Phase structure of the twisted SU(3)/U(1)2 flag sigma model on ℝ × S1

We consider the SU (N ) Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of p. We can formulate such a quantum field theory maintaining locality and unitarity, and the model contains both 2πperiodic scalar and 3-form gauge fields. This can be interpreted as coupling a topological theory to Yang-Mills theory, so the local dynamics becomes identical with that of pure Yang-Mills theory. The theory has not only Z N 1-form symmetry but also Z p 3-form symmetry, and we study the global nature of this theory from the recent 't Hooft anomaly matching. The computation of 't Hooft anomaly incorporates an intriguing higher-group structure. We also carefully examine that how such kinematical constraint is realized in the dynamics by using the large-N and also the reliable semiclassics on R 3 × S 1 , and we find that the topological susceptibility plays a role of the order parameter for the Z p 3-form symmetry. Introducing a fermion in the fundamental or adjoint representation, we find that the chiral symmetry becomes larger than the usual case by Z p , and it leads to the extra p vacua by discrete chiral symmetry breaking. No dynamical domain wall can interpolate those extra vacua since such objects must be charged under the 3-form symmetry in order to match the 't Hooft anomaly.

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“…[97,98], and it (and its cousins) have been discussed in details in Refs. [99][100][101][102][103][104][105][106][107].…”

Section: Connection Between Modified Instanton Sums In 4d and 2dmentioning

confidence: 99%

Modified instanton sum in QCD and higher-groups

Tanizaki¹,

Ünsal²

2020

J. High Energ. Phys.

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121

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“…See also Ref. [19]. For the two-dimensional (2D) CP N −1 model, which shares many similarities with 4D gauge theory, the beta function is simply β 0 = 1 and one might further push the above semi-classical interpretation of the renormalon.…”

Section: Introductionmentioning

confidence: 99%

Infrared renormalon in the supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$

Ishikawa

Morikawa

Nakayama

et al. 2020

Progress of Theoretical and Experimental Physics

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Abstract In the leading order of the large-$N$ approximation, we study the renormalon ambiguity in the gluon (or, more appropriately, photon) condensate in the 2D supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$ with the $\mathbb{Z}_N$ twisted boundary conditions. In our large-$N$ limit, the combination $\Lambda R$, where $\Lambda$ is the dynamical scale and $R$ is the $S^1$ radius, is kept fixed (we set $\Lambda R\ll1$ so that the perturbative expansion with respect to the coupling constant at the mass scale $1/R$ is meaningful). We extract the perturbative part from the large-$N$ expression of the gluon condensate and obtain the corresponding Borel transform $B(u)$. For $\mathbb{R}\times S^1$, we find that the Borel singularity at $u=2$, which exists in the system on the uncompactified $\mathbb{R}^2$ and corresponds to twice the minimal bion action, disappears. Instead, an unfamiliar renormalon singularity emerges at $u=3/2$ for the compactified space $\mathbb{R}\times S^1$. The semi-classical interpretation of this peculiar singularity is not clear because $u=3/2$ is not dividable by the minimal bion action. It appears that our observation for the system on $\mathbb{R}\times S^1$ prompts reconsideration on the semi-classical bion picture of the infrared renormalon.

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“…In that case the systems have several θ-parameters. Recently studied examples include systems that flow to 2d sigma-models whose target space is the flag manifold U pN q U pN1qˆ¨¨¨ˆU pNmq[65,39,66,67].…”

mentioning

confidence: 99%

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

et al. 2020

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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.2 In condensed matter physics, symmetry protected topological orders (SPTs) are also characterized at low energies by such actions. Depending on the precise definitions and context, "SPT" may be synonymous with "invertible field theory", or may instead refer to the deformation class of an invertible field theory, i.e. the equivalence class of invertible theories obtained by continuously varying parameters.3 In certain cases, there is no Y such that BY " X and A on X is extended into Y . Then, one can construct an anomaly free partition function by assuming that X is a component of the boundary of Y and Y has additional boundary components.

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Phase structure of the twisted SU(3)/U(1)2 flag sigma model on ℝ × S1

Cited by 25 publications

References 136 publications

Modified instanton sum in QCD and higher-groups

Modified instanton sum in QCD and higher-groups

Infrared renormalon in the supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$

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

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