Anomaly matching in QCD thermal phase transition

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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“…. For more recent related discussions in 4d see[51,52,26,[53][54][55][56][57] and in 3d see[14,15] and references therein.…”

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confidence: 99%

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

et al. 2020

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“…In general, T Mag can be different from T Néel , but the anomalies yield the important 7 Note that T Néel and T Mag are analogous to the temperatures for CP symmetry breaking and deconfinement in the pure Yang-Mills theory at θ = π, respectively [23]. See also similar discussions for other gauge theories [20,25,27,32]. constraint for the transition temperatures:…”

Section: Possible Phase Structurementioning

confidence: 97%

“…[23] for an analogous restriction in the pure Yang-Mills theory at θ = π and Refs. [20,25,27,32] for the discussion on other gauge theories). We also mention its consistency with the large-N analysis on the CP N −1 nonlinear sigma model.…”

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confidence: 99%

Global anomaly matching in the higher-dimensional CPN−1 model

Furusawa

Hongo

2020

Phys. Rev. B

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We investigate 't Hooft anomalies in the CP N −1 model in spacetime dimensions higher than two and identify two types of anomalies: One is a mixed anomaly between the PSU(N ) flavor-rotation and magnetic symmetries, and the other is between the reflection and magnetic symmetries. The latter indicates that even in the absence of the flavor symmetry, the model cannot have a unique gapped ground state as long as the reflection and magnetic symmetries are respected. We also clarified the condition for the 't Hooft anomalies to survive under monopole deformations, which explicitly break the magnetic symmetry down to its discrete subgroup. Besides, we explicitly show how the identified 't Hooft anomalies match in the low-energy effective description of symmetry broken phases-the Néel, U(1) spin liquid, and the valence bond solid phases. An application to the finite-temperature phase diagram of the four-dimensional CP N −1 model is also discussed.

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“…The appearance of the topological order can be explained also by a 't Hooft anomaly [43,[48][49][50] (see also [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69] for recent applications), which is an obstruction in gauging a global symmetry. To see this, we introduce background gauge fields for a pair of discrete 1-form and 2-form symmetries.…”

Section: Fate Of the Symmetries And Topological Ordermentioning

confidence: 99%

Effective gauge theories of superfluidity with topological order

Hirono

Tanizaki

2019

J. High Energ. Phys.

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We discuss the low-energy dynamics of superfluidity with topological order in (3 + 1) spacetime dimensions. We generalize a topological BF theory by introducing a nonsquare K matrix, and this generalized BF theory can describe massless Nambu-Goldstone bosons and anyonic statistics between vortices and quasiparticles. We discuss the general structure of discrete and continuous higher-form symmetries in this theory, which can be used to classify quantum phases. We describe how to identify the appearance of topological order in such systems and discuss its relation to a mixed 't Hooft anomaly between discrete higher-form symmetries. We apply this framework to the color-flavor locked phase of dense QCD, which shows anyonic particle-vortex statistics while no topological order appears. An explicit example of superfluidity with topological order is discussed.

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Anomaly matching in QCD thermal phase transition

Cited by 40 publications

References 203 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

Global anomaly matching in the higher-dimensional CPN−1 model

Effective gauge theories of superfluidity with topological order

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