https://cds.cern.ch/record/457096/files/0009061.pdf

Magnetic Fields in the Early Universe

We review cosmological inflation and its realization in quantum field theory and in string theory. This material is a portion of a book, also entitled "Inflation and String Theory", to be published by Cambridge University Press.

Inflation and String Theory

The purpose of this paper is to describe a relationship between the moduli space of vortices and the moduli space of instantons. We study charge vortices in Yang-Mills-Higgs theories and show that the moduli space is isomorphic to a special lagrangian submanifold of the moduli space of instantons in non-commutative Yang-Mills theories. This submanifold is the fixed point set of a action on the instanton moduli space which rotates the instantons in a plane. To derive this relationship, we present a D-brane construction in which the dynamics of vortices is described by the Higgs branch of a gauge theory with 4 supercharges which is a truncation of the familiar ADHM gauge theory. We further describe a moduli space construction for semi-local vortices, lumps in the and grassmannian sigma-models, and vortices on the non-commutative plane. We argue that this relationship between vortices and instantons underlies many of the quantitative similarities between quantum field theories in two and four dimensions.

Vortices, instantons and branes

Nonabelian superconductors: vortices and confinement in N=2 SQCD

We review our recent work on solitons in the Higgs phase. We use U(NC) gauge theory with NF Higgs scalar fields in the fundamental representation, which can be extended to possess eight supercharges. We propose the moduli matrix as a fundamental tool to exhaust all BPS solutions, and to characterize all possible moduli parameters. Moduli spaces of domain walls (kinks) and vortices, which are the only elementary solitons in the Higgs phase, are found in terms of the moduli matrix. Stable monopoles and instantons can exist in the Higgs phase if they are attached by vortices to form composite solitons. The moduli spaces of these composite solitons are also worked out in terms of the moduli matrix. Webs of walls can also be formed with characteristic difference between Abelian and non-Abelian gauge theories. Instanton–vortex systems, monopole–vortex–wall systems, and webs of walls in Abelian gauge theories are found to admit negative energy objects with the instanton charge (called intersectons), the monopole charge (called boojums) and the Hitchin charge, respectively. We characterize the total moduli space of these elementary as well as composite solitons. In particular the total moduli space of walls is given by the complex Grassmann manifold SU(NF)/[SU(NC) × SU(NF − NC) × U(1)] and is decomposed into various topological sectors corresponding to boundary condition specified by particular vacua. The moduli space of k vortices is also completely determined and is reformulated as the half ADHM construction. Effective Lagrangians are constructed on walls and vortices in a compact form. We also present several new results on interactions of various solitons, such as monopoles, vortices and walls. Review parts contain our works on domain walls (Isozumi Y et al 2004 Phys. Rev. Lett. 93 161601 (Preprint hep-th/0404198), Isozumi Y et al 2004 Phys. Rev. D 70 125014 (Preprint hep-th/0405194), Eto M et al 2005 Phys. Rev. D 71 125006 (Preprint hep-th/0412024), Eto M et al 2005 Phys. Rev. D 71 105009 (Preprint hep-th/0503033), Sakai N and Yang Y 2005 Comm. Math. Phys. (in press) (Preprint hep-th/0505136)), vortices (Eto M et al 2005 Phys. Rev. Lett. 96 161601 (Preprint hep-th/0511088), Eto M et al 2006 Phys. Rev. D 73 085008 (Preprint hep-th/0601181)), domain wall webs (Eto M et al 2005 Phys. Rev. D 72 085004 (Preprint hep-th/0506135), Eto M et al 2006 Phys. Lett. B 632 384 (Preprint hep-th/0508241), Eto M et al 2005 AIP Conf. Proc. 805 354 (Preprint hep-th/0509127)), monopole–vortex–wall systems (Isozumi Y et al 2005 Phys. Rev. D 71 065018 (Preprint hep-th/0405129), Sakai N and Tong D 2005 J. High Energy Phys. JHEP03(2005)019 (Preprint hep-th/0501207)), instanton–vortex systems (Eto M et al 2005 Phys. Rev. D 72 025011 (Preprint hep-th/0412048)), effective Lagrangian on walls and vortices (Eto M et al 2006 Phys. Rev. D (in press) (Preprint hep-th/0602289)), classification of BPS equations (Eto M et al 2005 Preprint hep-th/0506257) and Skyrmions (Eto M et al 2005 Phys. Rev. Lett. 95 252003 (Preprint hep-th/0508130)).

