms of wordlines and worldsheets. The exact reformulation is carried out using the recently developed abelian color flux method where the action is decomposed into commuting minimal terms that connect different colors on neighboring sites. Expanding the Boltzmann factors for these commuting terms allows one to reorganize the gauge field contributions according to links such that the gauge fields can be integrated out in closed form. The emerging constraints give the dual variables the structure of worldlines for the fermions and worldsheets for the gauge degrees of freedom. The partition sum has the form of a strong coupling expansion and with the abelian color flux approach discussed here all coefficients of the expansion are known in closed form. We present the dual form for three cases: pure SU(3) lattice gauge theory, strong coupling QCD and full QCD, and discuss in detail the constraints for the color fluxes and their physical interpretation.
Highlights
An important strategy in theoretical physics is to find different representations of a system, such that after rewriting a model in terms of new degrees of freedom different physical aspects are revealed or new methods can be applied
In the context of lattice field theories exact transformations to representations in terms of worldlines for matter fields and worldsheets for gauge degrees of freedom have been studied in recent years
Recently more abstract questions were addressed concerning the form of the constraints for the dual variables for different symmetries of the conventional representation
Summary
An important strategy in theoretical physics is to find different representations of a system, such that after rewriting a model in terms of new degrees of freedom different physical aspects are revealed or new methods can be applied. In WG1⁄2p we collect all weights from the expansion of the individual Boltzmann factors and the beta functions resulting from the Haar measure integrals These weight factors are organized with respect to powers of the inverse gauge coupling β, i.e., the dual formulation in terms of ACC cycle occupation numbers which we develop here is a strong coupling expansion. The configurations of the cycle occupation numbers cPome with weight factors W1⁄2p that are themselves sums fl;m;mg over configurations of the auxiliary plaquette variables lax;bμcνd and the link-based auxiliary variables max;bμ and max;bμ In these sums the constraint (22) restricts the configurations of the max;bμ and max;bμ by connecting their differences jax;bμ 1⁄4 max;bμ − max;bμ to J1x;2μ.
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