Anomalies in the space of coupling constants and their dynamical applications I
Clay Córdova, Daniel S. Freed, Ho Tat Lam, Nathan Seiberg
SciPost Phys. 8, 001 (2020) · published 6 January 2020
- doi: 10.21468/SciPostPhys.8.1.001
- Submissions/Reports
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Abstract
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 Poincar\'{e} symmetry) to background gauge fields (and a metric for the Poincar\'{e} 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.
TY - JOUR
PB - SciPost Foundation
DO - 10.21468/SciPostPhys.8.1.001
TI - Anomalies in the space of coupling constants and their dynamical applications I
PY - 2020/01/06
UR - https://scipost.org/SciPostPhys.8.1.001
JF - SciPost Physics
JA - SciPost Phys.
VL - 8
IS - 1
SP - 001
A1 - Córdova, Clay
AU - Freed, Daniel
AU - Lam, Ho Tat
AU - Seiberg, Nathan
AB - 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 Poincar\'{e} symmetry) to background gauge fields (and a metric for the Poincar\'{e} 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.
ER -@Article{10.21468/SciPostPhys.8.1.001,
title={{Anomalies in the space of coupling constants and their dynamical applications I}},
author={Clay Córdova and Daniel S. Freed and Ho Tat Lam and Nathan Seiberg},
journal={SciPost Phys.},
volume={8},
pages={001},
year={2020},
publisher={SciPost},
doi={10.21468/SciPostPhys.8.1.001},
url={https://scipost.org/10.21468/SciPostPhys.8.1.001},
}
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Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Clay Córdova,
- 2 Daniel Freed,
- 3 Ho Tat Lam,
- 1 Nathan Seiberg
- 1 Institute for Advanced Study [IAS]
- 2 The University of Texas at Austin [UT Austin]
- 3 Princeton University
Funders for the research work leading to this publication