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Register a new userNon-perturbative methods for false vacuum decay
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We propose a simple non-perturbative formalism for false vacuum decay using functional methods. We introduce the quasi-stationary effective action, a bounce action that non-perturbatively incorporates radiative corrections and is robust to strong couplings. The quasi-stationary effective action obeys an exact flow equation in a modified functional renormalization group with a motivated regulator functional. We demonstrate the use of this formalism in a simple toy model and compare our result with that obtained in perturbation theory.
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We consider the Skyrme model modified by the addition of mass terms which explicitly break chiral symmetry and pick out a specific point on the models target space as the unique true vacuum. However, they also allow the possibility of false vacua, local minima of the potential energy. These false vacuum configurations admit metastable skyrmions, which we call false skyrmions. False skyrmions can decay due to quantum tunnelling, consequently causing the decay of the false vacuum. We compute the rate of decay of the false vacuum due to the existence of false skyrmions.
The decay rate of a false vacuum is studied in gauge theory, paying particular attention to its gauge invariance. Although the decay rate should not depend on the gauge parameter $xi$ according to the Nielsen identity, the gauge invariance of the result of a perturbative calculation has not been clearly shown. We give a prescription to perform a one-loop calculation of the decay rate, with which a manifestly gauge-invariant expression of the decay rate is obtained. We also discuss the renormalization necessary to make the result finite, and show that the decay rate is independent of the gauge parameter even after the renormalization.
Chiral Effective Field Theory ($chi$EFT) has been extensively used to study the $NN$ interaction during the last three decades. In Effective Field Theories (EFTs) the renormalization is performed order by order including the necessary counter terms. Due to the strong character of the $NN$ interaction a non-perturbative resummation is needed. In this work we will review some of the methods proposed to completely remove cutoff dependencies. The methods covered are renormalization with boundary conditions, renormalization with one counter term in momentum space (or equivalently substractive renormalization) and the exact $N/D$ method. The equivalence between the methods up to one renormalization condition will be checked showing results in the $NN$ system. The exact $N/D$ method allows to go beyond the others, and using a toy model it is shown how it can renormalize singular repulsive interactions.
At large N, a field theory and its orbifolds (given by projecting out some of its fields) share the same planar graphs. If the parent-orbifold relation continues even nonperturbatively, then properties such as confinement and chiral symmetry breaking will appear in both parent and orbifold. N=1 supersymmetric Yang-Mills has many nonsupersymmetric orbifolds which resemble QCD. A nonperturbative parent-orbifold relation predicts many surprising effects, exactly valid at large N, and expected to suffer only mild 1/N corrections. These include degeneracies among bosonic hadrons and exact predictions for domain wall tensions. Other predictions are valid even when supersymmetry in the parent is broken. Since these theories are QCD-like, simulation is possible, so these predictions may be numerically tested. The method also relates wide classes of nonsupersymmetric theories.
The Krylov-Fock expression of non-decay (or survival) probability, which allows to evaluate the deviations from the exponential decay law (nowadays well established experimentally), is more informative as it readily provides the distribution function for the lifetime as a random quantity. Guided by the well established formalism for describing nuclear alpha decay, we use this distribution function to figure out the mean value of lifetime and its fluctuation rate. This theoretical framework is of considerable interest inasmuch as it allows an experimental verification. Next, we apply the Krylov-Fock approach to the decay of a metastable state at a finite temperature in the framework of thermo-field dynamics. In contrast to the existing formalism, this approach shows the interference effect between the tunnelings from different metastable states as well as between the tunneling and the barrier hopping. This effect looks quite natural in the framework of consistent quantum mechanical description as a manifestation of the double-slit experiment. In the end we discuss the field theory applications of the results obtained.
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