Solitons in the Higgs phase: the moduli matrix approach

http://cds.cern.ch/record/383983/files/9904229.pdf

Semilocal and electroweak strings

An important ingredient in the construction of phenomenologically viable superstring models is the uplifting of Anti-de Sitter supersymmetric critical points in the moduli sector to metastable Minkowski or de Sitter vacua with broken supersymmetry. In all cases described so far, uplifting results in a displacement of the potential minimum away from the critical point and, if the uplifting is large, can lead to the disappearance of the minimum altogether. We propose a variant of F-term uplifting which exactly preserves supersymmetric critical points and shift symmetries at tree level. In spite of a direct coupling, the moduli do not contribute to supersymmetry breaking. We analyse the stability of the critical points in a toy one-modulus sector before and after uplifting, and find a simple stability condition depending solely on the amount of uplifting and not on the details of the uplifting sector. There is a region of parameter space, corresponding to the uplifting of local AdS {\em maxima} --or, more importantly, local minima of the Kahler function-- where the critical points are stable for any amount of uplifting. On the other hand, uplifting to (non- supersymmetric) Minkowski space is special in that all SUSY critical points, that is, for all possible compactifications, become stable or neutrally stable.

F-term uplifting and moduli stabilization consistent with Kahler invariance

An important ingredient in the construction of phenomenologically viable superstring models is the uplifting of Anti-de Sitter supersymmetric critical points in the moduli sector to metastable Minkowski or de Sitter vacua with broken supersymmetry. In all cases described so far, uplifting results in a displacement of the potential minimum away from the critical point and, if the uplifting is large, can lead to the disappearance of the minimum altogether. We propose a variant of F-term uplifting which exactly preserves supersymmetric critical points and shift symmetries at tree level. In spite of a direct coupling, the moduli do not contribute to supersymmetry breaking. We analyse the stability of the critical points in a toy one-modulus sector before and after uplifting, and find a simple stability condition depending solely on the amount of uplifting and not on the details of the uplifting sector. There is a region of parameter space, corresponding to the uplifting of local AdS maxima—or, more importantly, local minima of the Kahler function—where the critical points are stable for any amount of uplifting. On the other hand, uplifting to (non-supersymmetric) Minkowski space is special in that all SUSY critical points, that is, for all possible compactifications, become stable or neutrally stable.

http://iopscience.iop.org/article/10.1088/1126-6708/2008/03/002/pdf

F-term uplifting and moduli stabilization consistent with Kähler invariance

We use large-scale numerical simulations to study the formation and evolution of non-topological defects in a generalized electroweak phase transition described by the Glashow-Salam-Weinberg model without fermions. Such defects include dumbbells, comprising a pair of monopoles joined by a segment of electroweak string. These exhibit complex dynamics, with some shrinking under the string tension and others growing due to the monopole-antimonopole attractions between near neighbours. We estimate the range of parameters where the network of dumbbells persists, and show that this region is narrower than the region within which infinite straight electroweak strings are perturbatively stable.

The evolution and persistence of dumbbells in electroweak theory

/pdf/the-evolution-and-persistence-of-dumbbells-1postosk3u.pdf

Ana Achucarro

Papers

Semilocal and electroweak strings

F-term uplifting and moduli stabilization consistent with Kahler invariance

F-term uplifting and moduli stabilization consistent with Kähler invariance

The evolution and persistence of dumbbells in electroweak theory

The evolution and persistence of dumbbells