The emerging study of fractons, a new type of quasi‐particle with restricted mobility, has motivated the construction of several classes of interesting continuum quantum field theories with novel properties. One such class consists of
Chern-Weil global symmetries and how quantum gravity avoids them
A bstract 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 F 2 ∧ H 3 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.
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- NSF-PAR ID:
- 10313111
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2021
- Issue:
- 11
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract foliated field theories which, roughly, are built by coupling together fields supported on the leaves of foliations of spacetime. Another approach, which we refer to asexotic field theory , focuses on constructing Lagrangians consistent with special symmetries (like subsystem symmetries) that are adjacent to fracton physics. A third framework is that ofinfinite‐component Chern‐Simons theories , which attempts to generalize the role of conventional Chern‐Simons theory in describing (2+1)D Abelian topological order to fractonic order in (3+1)D. The study of these theories is ongoing, and many of their properties remain to be understood. Historically, it has been fruitful to study QFTs by embedding them into string theory. One way this can be done is via D‐branes, extended objects whose dynamics can, at low energies, be described in terms of conventional quantum field theory. QFTs that can be realized in this way can then be analyzed using the rich mathematical and physical structure of string theory. In this paper, we show that foliated field theories, exotic field theories, and infinite‐component Chern‐Simons theories can all be realized on the world‐volumes of branes. We hope that these constructions will ultimately yield valuable insights into the physics of these interesting field theories. -
BACKGROUND Landau’s Fermi liquid theory provides the bedrock on which our understanding of metals has developed over the past 65 years. Its basic premise is that the electrons transporting a current can be treated as “quasiparticles”—electron-like particles whose effective mass has been modified, typically through interactions with the atomic lattice and/or other electrons. For a long time, it seemed as though Landau’s theory could account for all the many-body interactions that exist inside a metal, even in the so-called heavy fermion systems whose quasiparticle mass can be up to three orders of magnitude heavier than the electron’s mass. Fermi liquid theory also lay the foundation for the first successful microscopic theory of superconductivity. In the past few decades, a number of new metallic systems have been discovered that violate this paradigm. The violation is most evident in the way that the electrical resistivity changes with temperature or magnetic field. In normal metals in which electrons are the charge carriers, the resistivity increases with increasing temperature but saturates, both at low temperatures (because the quantized lattice vibrations are frozen out) and at high temperatures (because the electron mean free path dips below the smallest scattering pathway defined by the lattice spacing). In “strange metals,” by contrast, no saturation occurs, implying that the quasiparticle description breaks down and electrons are no longer the primary charge carriers. When the particle picture breaks down, no local entity carries the current. ADVANCES A new classification of metallicity is not a purely academic exercise, however, as strange metals tend to be the high-temperature phase of some of the best superconductors available. 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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP11(2021)053
