BPS Domain Walls Research Articles

Two species of vortices in massive gauged non-linear sigma models

Non-linear sigma models with scalar fields taking values on $\mathbb{C}\mathbb{P}^n$ complex manifolds are addressed. In the simplest $n=1$ case, where the target manifold is the $\mathbb{S}^2$ sphere, we describe the scalar fields by means of stereographic maps. In this case when the $\mathbb{U}(1)$ symmetry is gauged and Maxwell and mass terms are allowed, the model accommodates stable self-dual vortices of two kinds with different energies per unit length and where the Higgs field winds at the cores around the two opposite poles of the sphere. Allowing for dielectric functions in the magnetic field, similar and richer self-dual vortices of different species in the south and north charts can be found by slightly modifying the potential. Two different situations are envisaged: either the vacuum orbit lies on a parallel in the sphere, or one pole and the same parallel form the vacuum orbit. Besides the self-dual vortices of two species, there exist BPS domain walls in the second case. Replacing the Maxwell contribution of the gauge field to the action by the second Chern-Simons secondary class, only possible in $(2+1)$-dimensional Minkowski space-time, new BPS topological defects of two species appear. Namely, both BPS vortices and domain ribbons in the south and the north charts exist because the vacuum orbit consits of the two poles and one parallel. Formulation of the gauged $\mathbb{C}\mathbb{P}^2$ model in a Reference chart shows a self-dual structure such that BPS semi-local vortices exist. The transition functions to the second or third charts break the $\mathbb{U}(1)\times\mathbb{S}\mathbb{U}(2)$ semi-local symmetry, but there is still room for standard self-dual vortices of the second species. The same structures encompassing $N$ complex scalar fields are easily generalized to gauged $\mathbb{C}\mathbb{P}^N$ models.

BPS states in supersymmetric chiral models with higher derivative terms

We study the higher derivative chiral models with four supercharges and BPS states in these models. The off-shell Lagrangian generically includes higher powers of the auxiliary fields F which causes distinct on-shell branches associated with the solutions to the auxiliary fields equation. We point out that the model admits a supersymmetric completion of arbitrary higher derivative bosonic models of a single complex scalar field and an arbitrary scalar potential can be introduced even without superpotentials. As an example, we present a supersymmetric extension of the Faddeev-Skyrme model without four time derivatives, in contrast to the previously proposed supersymmetric Faddeev-Skyrme-like model containing four time derivatives. In general, higher derivative terms together with a superpotential result in deformed scalar potentials. We find that higher derivative corrections to 1/2 BPS domain walls and 1/2 BPS lumps are exactly canceled out while the 1/4 BPS lumps (as compact baby Skyrmions) depend on a characteristic feature of the higher derivative models. We also find a new 1/4 BPS condition for domain wall junctions which generically receives higher derivative corrections.

BPS domain walls from backreacted orientifolds

Compactifications with D-brane and orientifold sources lead to standard gauged supergravity theories if the sources are smeared over the internal directions. It is therefore of interest to find how the solutions described by the gauged supergravity are altered by properly localising the sources. In this paper we analyse this for BPS domain wall solutions in the seven-dimensional gauged supergravity obtained from an O6 toroidal orientifold compactification in massive IIA supergravity. This is one of the simplest no-scale supergravities that can be constructed and analysed in full detail. We find and discuss the BPS domain walls both when the O6 planes are smeared and localised. When the O6 planes are localised the domain wall solutions live in a warped compactification. In order to get explicit expressions we also consider the non-compact versions of the solutions for which the O6 planes have been traded for D6 branes. Through T-duality we obtain partially localised solutions for compactifications to four dimensions using O3 planes with 3-form fluxes.

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

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 $N\times N$ 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.

Supersymmetric gauge theory, (2,0) theory and twisted 5d Super-Yang-Mills

Twisted compactification of the 6d N=(2,0) theories on a punctured Riemann surface give a large class of 4d N=1 and N=2 gauge theories, called class S. We argue that nonperturbative dynamics of class S theories are described by 5d maximal Super-Yang-Mills (SYM) twisted on the Riemann surface. In a sense, twisted 5d SYM might be regarded as a "Lagrangian" for class S theories on R^{1,2} times S^1. First, we show that twisted 5d SYM gives generalized Hitchin's equations which was proposed recently. Then, we discuss how to identify chiral operators with quantities in twisted 5d SYM. Mesons, or holomorphic moment maps, are identified with operators at punctures which are realized as 3d superconformal theories T_rho[G] coupled to twisted 5d SYM. "Baryons" are identified qualitatively through a study of 4d N=2 Higgs branches. We also derive a simple formula for dynamical superpotential vev which is relevant for BPS domain wall tensions. With these tools, we examine many examples of 4d N=1 theories with several phases such as confining, Higgs, and Coulomb phases, and show perfect agreements between field theories and twisted 5d SYM. Spectral curve is an essential tool to solve generalized Hitchin's equations, and our results clarify the physical information encoded in the curve.

