Quantum Flag Manifold $$\sigma $$-Models and Hermitian Ricci Flow

Bykov, Dmitri

doi:10.1007/s00220-022-04532-5

Cited by 8 publications

(11 citation statements)

References 77 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another interesting problem is to consider several copies of the βγ-system with the interaction term proportional to r ijkl β(i) β (j) γ(k) γ (l) , where the indices (i) denote the isotopic index of the field, as it was done in [18,19]. It was shown there that a theory with such an interaction is classically integrable provided that r ijkl satisfies classical Yang-Baxter equation.…”

Section: Discussionmentioning

confidence: 99%

On bosonic Thirring model in Minkowski signature

Алфимов¹,

Kurakin²

2023

Preprint

View full text Add to dashboard Cite

We present the way to continue the bosonic Thirring model or βγ-system with quartic interaction to Minkowski signature, based on the symmetries of this model. It is shown that the considered Minkowski version of the model is one-loop renormalizable. Based on this, we find the amplitudes of the scattering of the excitations corresponding to the γ and γ fields up to one loop order. In particular, it was computed that the 2 → 2 amplitudes of these excitations possess the property of reflectionless scattering and thus the corresponding S-matrix of such excitations satisfies the Yang-Baxter equation. The obtained S-matrix elements for γ and γ are shown to coincide with the corresponding matrix elements of the solitons in the complex sine-Gordon model proposed by Dorey and Hollowood.

show abstract

Section: Discussionmentioning

confidence: 99%

On bosonic Thirring model in Minkowski signature

Алфимов¹,

Kurakin²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…2 Ordinary CP n−1 Our approach has its roots in two-dimensional sigma models with target spaces such as CP n−1 , which have recently been reformulated in a more algebraic form by one of the authors [13,14,15]. Physically, this relation is an equivalence between sigma models and the Gross-Neveu models, i.e.…”

Section: Cp N−1 Monopolesmentioning

confidence: 99%

“…9 of the book [4]. 13 More known is the model involving real superfields and describing the geometry of the de Rham complex [27,28]. The model (3.18) describes the Dolbeault complex and, in contrast to the model considered in Refs.…”

Section: Inhomogeneous Descriptionmentioning

confidence: 99%

Monopole harmonics on $\mathbb{CP}^{n-1}$

Bykov¹,

Smilga²

2023

Preprint

View full text Add to dashboard Cite

We find the spectra and eigenfunctions of both ordinary and supersymmetric quantummechanical models describing the motion of a charged particle over the CP n−1 manifold in the presence of a background monopole-like gauge field. The states form degenerate SU (n) multiplets and their wave functions acquire a very simple form being expressed via homogeneous coordinates. Their relationship to multidimensional orthogonal polynomials of a special kind is discussed. By the well-known isomorphism between the twisted Dolbeault and Dirac complexes, our construction also gives the eigenfunctions and eigenvalues of the Dirac operator on complex projective spaces in a monopole background.

show abstract

“…Our approach has its roots in two-dimensional sigma models with target spaces such as n−1 , which have recently been reformulated in a more algebraic form by one of the authors [13][14][15]. Physically, this relation is an equivalence between sigma models and the Gross-Neveu models, i.e.…”

Section: N−1mentioning

confidence: 99%

“…9 of the book [4]. 13 More known is the model involving real superfields and describing the geometry of the de Rham complex [27,28]. The model (3.3) describes the Dolbeault complex and, in contrast to the model considered in Refs.…”

Section: Inhomogeneous Descriptionmentioning

confidence: 99%

Monopole harmonics on $\mathbb{CP}^{n-1}$

Bykov,

Smilga

2023

SciPost Phys.

Self Cite

View full text Add to dashboard Cite

We find the spectra and eigenfunctions of both ordinary and supersymmetric quantum-mechanical models describing the motion of a charged particle over the \mathbb{CP}^{n-1}ℂℙn−1 manifold in the presence of a background monopole-like gauge field. The states form degenerate SU(n)SU(n) multiplets and their wave functions acquire a very simple form being expressed via homogeneous coordinates. Their relationship to multidimensional orthogonal polynomials of a special kind is discussed. By the well-known isomorphism between the twisted Dolbeault and Dirac complexes, our construction also gives the eigenfunctions and eigenvalues of the Dirac operator on complex projective spaces in a monopole background.

show abstract

Quantum Flag Manifold $$\sigma $$-Models and Hermitian Ricci Flow

Cited by 8 publications

References 77 publications

On bosonic Thirring model in Minkowski signature

On bosonic Thirring model in Minkowski signature

Monopole harmonics on $\mathbb{CP}^{n-1}$

Monopole harmonics on $\mathbb{CP}^{n-1}$

Contact Info

Product

Resources

About