arXiv subjects

Norisuke Sakai

Publications and source records attributed to Norisuke Sakai.

At least 73 records · Page 4Linked to original sources

arXiv2007

Dynamics of Domain Wall Networks

Networks or webs of domain walls are admitted in Abelian or non-Abelian gauge theory coupled to fundamental Higgs fields with complex masses. We examine the dynamics of the domain wall loops by using the moduli approximation and find a phase rotation induces a repulsive force which can be understood as a Noether charge of Q-solitons. Non-Abelian gauge theory allows different types of loops which can be deformed to each other by changing a modulus. This admits the moduli geometry like a sandglass made by gluing the tips of the two cigar-(cone-)like metrics of a single triangle loop. We conclude that the sizes of all loops tend to grow for a late time in general models with complex Higgs masses, while the sizes are stabilized at some values once triplet masses are introduced for the Higgs fields. We also show that the stationary motion on the moduli space of the domain wall webs represents 1/4 BPS Q-webs of walls.

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arXiv2007

Radius stabilization by constant boundary superpotentials in warped space

A warped space model with a constant boundary superpotential has been an efficient model both to break supersymmetry and to stabilize the radius, when hypermultiplet, compensator and radion multiplet are taken into account. In such a model of the radius stabilization, the radion and moduli masses, the gravitino mass and the induced soft masses are studied. We find that a lighter physical mode composed of the radion and the moduli can have mass of the order of a TeV and that the gravitino mass can be of the order of 10$^7$ GeV. It is also shown that soft mass induced by the anomaly mediation can be of the order of 100GeV and can be dominant compared to that mediated by bulk fields. Localized F terms and D terms are discussed as candidates of cancelling the cosmological constant. We find that there is no flavor changing neutral current problem in a wide range of parameters.

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arXiv2007

Statistical Mechanics of Vortices from D-branes and T-duality

We propose a novel and simple method to compute the partition function of statistical mechanics of local and semi-local BPS vortices in the Abelian-Higgs model and its non-Abelian extension on a torus. We use a D-brane realization of the vortices and T-duality relation to domain walls. We there use a special limit where domain walls reduce to gas of hard (soft) one-dimensional rods for Abelian (non-Abelian) cases. In the simpler cases of the Abelian-Higgs model on a torus, our results agree with exact results which are geometrically derived by an explicit integration over the moduli space of vortices. The equation of state for U(N) gauge theory deviates from van der Waals one, and the second virial coefficient is proportional to 1/sqrt{N}, implying that non-Abelian vortices are "softer" than Abelian vortices. Vortices on a sphere are also briefly discussed.

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arXiv2007

Effective Lagrangians on Domain Walls and Other Solitons

Maintaining the preserved supersymmetry helps to find the effective Lagrangian on the BPS background in gauge theories with eight supercharges. As concrete examples, we take 1/2 BPS domain walls. The Lagrangian is given in terms of the superfields with manifest four preserved supercharges and is expanded in powers of the slow-movement parameter lambda. The O(lambda^0) gives the superfield form of the BPS equations, whereas all the fluctuation fields follow at O(lambda^1). The effective Lagrangian is given by the density of the K"ahler potential which emerges automatically from the lambda expansion making four preserved supercharges manifest. More complete account of our method and applications is given in hep-th/0602289 in which the case of non-Abelian vortices is also worked out.

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arXiv2007

Effective Action of Domain Wall Networks

U(Nc) gauge theory with Nf fundamental scalars admits BPS junctions of domain walls. When the networks/webs of these walls contain loops, their size moduli give localized massless modes. We construct Kahler potential of their effective action. In the large size limit Kahler metric is well approximated by kinetic energy of walls and junctions, which is understood in terms of tropical geometry. Kahler potential can be expressed in terms of hypergeometric functions which are useful to understand small size behavior. Even when the loop shrinks, the metric is regular with positive curvature. Moduli space of a single triangle loop has a geometry between a cone and a cigar.

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arXiv2006

Solitons in Supersymmetric Gauge Theories: Moduli Matrix Approach

We review our recent works on solitons in U(Nc) gauge theories with Nf (>Nc) Higgs fields in the fundamental representation, which possess eight supercharges. The moduli matrix is proposed as a crucial tool to exhaust all BPS solutions, and to characterize all possible moduli parameters. Since vacua are in the Higgs phase, we find domain walls (kinks) and vortices as the only elementary solitons. Stable monopoles and instantons can exist as composite solitons with vortices attached. Webs of walls are also found as another composite soliton. The moduli space of all these elementary as well as composite solitons are found in terms of the moduli matrix. The total moduli space of walls is given by the complex Grassmann manifold SU(Nf)/[SU(Nc)x SU(Nf-Nc) x U(1)] and is decomposed into various topological sectors corresponding to boundary conditions specified by particular vacua. We found charges characterizing composite solitons contribute negatively (either positively or negatively) in Abelian (non-Abelian) gauge theories. Effective Lagrangians are constructed on walls and vortices in a compact form. The power of the moduli matrix is illustrated by an interaction rule of monopoles, vortices, and walls, which is difficult to obtain in other methods. More thorough description of the moduli matrix approach can be found in our review article (hep-th/0602170).