$ \frac{1}{2} $ -BPS Domain wall from N = 10 three dimensional gauged supergravity

We explicitly construct N = 10 Chern-Simons gaged supergravity in three dimensions with non-semisimple gauge group SO(5) ⋉ T 10. The gauge group is embedded in E 6(−14) which is the isometry group of the 32-dimensional scalar manifold E 6(−14)/SO(10) × U(1). The resulting theory is on-shell equivalent to SO(5) Yang-Mills gauged supergravity coming from dimensional reduction on S 1 of SO(5) N = 5 gauged supergravity in four dimensions. We discuss the spectrum of the corresponding reduction. The SO(5) ⋉ T 10 gauged supergravity, describing the reduced theory, admits a $ \frac{1}{2} $ -BPS domain wall vacuum solution whose explicit form is also given. This provides an example of a domain wall in non-maximal gauged supergravity.

Localization method for volume of domain-wall moduli spaces

The volume of the moduli space of non-Abelian Bogomol'nyi–Prasad–Sommerfield (BPS) domain walls is obtained exactly in |$U(N_c)$| gauge theory with Nf matters. The volume of the moduli space is formulated, without an explicit metric, by a path integral under constraints on BPS equations. The path integral over fields reduces to a finite-dimensional contour integral by a localization mechanism. Our volume formula satisfies a Seiberg-like duality between moduli spaces of the |$U(N_c)$| and |$U(N_f-N_c)$| non-Abelian BPS domain walls in a strong coupling region. We also find a T-duality between domain walls and vortices on a cylinder. The moduli space volume of non-Abelian local (⁠|$N_c=N_f$|⁠) vortices on the cylinder agrees exactly with that on a sphere. The volume formula reveals various geometrical properties of the moduli space.

Strongly warped BPS domain walls

We present analytical solutions of BPS domain walls in the Einstein-Maxwell flux landscape. We also remove the smeared-branes approximation and write down solutions with localized branes. In these solutions the domain walls induce strong (if not infinite) warping.

Hydrodynamics of a 5D Einstein-dilaton black hole solution and the corresponding BPS state

We apply the potential reconstruction approach to generate a series of asymp-totically AdS (aAdS) black hole solutions, with a self-interacting bulk scalar field. Based on the method, we reproduce the pure AdS solution as a consistency check and we also generate a simple analytic 5D black hole solution. We then study various aspects of this solution, such as temperature, entropy density and conserved charges. Furthermore, we study the hydrodynamics of this black hole solution in the framework of fluid/gravity duality, e.g. the ratio of the shear viscosity to the entropy density. In a degenerate case of the 5D black hole solution, we find that the c function decreases monotonically from UV to IR as expected. Finally, we investigate the stability of the degenerate solution by studying the bosonic functional energy of the gravity and the Witten-Nester energy E WN. We confirm that the degenerate solution is a BPS domain wall solution. The corresponding superpotential and the solution of the killing spinor equation are found explicitly.

N = 1 supergravity BPS domain walls on Kähler–Ricci soliton

This paper provides a study of some aspects of flat and curved BPS domam walls together with their Lorentz invariant vacua of four-dimensional chiral N=1 supergravity. The scalar manifold can be viewed as a one-parameter family of Kähler manifolds generated by a Kähler–Ricci flow equation. Consequently, a vacuum manifold characterized by (m,λ) where m and λ are the dimension and the index of the manifold, respectively, does deform with respect to the flow parameter related to the geometric soliton. Moreover, one has to carry out the renormalization group analysis to verify the existence of such a vacuum manifold in the ultraviolet or infrared regions. At the end, we discuss a simple model with linear superpotential on U(n) symmetric Kähler–Ricci orbifolds.

Non-Abelian Gauge Field Localized on Walls with Four-Dimensional World Volume

A mechanism using the position-dependent gauge coupling is proposed to localize non-Abelian gauge fields on domain walls in five-dimensional space-time. Low-energy effective theory posseses a massless vector field, and a mass gap. The four-dimensional gauge invariance is maintained intact. We obtain perturbatively the four-dimensional Coulomb law for static sources on the domain wall. BPS domain wall solutions with the localization mechanism are explicitly constructed in the U(1)xU(1) supersymmetric gauge theory coupling to the non-Abelian gauge fields only through the cubic prepotential, which is consistent with the general principle of supersymmetry in five-dimensional space-time.

