Higher Derivative Corrections to Non-Abelian Vortex Effective Theory

Low energy dynamics of magnetic monopoles and anti-monopoles in the U(2) C gauge theory is studied in the Higgs (non-Abelian superconducting) phase. The monopoles in this superconducting phase are not spherical but are of slender ellipsoid which are pierced by a vortex string. We investigate scattering of the slender monopole and anti-monopole, and find that they do not always decay into radiation, contrary to our naive intuition. They can repel, make bound states (magnetic mesons) or resonances. Analytical solutions including any number of monopoles and anti-monopoles are obtained in the first non-trivial order of rigid-body approximation. We point out that some part of solutions of slender monopole system in 1 + 3 dimensions can be mapped exactly onto the sine-Gordon system in 1 + 1 dimensions. This observation allows us to visualize dynamics of monopole and anti-monopole scattering easily.

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“…This can be seen from the solution [3,43,44] of first order equations (4.21)-(4.22) for an arbitrary φ(x 0 , x 3 )…”

Section: Jhep09(2014)172mentioning

confidence: 99%

Dynamics of slender monopoles and anti-monopoles in non-Abelian superconductor

Arai

Blaschke

Eto

et al. 2014

J. High Energ. Phys.

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“…According to appendix A.1 the above equation show that the solution ψ is strictly increasing with respect to each ν I , ∂ψ/∂ν I > 0. In the limit of the vanishing source J = 0, furthermore we find 19) where the modified Bessel function of the second kind K 0 (x) emerges as a two-dimensional Green's function. That is, in this limit a vortex solution is exactly solved and treated as a linear combination of free massive particles and for small |ν I | ≪ 1 at least, ψ is approximated well everywhere as…”

Section: Extension Of Taubes' Equation and Particle Descriptionmentioning

confidence: 81%

“…(5.2) of a paper [19]. 8 It is natural to expect the following inequalities on values of total energies E k for axially-symmetric vortex-solutions,…”

Section: Numerical Datamentioning

confidence: 99%

Small winding-number expansion: vortex solutions at critical coupling

Ohashi

2015

J. High Energ. Phys.

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Abstract:We study an axially symmetric solution of a vortex in the Abelian-Higgs model at critical coupling in detail. Here we propose a new idea for a perturbative expansion of a solution, where the winding number of a vortex is naturally extended to be a real number and the solution is expanded with respect to it around its origin. We test this idea on three typical constants contained in the solution and confirm that this expansion works well with the help of the Padé approximation. For instance, we analytically reproduce the value of the scalar charge of the vortex with an error of O(10 −6 ). This expansion is also powerful even for large winding numbers.

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“…The higher derivative terms free from these problems given in Refs. [61][62][63][64][65] were applied to many topics such as low-energy effective theories [77][78][79][80], SUGRA [63,81], SUSY extension [62,82] of Galileons [83], ghost condensation [61,64], the Dirac-Born-Infeld (DBI) inflation [84], flattening of the inflaton potential [85,86], baby Skyrme models [65,[87][88][89][90][91][92], Skyrme-like models [93][94][95], solitons [65,89,96,97], nonlinear realizations [98], SUSY breaking in modulated vacua [99,100], and a formulation of a liberated SUGRA [101]. For the vector superfield case, ghost-free higher derivative actions were considered in the context of a correction to a scalar potential in SUGRA [102], SUSY Euler-Heisenberg model [53,81,103], nonlinearly self-dual actions [104,105], and the DBI action [106,…”

Section: Hd (Bulk)mentioning

confidence: 99%

Higher derivative three-form gauge theories and their supersymmetric extension

Nitta

Yokokura

2018

J. High Energ. Phys.

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We investigate three-form gauge theories with higher derivative interactions and their supersymmetric extensions in four space-time dimensions. For the bosonic three-form gauge theories, we show that derivatives on the field strength of the 3-form gauge field yield a tachyon as far as the Lagrangian contains a quadratic kinetic term, while such the term with opposite sign gives rise to a ghost. We confirm that there is neither a tachyon nor a ghost when all higher derivative terms are given by functions of the field strength. For this ghost/tachyon-free Lagrangian, we determine the boundary term necessary for the consistency between the equation of motion and energy-momentum tensor. For supersymmetric extensions, we present ghost/tachyon-free higher derivative interactions of arbitrary order of the field strength and corresponding boundary terms as well. * nitta@phys-h.keio.ac.jp † ryokokur@keio.jp 1 Introduction 3-form gauge theories in four-dimensional (4D) spacetime have been studied extensively in the past decades. They were first considered in the context of quantum chromodynamics (QCD) to describe a long-range confinement force between quarks [1,2]. Furthermore, a 3-form gauge field can be regarded to provide an effective description of a Chern-Simons 3-form in Yang-Mills theories [2,3], in particular in the context of the U(1) problem [4,5] and the strong CP problem [6][7][8]. In cosmology, a 3-form gauge field was used for dynamical neutralization of the cosmological constant [9-16], quintessence [17], inflationary models [18][19][20][21][22][23]. A relation between the 3-form gauge theories and condensed matter physics was also discussed, see e.g. [24]. A supersymmetric (SUSY) extension of the 3-form gauge fields was first formulated in Ref. [25]. The SUSY 3-form gauge fields naturally appear in superstring theory and M-theory, therefore they were studied extensively with various applications: supergravity (SUGRA) [26][27][28] (see Refs. [29,30] as a review), Stückelberg coupling [31-34], topological coupling [33,35,36], coupling with a membrane [37-39], alternative formulation of old-minimal SUGRA [37, 40-42], gaugino condensation in SUSY Yang-Mills theories [43, 44], the cosmological constant problem [41], SUSY breaking [41,45], string effective theories [42,[46][47][48], and inflationary models [35,49]. Complex 3-form gauge theories were also considered in Refs. [38,39,42].One of the characterizations of p-form gauge fields is their couplings to extended objects. As 1-form and 2-form gauge fields can be electrically coupled to a particle and string, respectively in 4D spacetime, a 3-form gauge field can be electrically coupled to a membrane [1]. Since membranes and 3-form gauge fields naturally arise in string theory and M-theory as fundamental degrees of freedom, 3-form gauge fields in 4D spacetime appear as 4D compactification of these theories. Another characteristic feature of the 3form gauge field is its coupling to scalar fields. Since a field strength of the 3-form gauge field is a 4-form, the ...

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Higher Derivative Corrections to Non-Abelian Vortex Effective Theory

Cited by 29 publications

References 102 publications

Dynamics of slender monopoles and anti-monopoles in non-Abelian superconductor

Dynamics of slender monopoles and anti-monopoles in non-Abelian superconductor

Small winding-number expansion: vortex solutions at critical coupling

Higher derivative three-form gauge theories and their supersymmetric extension

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