One-loop corrections to the mass of self-dual semi-local planar topological solitons

Izquierdo, A. Alonso; Fuertes, W. Garcia; Mayado, M. de la Torre; Guilarte, J. Mateos

doi:10.1016/j.nuclphysb.2007.11.023

Cited by 16 publications

(30 citation statements)

References 22 publications

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“…which explicitly shows the meromorphic structure of this difference of generalized zeta functions with isolated poles located at the poles of the Euler Gamma function Γðs þ n − 1Þ and the singularities due to the zero modes regularized in the last term in (34). The residua at the poles are also easily identified.…”

Section: B Bps Vortex Heat Kernel Asymptotic Expansion: Impact Of Zementioning

confidence: 75%

“…In Refs. [8,9,34], see also the reviews [28,29], we performed these calculations by applying the spectral zeta function regularization procedure to the second-order small vortex fluctuation operator H þ both in the Abelian Higgs model and in Semilocal Abelian gauge systems. The scheme developed by our group was based in the standard Gilkey-de Witt heat kernel asymptotic expansion.…”

Section: B Bps Vortex Heat Kernel Asymptotic Expansion: Impact Of Zementioning

confidence: 99%

“…The ghost degrees of freedom give rise to its own Casimir energy and mass renormalization couterterms, which is subtractedthe ghosts are fermionic particles-to the corresponding energies coming from the bosonic field fluctuations. This routine is well established and standardized in the physical literature, see [8,9,28,29,34]. We shall denote the total contribution of the Casimir energies to the vortex classical energy as ΔE C V , that of the mass renormalization counterterms as ΔE R V , while the total vortex mass shift will be…”

Section: Spectral Zeta Function Regularization Of One-loop Vortex mentioning

confidence: 99%

“…Use of the vacuum spectral zeta function is convenient to regularize the pertinent divergent graphs. We will not develop this delicate procedure here, see [8,9,28,29,34] to see how this renormalization works in the superenormalizable, henceforth, easier planar AHM. Simply we shall take equal to zero the contribution written in the first line legitimated by the heat kernel renormalization criterion 4 (2).…”

Section: One-loop String Tension Shifts For Cylindrically Symmetmentioning

confidence: 99%

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Quantum magnetic flux lines, BPS vortex zero modes, and one-loop string tension shifts

2016

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Spectral heat kernel/zeta function regularization procedures are employed in this paper to control the divergences arising from vacuum fluctuations of Bogomolnyi-Prasad-Sommerfield vortices in the Abelian Higgs model. Zero modes of vortex fluctuations are the source of difficulties appearing when the standard Gilkey-de Witt expansion is the tool used in the calculations of one-loop shifts of vortex masses and string tensions. A modified GdW expansion is developed to diminish the impact of the infrared divergences due to the vortex zero modes of fluctuation. With this new technique at our disposal we compute the one-loop vortex mass shifts in the planar AHM and the quantum corrections to the string tension of the magnetic flux tubes living in three dimensions. In both cases it is observed that weak repulsive forces surge between these classically noninteracting topological defects caused by vacuum quantum fluctuations.

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Section: B Bps Vortex Heat Kernel Asymptotic Expansion: Impact Of Zementioning

confidence: 75%

Section: B Bps Vortex Heat Kernel Asymptotic Expansion: Impact Of Zementioning

confidence: 99%

Section: Spectral Zeta Function Regularization Of One-loop Vortex mentioning

confidence: 99%

Section: One-loop String Tension Shifts For Cylindrically Symmetmentioning

confidence: 99%

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Quantum magnetic flux lines, BPS vortex zero modes, and one-loop string tension shifts

2016

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“…In fact, the main part of this correction comes from the trace of D † D once a convenient regularization scheme, based for instance on zeta-function methods [21], is stipulated. For the commutative U (1) and semilocal vortices, the computation of the leading a n (D † D) needeed for the quantum corrections has been performed in [28,29]. We think that it would be a worthwhile project to study the precise way in which the methods described there can be generalized in order to be applied to the case of noncommutative solutions.…”

Section: Discussionmentioning

confidence: 99%

Self-dual vortices in Abelian Higgs models with dielectric function on the noncommutative plane

Fuertes

Guilarte

2014

Eur. Phys. J. C

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We show that Abelian Higgs Models with a dielectric function defined on the noncommutative plane enjoy self-dual vorticial solutions. By choosing a particular form of the dielectric function, we provide a family of solutions whose Higgs and magnetic fields interpolate between the profiles of the noncommutative Nielsen-Olesen and Chern-Simons vortices. This is done both for the usual U (1) model and for the SU (2) × U (1) semilocal model with a doublet of complex scalar fields. The variety of known noncommutative self-dual vortices which display a regular behavior when the noncommutativity parameter tends to zero results in this way considerably enlarged.

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Quantum-induced interactions in the moduli space of degenerate BPS domain walls

Izquierdo

Guilarte

2014

J. High Energ. Phys.

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In this paper quantum effects are investigated in a very special two-scalar field model having a moduli space of BPS topological defects. In a (1 + 1)-dimensional space-time the defects are classically degenerate in mass kinks, but in (3 + 1) dimensions the kinks become BPS domain walls, all of them sharing the same surface tension at the classical level. The heat kernel/zeta function regularization method will be used to control the divergences induced by the quantum kink and domain wall fluctuations. A generalization of the Gilkey-DeWitt-Avramidi heat kernel expansion will be developed in order to accommodate the infrared divergences due to zero modes in the spectra of the second-order kink and domain wall fluctuation operators, which are respectively N × N matrix ordinary or partial differential operators. Use of these tools in the spectral zeta function associated with the Hessian operators paves the way to obtain general formulas for the one-loop kink mass and domain wall tension shifts in any (1 + 1)-or (3 + 1)-dimensional N -component scalar field theory model. Application of these formulae to the BPS kinks or domain walls of the N = 2 model mentioned above reveals the breaking of the classical mass or surface tension degeneracy at the quantum level. Because the main parameter distinguishing each member in the BPS kink or domain wall moduli space is essentially the distance between the centers of two basic kinks or walls, the breaking of the degeneracy amounts to the surge in quantum-induced forces between the two constituent topological defects. The differences in surface tension induced by one-loop fluctuations of BPS walls give rise mainly to attractive forces between the constituent walls except if the two basic walls are very far apart. Repulsive forces between two close walls only arise if the coupling is approaches the critical value from below.

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One-loop corrections to the mass of self-dual semi-local planar topological solitons

Cited by 16 publications

References 22 publications

Quantum magnetic flux lines, BPS vortex zero modes, and one-loop string tension shifts

Quantum magnetic flux lines, BPS vortex zero modes, and one-loop string tension shifts

Self-dual vortices in Abelian Higgs models with dielectric function on the noncommutative plane

Quantum-induced interactions in the moduli space of degenerate BPS domain walls

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