BPS Skyrme model and baryons at large<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>

Adam, C.; Sánchez-Guillén, J.; Wereszczyński, A.

doi:10.1103/physrevd.82.085015

Cited by 126 publications

(149 citation statements)

References 73 publications

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“…In fact, every hedgehog skyrme field is restricted harmonic (though stability is an open question). By contrast, the axially symmetric BPS skyrmions ϕ B used in [3,4,2,11,10] are never restricted harmonic, for |B| > 1, so there certainly exist fields in their SDiff orbits with lower E 2 , which better approximate near-BPS skyrmions in the model E BP S + c 2 E 2 . Another natural family of skyrme fields, those within the rational map ansatz, can also be shown to have no restricted harmonic members with |B| > 1.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, ϕ should minimize E 2 within all fields in its SDiff(R 3 ) orbit. It is not hard to show that, for |B| > 1, the axially symmetric BPS skyrmions ϕ B used in [3,4,2,10,11] do not have this property, and that their failure to minimize E 2 gets worse as B grows. Recall that a function ϕ : (M, g) → (N, h) between Riemannian manifolds which locally extremizes the Dirichlet energy E 2 with respect to all smooth variations is called a harmonic map.…”

Section: Introductionmentioning

confidence: 99%

“…Second, in the case M = R k , if one is (much) less ambitious, and seeks to minimize E 2 only over the orbit of the finite dimensional subgroup of SDiff(R k ) consisting of linear volume preserving diffeomorphisms, SL(k, R), the problem has an easy and neat explicit solution. This allows us to construct a better sequence of maps ϕ ′ B = ϕ B • A B by linearly deforming those used in previous analytic studies [3,4,2,11,10]. These are still not restricted harmonic, but they have much lower E 2 than ϕ B , particularly at large…”

Section: Introductionmentioning

confidence: 99%

“…This proposal has been analyzed in detail in a sequence of papers by ASW and collaborators [3,4,2]. In [4], the BPS model with the usual pion mass potential is treated, a sequence of axially symmetric BPS skyrmions constructed and a rigid body semi-classical quantization of these performed to obtain phenomenological predictions of nuclear masses and radii.…”

Section: Introductionmentioning

confidence: 99%

“…In [4], the BPS model with the usual pion mass potential is treated, a sequence of axially symmetric BPS skyrmions constructed and a rigid body semi-classical quantization of these performed to obtain phenomenological predictions of nuclear masses and radii. In [2] the rigid body quantization is improved for B = 1 by including a dynamical dilation mode, allowing the prediction of so-called Roper resonances.…”

Section: Introductionmentioning

confidence: 99%

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Near BPS skyrmions and restricted harmonic maps

Speight

2015

Journal of Geometry and Physics

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Motivated by a class of near BPS Skyrme models introduced by Adam, Sánchez-Guillén and Wereszczyński, the following variant of the harmonic map problem is introduced: a map ϕ : (M, g) → (N, h) between Riemannian manifolds is restricted harmonic if it locally extremizes E 2 on its SDiff(M ) orbit, where SDiff(M ) denotes the group of volume preserving diffeomorphisms of (M, g), and E 2 denotes the Dirichlet energy. It is conjectured that near BPS skyrmions tend to restricted harmonic maps in the BPS limit. It is shown that ϕ is restricted harmonic if and only if ϕ * h has exact divergence, and a linear stability theory of restricted harmonic maps is developed, from which it follows that all weakly conformal maps are stable restricted harmonic. Examples of restricted harmonic maps in every degree class R 3 → SU (2) and R 2 → S 2 are constructed. It is shown that the axially symmetric BPS skyrmions on which all previous analytic studies of near BPS Skyrme models have been based, are not restricted harmonic, casting doubt on the phenomenological predictions of such studies. The problem of minimizing E 2 for ϕ : R k → N over all linear volume preserving diffeomorphisms is solved explicitly, and a deformed axially symmetric family of Skyrme fields constructed which are candidates for approximate near BPS skyrmions at low baryon number. The notion of restricted harmonicity is generalized to restricted F -criticality where F is any functional on maps (M, g) → (N, h) which is, in a precise sense, geometrically natural. The case where F is a linear combination of E 2 and E 4 , the usual Skyrme term, is studied in detail, and it is shown that inverse stereographic projection R 3 → S 3 ≡ SU (2) is stable restricted F -critical for every such F .

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Near BPS skyrmions and restricted harmonic maps

Speight

2015

Journal of Geometry and Physics

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Topological solitons in the supersymmetric Skyrme model

Gudnason

Nitta

Sasaki

2017

J. High Energ. Phys.

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A supersymmetric extension of the Skyrme model was obtained recently, which consists of only the Skyrme term in the Nambu-Goldstone (pion) sector complemented by the same number of quasi-Nambu-Goldstone bosons. Scherk-Schwarz dimensional reduction yields a kinetic term in three or lower dimensions and a potential term in two dimensions, preserving supersymmetry. Euclidean solitons (instantons) are constructed in the supersymmetric Skyrme model. In four dimensions, the soliton is an instanton first found by Speight. Scherk-Schwarz dimensional reduction is then performed once to get a 3-dimensional theory in which a 3d Skyrmion-instanton is found and then once more to get a 2d theory in which a 2d vortex-instanton is obtained. Although the last one is a global vortex it has finite action in contrast to conventional theory. All of them are non-BPS states breaking all supersymmetries.

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Fractional instantons and bions in the O(N) model with twisted boundary conditions

Nitta

2015

J. High Energ. Phys.

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Recently, multiple fractional instanton configurations with zero instanton charge, called bions, have been revealed to play important roles in quantum field theories on compactified spacetime. In two dimensions, fractional instantons and bions have been extensively studied in the CP N −1 model and the Grassmann sigma model on R 1 × S 1 with the Z N symmetric twisted boundary condition. Fractional instantons in these models are domain walls with a localized U(1) modulus twisted half along their world volume. In this paper, we classify fractional instantons and bions in the O(N ) nonlinear sigma model on R N −2 × S 1 with more general twisted boundary conditions in which arbitrary number of fields change sign. We find that fractional instantons have more general composite structures, that is, a global vortex with an Ising spin (or a half-lump vortex), a half sineGordon kink on a domain wall, or a half lump on a "space-filling brane" in the O(3) model (CP 1 model) on R 1 × S 1 , and a global monopole with an Ising spin (or a half-Skyrmion monopole), a half sine-Gordon kink on a global vortex, a half lump on a domain wall, or a half Skyrmion on a "space-filling brane" in the O(4) model (principal chiral model or Skyrme model) on R 2 × S 1 . We also construct bion configurations in these models.

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BPS Skyrme model and baryons at largeNc

Cited by 126 publications

References 73 publications

Near BPS skyrmions and restricted harmonic maps

Near BPS skyrmions and restricted harmonic maps

Topological solitons in the supersymmetric Skyrme model

Fractional instantons and bions in the O(N) model with twisted boundary conditions

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