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Register a new userSpectrum of Yang-Mills theory in 3 and 4 dimensions
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Authors
Marco Frasca
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We solve exactly the Dyson-Schwinger equations for Yang-Mills theory in 3 and 4 dimensions. This permits us to obtain the exact correlation functions till order 2. In this way, the spectrum of the theory is straightforwardly obtained and comparison with lattice data can be accomplished. The results are in exceedingly good agreement with an error well below 1%. This extends both to 3 and 4 dimensions and varying the degree of the gauge group. These results provide a strong support to the value of the lattice computations and show once again how precise can be theoretical computations in quantum field theory.
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We give a comparison of the spectrum of Yang-Mills theory in $D=3+1$, recently derived with a strong coupling expansion, with lattice data. We verify excellent agreement also for 2$^{++}$ glueball. A deep analogy with the $D=2+1$ case is obtained and a full quantum theory of this approach is also given.
We obtain the next-to-leading order correction to the spectrum of a SU(N) Yang-Mills theory in four dimensions and we show agreement well-below 1% with respect to the lattice computations for the ground state and one of the higher states.
To set the stage, I discuss the $beta$-function of the massless O(N) model in three dimensions, which can be calculated exactly in the large N limit. Then, I consider SU(N) Yang-Mills theory in 2+1 space-time dimensions. Relating the $beta$-function to the expectation value of the action in lattice gauge theory, and the latter to the trace of the energy-momentum tensor, I show that $frac{d ln g^2/mu}{dln mu}=-1$ for all $g$ and all N in one particular renormalization scheme. As a consequence, I find that the Yang-Mills $beta$-function in three dimensions must have the same sign for all finite and positive bare coupling parameters in any renormalization scheme, and all non-trivial infrared fixed points are unreachable in practice.
It is shown how, starting from a mapping theorem recently proved between massless quartic scalar field theory and Yang-Mills theory, both two-point functions and spectrum of the Yang-Mills theory can be obtained. These results compare very well with respect to lattice computations.
We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a marginally confining theory. The potential we obtain agrees fairly well with preceding findings in literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali-Kim-Nair analysis. Classical solutions depend on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory and is now fully justified. The agreement obtained with the lattice results for the ground state of the theory is well below 1% at any value of the degree of the group.
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