Flag manifold sigma models

Affleck, Ian; Bykov, Dmitri; Wamer, Kyle

doi:10.1016/j.physrep.2021.09.004

Cited by 15 publications

(8 citation statements)

References 242 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Analysis of phenomena induced by coupling between fermions and such CP 2 Skyrmions is of great importance. Another interesting direction is the generalization to the sigma model on the flag manifold SU(N )/U(1) N −1 [24,25,26,27]. The second homotopy group of the flag manifold is not Z but Z N −1 .…”

Section: Discussionmentioning

confidence: 99%

Instanton size dependence on fermion energy spectra in a ℂP² fermionic sigma model

Amari,

Sawado,

Yamamoto

2023

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Spectral flow is a fascinating behavior of fermion’s energy levels that cross zero as a parameter varies. In fermion-soliton system, it owes the topology of the soliton. We examine the spectral flow in a (2 + 1)-dimensional ℂP2 fermionic sigma model. We employ an axisymmetric instanton solution of the ℂP2 non-linear sigma model as a background bosonic field to the Dirac fermion. The explicit form of the solutions contains two parameters concerning the size. We show that some energy levels flow from positive (negative) to negative (positive) as the parameters vary. We propose that the behavior of the energy levels can easily be understood by carefully examining the topological property of the instanton in the entire range of parameters, including the limit of zero and infinity.

show abstract

Section: Discussionmentioning

confidence: 99%

Instanton size dependence on fermion energy spectra in a ℂP² fermionic sigma model

Amari,

Sawado,

Yamamoto

2023

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

show abstract

“…Distinct scalar fields take thus value in the manifold U(3)/U(1) 3 ∼ SU(3)/U(1) 2 , which is the flag manifold. 88 The next step of the approach is to replace the identification (C4) into the action (C2) to derive the low-energy effective field theory for the complex fields Φ i . The action…”

Section: Sign Ambiguitymentioning

confidence: 99%

Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain

Herviou¹,

Capponi²,

Lecheminant³

2023

Preprint

View full text Add to dashboard Cite

“…Thus we find for the log divergent part of (6.9) (we assume τ > 0) 35 34 We explicitly extracted the 1 R 2 prefactor which is due to the normalization of χ r ≡ η r in (6.4); ηr (τ )η s (0) = δ rs D(τ). 35 Note that here the UV scale Λ enters only together with τ so that there are no IR divergences.…”

Section: One-loop 1/r 2 Contributionmentioning

confidence: 99%

“…This is an example of representing the trace in some representation in terms of an integral over group orbit[32], cf also[33,34] for a more general discussion.…”

mentioning

confidence: 99%

Wilson loop in general representation and RG flow in 1D defect QFT

Beccaria

Giombi

Tseytlin

2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop in N=4 SYM theory provides an interesting example of renormalization group ﬂow on a line defect: the scalar coupling parameter ζ has a non-trivial beta function and may be viewed as a running coupling constant in a 1d defect QFT. In this paper we continue the study of this operator, generalizing previous results for the beta function and Wilson loop expectation value to the case of an arbitrary representation of the gauge group and beyond the planar limit. Focusing on the scalar ladder limit where the generalized Wilson loop reduces to a purely scalar line operator in a free adjoint theory, and specializing to the case of the rank k symmetric representation of SU(N), we also consider a certain “semiclassical” limit where k is taken to inﬁnity with the product k ζ^2 ﬁxed. This limit can be conveniently studied using a 1d defect QFT representation in terms of N commuting bosons. Using this representation, we compute the beta function and the circular loop expectation value in the large k limit, and use it to derive constraints on the structure of the beta function for general representation. We discuss the corresponding 1d RG ﬂow and comment on the consistency of the results with the 1d defect version of the F-theorem.

show abstract

Flag manifold sigma models

Cited by 15 publications

References 242 publications

Instanton size dependence on fermion energy spectra in a ℂP² fermionic sigma model

Instanton size dependence on fermion energy spectra in a ℂP² fermionic sigma model

Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain

Wilson loop in general representation and RG flow in 1D defect QFT

Contact Info

Product

Resources

About

Flag manifold sigma models

Cited by 15 publications

References 242 publications

Instanton size dependence on fermion energy spectra in a ℂP2 fermionic sigma model

Instanton size dependence on fermion energy spectra in a ℂP2 fermionic sigma model

Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain

Wilson loop in general representation and RG flow in 1D defect QFT

Contact Info

Product

Resources

About

Instanton size dependence on fermion energy spectra in a ℂP² fermionic sigma model

Instanton size dependence on fermion energy spectra in a ℂP² fermionic sigma model