Chern-Weil global symmetries and how quantum gravity avoids them

We draw attention to a class of generalized global symmetries, which we call “Chern-Weil global symmetries,” that arise ubiquitously in gauge theories. The Noether currents of these Chern-Weil global symmetries are given by wedge products of gauge field strengths, such as F2 ∧ H3 and tr($$ {F}_2^2 $$ F 2 2 ), and their conservation follows from Bianchi identities. As a result, they are not easy to break. However, it is widely believed that exact global symmetries are not allowed in a consistent theory of quantum gravity. As a result, any Chern-Weil global symmetry in a low-energy effective field theory must be either broken or gauged when the theory is coupled to gravity. In this paper, we explore the processes by which Chern-Weil symmetries may be broken or gauged in effective field theory and string theory. We will see that many familiar phenomena in string theory, such as axions, Chern-Simons terms, worldvolume degrees of freedom, and branes ending on or dissolving in other branes, can be interpreted as consequences of the absence of Chern-Weil symmetries in quantum gravity, suggesting that they might be general features of quantum gravity. We further discuss implications of breaking and gauging Chern-Weil symmetries for particle phenomenology and for boundary CFTs of AdS bulk theories. Chern-Weil global symmetries thus offer a unified framework for understanding many familiar aspects of quantum field theory and quantum gravity.

Inflation in Supergravity from Field Redefinitions

Supergravity (SUGRA) theories are specified by a few functions, most notably the real Kähler function denoted by G ( T i , T ¯ i ) = K + log | W | 2 , where K is a real Kähler potential, and W is a holomorphic superpotential. A field redefinition T i → f 1 ( T i ) changes neither the theory nor the Kähler geometry. Similarly, the Kähler transformation, K → K + f 2 + f ¯ 2 , W → e − f 2 W where f 2 is holomorphic and leaves G and hence the theory and the geometry invariant. However, if we perform a field redefinition only in K ( T i , T ¯ i ) → K ( f ( T i ) , f ( T ¯ i ) ) , while keeping the same superpotential W ( T i ) , we get a different theory, as G is not invariant under such a transformation while maintaining the same Kähler geometry. This freedom of choosing f ( T i ) allows construction of an infinite number of new theories given a fixed Kähler geometry and a predetermined superpotential W. Our construction generalizes previous ones that were limited by the holomorphic property of W. In particular, it allows for novel inflationary SUGRA models and particle phenomenology model building, where the different models correspond to different choices of field redefinitions. We demonstrate this possibility by constructing several prototypes of inflationary models (hilltop, Starobinsky-like, plateau, log-squared and bell-curve) all in flat Kähler geometry and an originally renormalizable superpotential W. The models are in accord with current observations and predict r ∈ [ 10 − 6 , 0.06 ] spanning several decades that can be easily obtained. In the bell-curve model, there also exists a built-in gravitational reheating mechanism with T R ∼ O ( 10 7 G e V ) .

Entropy and Gravitation—From Black Hole Computers to Dark Energy and Dark Matter

We show that the concept of entropy and the dynamics of gravitation provide the linchpin in a unified scheme to understand the physics of black hole computers, spacetime foam, dark energy, dark matter and the phenomenon of turbulence. We use three different methods to estimate the foaminess of spacetime, which, in turn, provides a back-door way to derive the Bekenstein-Hawking formula for black hole entropy and the holographic principle. Generalizing the discussion for a static spacetime region to the cosmos, we find a component of dark energy (resembling an effective positive cosmological constant of the correct magnitude) in the current epoch of the universe. The conjunction of entropy and gravitation is shown to give rise to a phenomenological model of dark matter, revealing the natural emergence, in galactic and cluster dynamics, of a critical acceleration parameter related to the cosmological constant; the resulting mass profiles are consistent with observations. Unlike ordinary matter, the quanta of the dark sector are shown to obey infinite statistics. This property of dark matter may lead to some non-particle phenomenology and may explain why dark matter particles have not been detected in dark matter search experiments. We also show that there are deep similarities between the problem of “quantum gravity” (more specifically, the holographic spacetime foam) and turbulence.