Gauge symmetry from decoupling

Abstract

Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang-Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.Comment: 18 pages, 1 figur

Reliability of Lattice Gauge Theories

“…Our results thus form a theoretical basis for some previous works, which have found evidence that quantum simulators may approximately retain gauge invariance [23][24][25][26][27][28][29], and they complement protection schemes based on classical noise [30]. Moreover, our work complements existing results on equilibrium theories: gauge-invariant equilibrium phases can emerge in a low-energy effective theory, even if the microscopic description breaks gauge invariance, e.g., in topological phases of matter [31], when the gauge degree of freedom decouples because of a large mass [32], or when gauge-noninvariant terms at a small scale renormalize away at large distances ("light from chaos") [33][34][35]. Model.-Here, we focus on out-of-equilibrium dynamics, which is highly pertinent for current quantum simulators in ultracold atomic gases [14,[16][17][18] and for which emergent gauge symmetry has received considerably less attention.…”

Gauge-invariant fields and flow equations for Yang–Mills theories

“…For α → 0 this realizes the decoupling scenario of ref. [14], with a diverging quadratic term for c ′ . Since eq.…”

Graviton fluctuations erase the cosmological constant

“…They are the basis of all computations in classical gravity and therefore well tested by experiment. Within functional renormalization it has been argued [17,28,29] that these properties indeed hold, provided one chooses a suitable physical gauge fixing or, equivalently, a constraint on conserved sources and physical fluctuations. These assumptions imply that the effective action for traceless transversal tensor fluctuations around flat space can be expanded as…”