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arXiv2006

Solitons in the Higgs phase -- the moduli matrix approach --

We review our recent work on solitons in the Higgs phase. We use U(N_C) gauge theory with N_F 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. We characterize the total moduli space of these elementary as well as composite solitons. 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 (hep-th/0404198, hep-th/0405194, hep-th/0412024, hep-th/0503033, hep-th/0505136), vortices (hep-th/0511088, hep-th/0601181), domain wall webs (hep-th/0506135, hep-th/0508241, hep-th/0509127), monopole-vortex-wall systems (hep-th/0405129, hep-th/0501207), instanton-vortex systems (hep-th/0412048), effective Lagrangian on walls and vortices (hep-th/0602289), classification of BPS equations (hep-th/0506257), and Skyrmions (hep-th/0508130).

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arXiv2006

Manifestly Supersymmetric Effective Lagrangians on BPS Solitons

A systematic method to obtain the effective Lagrangian on the BPS background in supersymmetric gauge theories is worked out, taking domain walls and vortices as concrete examples. The Lagrangian in terms of the superfields for four preserved SUSY is expanded in powers of the slow-movement parameter lambda. The expansion gives the superfield form of the BPS equations at {O}(lambda^0), and all the fluctuation fields at {O}(lambda^1). The density of the Kaehler potential for the effective Lagrangian follows as an automatic consequence of the lambda expansion with manifest (four preserved) SUSY.

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arXiv2006

Supersymmetry Breaking by Constant Boundary Superpotentials in Warped Space

Supersymmetry breaking by constant (field independent) superpotentials localized at boundaries is studied in a supersymmetric warped space model. We calculate the Kaluza-Klein mass spectrum of the hypermultiplet. We take into account of the radion and the compensator supermultiplets, as well as the bulk mass $c$ for the hypermultiplet. The mass splitting is similar to that of the Scherk-Schwarz supersymmetry breaking (in flat space) for large $|c|$, and has an interesting dependence on the bulk mass parameter $c$. We show that the radius is stabilized by the presence of the constant boundary superpotentials.

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arXiv2006

Non-Abelian Vortices on Cylinder -- Duality between vortices and walls

We investigate vortices on a cylinder in supersymmetric non-Abelian gauge theory with hypermultiplets in the fundamental representation. We identify moduli space of periodic vortices and find that a pair of wall-like objects appears as the vortex moduli is varied. Usual domain walls also can be obtained from the single vortex on the cylinder by introducing a twisted boundary condition. We can understand these phenomena as a T-duality among D-brane configurations in type II superstring theories. Using this T-duality picture, we find a one-to-one correspondence between the moduli space of non-Abelian vortices and that of kinky D-brane configurations for domain walls.

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arXiv2006

Moduli Space of Non-Abelian Vortices

We completely determine the moduli space M_{N,k} of k-vortices in U(N) gauge theory with N Higgs fields in the fundamental representation. Its open subset for separated vortices is found as the symmetric product (C x CP^{N-1})^k / S_k. Orbifold singularities of this space correspond to coincident vortices and are resolved resulting in a smooth moduli manifold. Relation to Kahler quotient construction is discussed.

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arXiv2006

Moduli Space of BPS Walls in Supersymmetric Gauge Theories

Existence and uniqueness of the solution are proved for the `master equation' derived from the BPS equation for the vector multiplet scalar in the U(1) gauge theory with Nf charged matter hypermultiplets with eight supercharges. This proof finally establishes the fact that the moduli space of the BPS domain wall solution is CP^(N_f-1) for the gauge theory at finite gauge couplings. Therefore the moduli space at finite gauge couplings is topologically the same manifold as that at infinite gauge coupling, where the gauged linear sigma model reduces to a nonlinear sigma model. The proof is extended to the U(Nc) gauge theory with Nf hypermultiplets in the fundamental representation, provided the moduli matrix of the domain wall solution is U(1)-factorizable. Thus the dimension of the moduli space of U(Nc) gauge theory is bounded from below by the dimension of the U(1)-factorizable part of the moduli space. We also obtain sharp estimates of the asymptotic exponential decay which depend on both the gauge coupling and the hypermultiplet mass differences.

