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Title: Anomalies in the space of coupling constants and their dynamical applications I

Journal Article · · SciPost Physics
 [1];  [2];  [3];  [1]
  1. Institute for Advanced Study, Princeton University
  2. The University of Texas at Austin
  3. Princeton University

It is customary to couple a quantum system to external classical fields. One application is to couple the global symmetries of the system (including the Poincaré symmetry) to background gauge fields (and a metric for the Poincaré symmetry). Failure of gauge invariance of the partition function under gauge transformations of these fields reflects ’t Hooft anomalies. It is also common to view the ordinary (scalar) coupling constants as background fields, i.e. to study the theory when they are spacetime dependent. We will show that the notion of ’t Hooft anomalies can be extended naturally to include these scalar background fields. Just as ordinary ’t Hooft anomalies allow us to deduce dynamical consequences about the phases of the theory and its defects, the same is true for these generalized ’t Hooft anomalies. Specifically, since the coupling constants vary, we can learn that certain phase transitions must be present. We will demonstrate these anomalies and their applications in simple pedagogical examples in one dimension (quantum mechanics) and in some two, three, and four-dimensional quantum field theories. An anomaly is an example of an invertible field theory, which can be described as an object in (generalized) differential cohomology. We give an introduction to this perspective. Also, we use Quillen’s superconnections to derive the anomaly for a free spinor field with variable mass. In a companion paper we will study four-dimensional gauge theories showing how our view unifies and extends many recently obtained results.

Sponsoring Organization:
USDOE
Grant/Contract Number:
SC0009988
OSTI ID:
1581204
Alternate ID(s):
OSTI ID: 1801989
Journal Information:
SciPost Physics, Journal Name: SciPost Physics Journal Issue: 1 Vol. 8; ISSN 2542-4653
Publisher:
Stichting SciPostCopyright Statement
Country of Publication:
Netherlands
Language:
English

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