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Register a new userThe Topological Theory of the Milnor Invariant $bar{mu}(1,2,3)$
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We study a topological Abelian gauge theory that generalizes the Abelian Chern-Simons one, and that leads in a natural way to the Milnors link invariant $bar{mu}(1,2,3)$ when the classical action on-shell is calculated.
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The subject of this work is a three-dimensional topological field theory with a non-semisimple group of gauge symmetry with observables consisting in the holonomies of connections around three closed loops. The connections are a linear combination of gauge potentials with coefficients containing a set of one-dimensional scalar fields. It is checked that these observables are both metric independent and gauge invariant. The gauge invariance is achieved by requiring non-trivial gauge transformations in the scalar field sector. This topological field theory is solvable and has only a relevant amplitude which has been computed exactly. From this amplitude it is possible to isolate a topological invariant which is Milnors triple linking invariant. The topological invariant obtained in this way is in the form of a sum of multiple contour integrals. The contours coincide with the trajectories of the three loops mentioned before. The introduction of the one-dimensional scalar field is necessary in order to reproduce correctly the particular path ordering of the integration over the contours which is present in the triple Milnor linking coefficient. This is the first example of a local topological gauge field theory that is solvable and can be associated to a topological invariant of the complexity of the triple Milnor linking coefficient.
We construct the one-dimensional topological sector of $mathcal N = 6$ ABJ(M) theory and study its relation with the mass-deformed partition function on $S^3$. Supersymmetric localization provides an exact representation of this partition function as a matrix integral, which interpolates between weak and strong coupling regimes. It has been proposed that correlation functions of dimension-one topological operators should be computed through suitable derivatives with respect to the masses, but a precise proof is still lacking. We present non-trivial evidence for this relation by computing the two-point function at twoloop, successfully matching the matrix model expansion at weak coupling and finite ranks. As a by-product we obtain the two-loop explicit expression for the central charge $c_T$ of ABJ(M) theory. Three- and four-point functions up to one-loop confirm the relation as well. Our result points towards the possibility to localize the one-dimensional topological sector of ABJ(M) and may also be useful in the bootstrap program for 3d SCFTs.
From the 2002 data taking with a neutral kaon beam extracted from the CERN-SPS, the NA48/1 experiment observed 97 $Xi^{0}rightarrow Sigma^{+} mu^{-} bar{ u}_{mu}$ candidates with a background contamination of $30.8 pm 4.2$ events. From this sample, the BR($Xi^{0}rightarrow Sigma^{+} mu^{-} bar{ u}_{mu}$) is measured to be $(2.17 pm 0.32_{mathrm{stat}}pm 0.17_{mathrm{syst}})times10^{-6}$.
We consider a general gauge theory with independent generators and study the problem of gauge-invariant deformation of initial gauge-invariant classical action. The problem is formulated in terms of BV-formalism and is reduced to describing the general solution to the classical master equation. We show that such general solution is determined by two arbitrary generating functions of the initial fields. As a result, we construct in explicit form the deformed action and the deformed gauge generators in terms of above functions. We argue that the deformed theory must in general be non-local. The developed deformation procedure is applied to Abelian vector field theory and we show that it allows to derive non-Abelain Yang-Mills theory. This procedure is also applied to free massless integer higher spin field theory and leads to local cubic interaction vertex for such fields.
The absolute branching fraction of $Lambda to p mu^- bar{ u}_{mu}$ is reported for the first time based on an $e^+e^-$ annihilation sample of ten billion $J/psi$ events collected with the BESIII detector at $sqrt{s}=3.097$ GeV. The branching fraction is determined to be ${mathcal B}(Lambda to pmu^- bar{ u}_{mu}) = [1.48pm0.21(rm stat) pm 0.08(rm syst)]times 10^{-4}$, which is a significant improvement in precision over the previous indirect measurements. Combining this result with the world average of ${mathcal B}(Lambda to p e^- bar{ u}_{e})$, we obtain the ratio, $frac{Gamma(Lambda to p mu^- bar{ u}_{mu})}{Gamma(Lambda to p e^- bar{ u}_{e})}$, to be $0.178 pm 0.028$, which agrees with the standard model prediction assuming lepton flavor universality. The asymmetry of the branching fractions of $Lambda to p mu^- bar{ u}_{mu}$ and $bar{Lambda} to bar{p} mu^+ u_{mu}$ is also determined, and no evidence for $CP$ violation is found.
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