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arXiv2005

D-brane Configurations for Domain Walls and Their Webs

Supersymmetric U(Nc) gauge theory with Nf massive hypermultiplets in the fundamental representation admits various BPS solitons like domain walls and their webs. In the first part we show as a review of the previous paper hep-th/0412024 that domain walls are realized as kinky fractional D3-branes interpolating between separated D7-branes. In the second part we discuss brane configurations for domain wall webs. This is a contribution to the conference based on the talk given by MN.

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arXiv2005

Non-Abelian Webs of Walls

Domain wall junctions are studied in N=2 supersymmetric U(Nc) gauge theory with Nf(>Nc) flavors. We find that all three possibilities are realized for positive, negative and zero junction charges. The positive junction charge is found to be carried by a topological charge in the Hitchin system of an SU(2) gauge subgroup. We establish rules of the construction of the webs of walls. Webs can be understood qualitatively by grid diagram and quantitatively by associating moduli parameters to web configurations.

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arXiv2005

Solitons in Supersymmetric Gauge Theories

Recent results on BPS solitons in the Higgs phase of supersymmetric (SUSY) gauge theories with eight supercharges are reviewed. For U(N_C) gauge theories with the N_F(>N_C) hypermultiplets in the fundamental representation, the total moduli space of walls are found to be the complex Grassmann manifold SU(N_F)/[SU(N_C)xSU(N_F-N_C)xU(1)]. The monopole in the Higgs phase has to accompany vortices, and preserves a 1/4 of SUSY. We find that walls are also allowed to coexist with them. We obtain all the solutions of such 1/4 BPS composite solitons in the strong coupling limit. Instantons in the Higgs phase is also obtained as 1/4 BPS states. As another instructive example, we take U(1)xU(1) gauge theories with four hypermultiplets. We find that the moduli space is the union of several special Lagrangian submanifolds of the Higgs branch vacua of the corresponding massless theory. We also observe transmutation of walls and repulsion and attraction of BPS walls. This is a review of recent works on the subject, which was given at the conference by N.Sakai.

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arXiv2005

Webs of Walls

Webs of domain walls are constructed as 1/4 BPS states in d=4, N=2 supersymmetric U(Nc) gauge theories with Nf hypermultiplets in the fundamental representation. Web of walls can contain any numbers of external legs and loops like (p,q) string/5-brane webs. We find the moduli space M of a 1/4 BPS equation for wall webs to be the complex Grassmann manifold. When moduli spaces of 1/2 BPS states (parallel walls) and the vacua are removed from M, the non-compact moduli space of genuine 1/4 BPS wall webs is obtained. All the solutions are obtained explicitly and exactly in the strong gauge coupling limit. In the case of Abelian gauge theory, we work out the correspondence between configurations of wall web and the moduli space CP^{Nf-1}.

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arXiv2005

D-brane Construction for Non-Abelian Walls

Supersymmetric U(Nc) gauge theory with Nf massive hypermultiplets in the fundamental representation is given by the brane configuration made of Nc fractional Dp-branes stuck at the Z_2 orbifold singularity on Nf separated D(p+4)-branes. We show that non-Abelian walls in this theory are realized as kinky fractional Dp-branes interpolating between D(p+4)-branes. Wall solutions and their duality between Nc and Nf - Nc imply extensions of the s-rule and the Hanany-Witten effect in brane dynamics. We also find that the reconnection of fractional D-branes occurs in this system. Diverse phenomena in non-Abelian walls found in field theory can be understood very easily by this brane configuration.

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arXiv2005

Instantons in the Higgs Phase

When instantons are put into the Higgs phase, vortices are attached to instantons. We construct such composite solitons as 1/4 BPS states in five-dimensional supersymmetric U(Nc) gauge theory with Nf(>=Nc) fundamental hypermultiplets. We solve the hypermultiplet BPS equation and show that all 1/4 BPS solutions are generated by an Nc x Nf matrix which is holomorphic in two complex variables, assuming the vector multiplet BPS equation does not give additional moduli. We determine the total moduli space formed by topological sectors patched together and work out the multi-instanton solution inside a single vortex with complete moduli. Small instanton singularities are interpreted as small sigma-model lump singularities inside the vortex. The relation between monopoles and instantons in the Higgs phase is also clarified as limits of calorons in the Higgs phase. Another type of instantons stuck at an intersection of two vortices and dyonic instantons in the Higgs phase are also discussed.

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