Topological Terms and Phases of Sigma Models

Thorngren, Ryan

doi:10.48550/arxiv.1710.02545

Cited by 13 publications

(17 citation statements)

References 39 publications

(48 reference statements)

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“…In [4], we generalized these concepts to include the dependence on scalar coupling constants. The analysis there extends previous work on this subject in [5][6][7][8]. (For a related discussion in another context see e.g.…”

supporting

confidence: 83%

Anomalies in the space of coupling constants and their dynamical applications II

et al. 2020

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We extend our earlier work on anomalies in the space of coupling constants to fourdimensional gauge theories. Pure Yang-Mills theory (without matter) with a simple and simply connected gauge group has a mixed anomaly between its one-form global symmetry (associated with the center) and the periodicity of the θ-parameter. This anomaly is at the root of many recently discovered properties of these theories, including their phase transitions and interfaces. These new anomalies can be used to extend this understanding to systems without discrete symmetries (such as time-reversal). We also study SUpNq and SppNq gauge theories with matter in the fundamental representation. Here we find a mixed anomaly between the flavor symmetry group and the θ-periodicity. Again, this anomaly unifies distinct recently-discovered phenomena in these theories and controls phase transitions and the dynamics on interfaces.

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confidence: 83%

Anomalies in the space of coupling constants and their dynamical applications II

et al. 2020

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“…It is by now well understood that such families can exhibit non-trivial topological winding in the space of all gapped H 0 -symmetric states [3][4][5][6][7][8][9]. A manifestation of such non-trivial winding will be topological terms [such as Eq.…”

Section: General Definition Of Quantum Topology Of Goldstone Modesmentioning

confidence: 99%

Topological Goldstone phases of matter

Else

2021

Preprint

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We consider the possibility for phases of matter in which a continuous symmetry is spontaneously broken in a topologically non-trivial way, which, roughly, means that the action for the Goldstone modes contains a quantized topological term, and could manifest in, for example, non-trivial quantum numbers of topological defects of the order parameter. We show that, in fact, such a scenario can occur only when the system is in a non-trivial symmetry-protected topological (SPT) or symmetryenriched topological (SET) phase with respect to the residual symmetry; or alternatively, if the original symmetry before spontaneous symmetry breaking acts on the system in an "anomalous" way. Our arguments are based on a general correspondence between topological defects of the order parameter and topological defects of a background gauge field for the residual symmetry.

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“…In the context of invertible phases and anomalies in physics, we can consider various types of X. If the manifold X is taken to be the target space of a sigma model, it is relevant to sigma model anomalies [MN84,MN85,Tho17]. On the other hand, if X is taken to be the space of coupling constants, it is relevant to more subtle anomalies discussed in e.g.…”

Section: Introductionmentioning

confidence: 99%

Differential models for the Anderson dual to bordism theories and invertible QFT's, I

Yamashita¹,

Yonekura²

2021

Preprint

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In this paper, we construct new models for the Anderson duals (IΩ G ) * to the stable tangential G-bordism theories and their differential extensions. The cohomology theory (IΩ G ) * is conjectured by Freed and Hopkins [FH21] to classify deformation classes of possibly non-topological invertible quantum field theories (QFT's). Our model is made by abstractizing certain properties of invertible QFT's, thus supporting their conjecture.

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Topological Terms and Phases of Sigma Models

Cited by 13 publications

References 39 publications

Anomalies in the space of coupling constants and their dynamical applications II

Anomalies in the space of coupling constants and their dynamical applications II

Topological Goldstone phases of matter

Differential models for the Anderson dual to bordism theories and invertible QFT's, I

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