Marginal stability and the metamorphosis of Bogomol’nyi-Prasad-Sommerfield states

Ritz, Adam; Shifman, M.; Vainshtein, A.I.; Voloshin, M.B.

doi:10.1103/physrevd.63.065018

Cited by 55 publications

(100 citation statements)

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“…This behavior has been examined for instance in Ref. [22]. In that work, we can also find Wess-Zumino models with two complex fields, and there it was shown that the system supports topological sectors of the non-BPS type.…”

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confidence: 66%

Complete factorization of equations of motion in supersymmetric field theories

Bazeia¹,

Menezes²,

Santos³

2002

Nuclear Physics B

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We investigate bosonic sectors of supersymmetric field theories. We consider superpotentials described by one and by two real scalar fields, and we show how the equations of motion can be factorized into a family of first order Bogomol'nyi equations, so that all the topological defects are of the Bogomol'nyi-Prasad-Sommerfield type. We examine explicit models, that engender the ZN symmetry, and we identify all the topological sectors, illustrating their integrability.PACS numbers: 11.27.+d, 11.30.Pb, 11.30.Er Domain walls are defect structures that appear in diverse branches of physics. They usually live in three spatial dimensions as bidimensional objects that arise in systems described by potentials that contain at least two isolated degenerate minima. They involve energy scales as different as the ones that appear in Condensed Matter [1] and in Cosmology [2].A lot of attention has been drawn recently to domain walls in field theories, in models that have been investigated under several distinct motivations [3][4][5][6][7][8][9][10][11][12][13][14][15]. A very specific motivation concerns the presence of domain walls arising in between non zero vacuum expectation values of scalar fields in supergravity [5,6]. Another line deals with the formation of defects inside domain walls [7][8][9]. A great deal of attention has also been drawn to SU (N ) supersymmetric gluodynamics, where nonperturbative effects give rise to gluino condensates that may form according to a set of N isolated degenerate chirally asymmetric vacua, from where domain walls spring interpolating between pairs of vacua [10].The interest in domain walls in general widens because of the interplay between Field Theory and the low energy world volume dynamics of branes in String Theory [16][17][18][19]. In the case of intersection of defects, in particular in Ref.[12] some aspects of wall junctions have been investigated when the discrete symmetry is the Z N symmetry, in systems described by a single complex field, with the superpotentialThe second work in Ref.[12] has shown that the tensions of the topological defects that appear in these systems can be cast to the formwhere [N/2] is the biggest integer not bigger than N/2 itself. In Ref.[3] the same result was obtained, in an investigation concerned with exact integrability, due to the presence of infinitely many conserved currents -see also Ref.[20] for other investigations, in particular on the explicit form of the BPS solutions at large N.In the present work we examine the bosonic portion of supersymmetric theories, similar to the above models, that are of general interest to supersymmetry. Our investigations follow the lines of the former work [15], and bring new results on the presence of domain defects in models described by one and two real scalar fields. We start investigating systems with a single real scalar field. We write the Lagrangian density in the standard formis the superpotential, and W φ = dW/dφ. We search for defect structures, for static solutions of the equation of motion. ...

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confidence: 66%

Complete factorization of equations of motion in supersymmetric field theories

Bazeia¹,

Menezes²,

Santos³

2002

Nuclear Physics B

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“…Fortunately, one finds that the qualitative insight drawn from V (r, λ) is nonetheless correct [54]. Indeed, this must be the case on the grounds that the condition ω(λ) = 0 describing the CMS is kinematic and protected by supersymmetry.…”

Section: Quantum Correctionsmentioning

confidence: 99%

“…However, it turns out that the latter relation is not stable to quantum corrections, and more work is required. In actual fact quantum corrections, associated with the fermionic content of the model, are very important and become increasingly so near the CMS [54].…”

Section: Quantum Correctionsmentioning

confidence: 99%

“…The leading order potential between the constituents can be determined by expanding the tension of wall two in the background of wall one (see also [54,55]). More precisely, we can write the tension of the second wall 10) where the second term is the leading order interaction potential V (r) between the constituent 1-walls positioned at z = z 0 and z = z 0 + r respectively (see The Bogomol'nyi equations decouple in the mass-eigenstate basis for the intermediate vacuum, where M is diagonal.…”

Section: Inter-wall Potential For Generic λmentioning

confidence: 99%

“…However, by a rescaling, g rr can always be absorbed into the potential, and this is implicitly the basis used here since we will in practice match to the full bosonic potential V (r) = g rr (W ′ QM ) 2 . Identifying the quantum mechanical superpotential W QM (r) in general requires a detailed analysis of the model at hand, as in [54]. However, we can easily extract the general structure near the CMS by comparison with the leading order classical potential in (4.16) [57].…”

Section: Quantum Correctionsmentioning

confidence: 99%

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A note on domain walls and the parameter space of Script N = 1 gauge theories

Ritz¹

2003

J. High Energy Phys.

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Abstract:We study the spectrum of BPS domain walls within the parameter space of N= 1 U(N) gauge theories with adjoint matter and a cubic superpotential. Using a low energy description obtained by compactifying the theory on R 3 × S 1 , we examine the wall spectrum by combining direct calculations at special points in the parameter space with insight drawn from the leading order potential between minimal walls, i.e those interpolating between adjacent vacua. We show that the multiplicity of composite BPS walls -as characterised by the CFIV index -exhibits discontinuities on marginal stability curves within the parameter space of the maximally confining branch. The structure of these marginal stability curves for large N appears tied to certain singularities within the matrix model description of the confining vacua.

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Abelianization of BPS quivers and the refined Higgs index

Lee

Wang

2014

J. High Energ. Phys.

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We count Higgs "phase" BPS states of general non-Abelian quiver, possibly with loops, by mapping the problem to its Abelian, or toric, counterpart and imposing Weyl invariance later. Precise Higgs index computation is particularly important for quivers with superpotentials; the Coulomb "phase" index is recently shown to miss important BPS states, dubbed intrinsic Higgs states or quiver invariants. We demonstrate how the refined Higgs index is naturally decomposed to a sum over partitions of the charge. We conjecture, and show in simple cases, that this decomposition expresses the Higgs index as a sum over a set of partition-induced Abelian quivers of the same total charge but generically of smaller rank. Unlike the previous approach inspired by a similar decomposition of the Coulomb index, our formulae compute the quiver invariants directly, and thus offer a self-complete routine for counting BPS states.

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Marginal stability and the metamorphosis of Bogomol’nyi-Prasad-Sommerfield states

Cited by 55 publications

References 54 publications

Complete factorization of equations of motion in supersymmetric field theories

Complete factorization of equations of motion in supersymmetric field theories

A note on domain walls and the parameter space of Script N = 1 gauge theories

Abelianization of BPS quivers and the refined Higgs index

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