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Register a new userInertial Symmetry Breaking
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Added by
Christopher T. Hill
Publication date
2018
fields
Physics
and research's language is
English
Authors
Christopher T. Hill
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We review and expand upon recent work demonstrating that Weyl invariant theories can be broken inertially, which does not depend upon a potential. This can be understood in a general way by the current algebra of these theories, independently of specific Lagrangians. Maintaining the exact Weyl invariance in a renormalized quantum theory can be accomplished by renormalization conditions that refer back to the VEVs of fields in the action. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential that breaks a U(1) symmetry together,with scale invariance.
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Weyl invariant theories of scalars and gravity can generate all mass scales spontaneously, initiated by a dynamical process of inertial spontaneous symmetry breaking that does not involve a potential. This is dictated by the structure of the Weyl current, $K_mu$, and a cosmological phase during which the universe expands and the Einstein-Hilbert effective action is formed. Maintaining exact Weyl invariance in the renormalised quantum theory is straightforward when renormalisation conditions are referred back to the VEVs of fields in the action of the theory, which implies a conserved Weyl current. We do not require scale invariant regulators. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential.
We demonstrate a novel feature of certain phase transitions in theories with large rank symmetry group that exhibit specific types of non-local interactions. A typical example of such a theory is a large-$N$ gauge theory where by `non-local interaction we mean the all-to-all coupling of color degrees of freedom. Recently it has been pointed out that nontrivial features of the confinement/deconfinement transition are understood as consequences of the coexistence of the confined and deconfined phases on the group manifold describing the color degrees of freedom. While these novel features of the confinement/deconfinement transition are analogous to the two-phase coexistence at the first order transition of more familiar local theories, various differences such as the partial breaking of the symmetry group appear due to the non-local interaction. In this article, we show that similar phase transitions with partially broken symmetry can exist in various examples from QFT and string theory. Our examples include the deconfinement and chiral transition in QCD, Gross-Witten-Wadia transition in two-dimensional lattice gauge theory, Douglas-Kazakov transition in two-dimensional gauge theory on sphere, and black hole/black string transition.
We consider the electroweak phase transition in the conformal extension of the standard model known as SU(2)cSM. Apart from the standard model particles, this model contains an additional scalar and gauge field that are both charged under the hidden SU(2)$_X$. This model generically exhibits a very strong phase transition that proceeds after a large amount of supercooling. We estimate the gravitational wave spectrum produced in this model and show that its amplitude and frequency fall within the observational window of LISA. We also discuss potential pitfalls and relevant points of improvement required to attain reliable estimates of the gravitational wave production in this - as well as in more general - class of models. In order to improve perturbativity during the early stages of transition that ends with bubble nucleation, we solve a thermal gap equation in the scalar sector inspired by the 2PI effective action formalism.
We study anomalous chiral symmetry breaking in two-flavour QCD induced by gravitational and QCD-instantons within asymptotically safe gravity within the functional renormalisation group approach. Similarly to QCD-instantons, gravitational ones, associated to a K3-surface connected by a wormhole-like throat in flat spacetime, generate contributions to the t~Hooft coupling proportional to $exp(-1/g_N)$ with the dimensionless Newton coupling $g_N$. Hence, in the asymptotically safe gravity scenario with a non-vanishing fixed point coupling $g_N^*$, the induced t Hooft coupling is finite at the Planck scale, and its size depends on the chosen UV-completion. Within this scenario the gravitational effects on anomalous $U(1)_A$-breaking at the Planck scale may survive at low energy scales. In turn, fermion masses of the order of the Planck scale cannot be present. This constrains the allowed asymptotically safe UV-completion of the Gravity-QCD system. We map-out the parameter regime that is compatible with the existence of light fermions in the low-energy regime.
We consider phase transitions on (eternal) de Sitter in an O(N) symmetric scalar field theory. Making use of Starobinskys stochastic inflation we prove that deep infrared scalar modes cannot form a condensate -- and hence they see an effective potential that allows no phase transition. We show that by proving convexity of the effective potential that governs deep infrared field fluctuations both at the origin as well as at arbitrary values of the field. Next, we present numerical plots of the scalar field probability distribution function (PDF) and the corresponding effective potential for several values of the coupling constant at the asymptotic future timelike infinity of de Sitter. For small field values the effective potential has an approximately quadratic form, corresponding to a positive mass term, such that the corresponding PDF is approximately Gaussian. However, the curvature of the effective potential shows qualitatively different (typically much softer) behavior on the coupling constant than that implied by the Starobinsky-Yokoyama procedure. For large field values, the effective potential as expected reduces to the tree level potential plus a positive correction that only weakly (logarithmically) depends on the background field. Finally, we calculate the backreaction of fluctuations on the background geometry and show that it is positive.
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