Brane dynamics and 3D Seiberg duality on the domain walls of 4D 𝒩 = 1 SYM

We study a three-dimensional U(k) Yang-Mills Chern-Simons theory with adjoint matter preserving two supersymmetries. According to Acharya and Vafa, this theory describes the low-energy worldvolume dynamics of BPS domain walls in four-dimensional = 1 SYM theory. We demonstrate how to obtain the same theory in a brane configuration of type IIB string theory that contains threebranes and fivebranes. A combination of string and field theory techniques allows us to re-formulate some of the well-known properties of = 1 SYM domain walls in a geometric language and to postulate a Seiberg-like duality for the Acharya-Vafa theory. In the process, we obtain new information about the dynamics of branes in setups that preserve two supersymmetries. Using similar methods we also study other = 1 CS theories with extra matter in the adjoint and fundamental representations of the gauge group.

Vortices, Q-balls and Domain Walls on Dielectric M2-branes

We study BPS solitons in = 6 U(N) × U(N) Chern-Simons-matter theory deformed by an F-term mass. The F-term mass generically breaks = 6 supersymmetry down to = 2. At vacua, M2-branes are polarized into a fuzzy S3 forming a spherical M5-brane with topology R1,2 × S3. The polarization is interpreted as Myers' dielectric effect caused by an anti-self-dual 4-form flux T4 in the eleven-dimensional supergravity. Assuming a polarized M2-brane configuration, the model effectively reduces to the well-known abelian Chern-Simons-Higgs model studied in detail by Jackiw-Lee-Weinberg. We find that the potential for the fuzzy S3 radius agrees with the one calculated from the M5-brane point of view at large N. This effective model admits not only BPS topological vortex and domain wall solutions but also non-topological solitons that keep 1/4 of the manifest = 2 supersymmetry. We also comment on the reduction of our configuration to ten dimensions.

Deformation of Curved BPS Domain Walls and Supersymmetric Flows on 2d Kähler-Ricci Soliton

We consider some aspects of the curved BPS domain walls and their supersymmetric Lorentz invariant vacua of the four dimensional N = 1 supergravity coupled to a chiral multiplet. In particular, the scalar manifold can be viewed as a two dimensional Kahler-Ricci soliton generating a one-parameter family of Kahler manifolds evolved with respect to a real parameter, τ. This implies that all quantities describing the walls and their vacua indeed evolve with respect to τ. Then, the analysis on the eigenvalues of the first order expansion of BPS equations shows that in general the vacua related to the field theory on a curved background do not always exist. In order to verify their existence in the ultraviolet or infrared regions one has to perform the renormalization group analysis. Finally, we discuss in detail a simple model with a linear superpotential and the Kahler-Ricci soliton considered as the Rosenau solution.

Kähler-Ricci flow, Morse theory, and vacuum structure deformation of <i>N</i> = 1 supersymmetry in four dimensions

We address some aspects of four-dimensional chiral N = 1 supersym- metric theories on which the scalar manifold is described by Kahler geometry and can further be viewed as Kahler-Ricci soliton generating a one-parameter family of Kahler geometries. All couplings and solu- tions, namely the BPS domain walls and their supersymmetric Lorentz invariant vacua turn out to be evolved with respect to the flow parameter related to the soliton. Two models are discussed, namely N = 1 theory on Kahler-Einstein manifold and U(n) symmetric Kahler-Ricci soliton with positive definite metric. In the first case, we find that the evolution of the soliton causes topological change and correspondingly, modifies the

Mass-deformed Bagger-Lambert theory and its BPS objects

We find a 16-supersymmetric mass-deformed Bagger-Lambert theory with $SO(4)\ifmmode\times\else\texttimes\fi{}SO(4)$ global $R$ symmetry. The $R$ charge plays the role of the noncentral term in the superalgebra. This theory has one symmetric vacuum and two inequivalent broken sectors of vacua. Each sector of the broken symmetry has $SO(4)$ geometry. We find the $1/2$ BPS domain walls connecting the symmetric phase and any broken phase, and $1/4$ BPS supertubelike objects, which may appear as anyonic $q$-balls in the symmetric phase or vortices in the broken phase. We also discuss mass deformations, which reduce the number of supersymmetries.

BPS domain walls and vacuum structure of N=1 supergravity coupled to a chiral multiplet

We study BPS domain walls of N=1 supergravity coupled to a chiral multiplet and their Lorentz invariant vacuums which can be viewed as critical points of BPS equations and the scalar potential. Supersymmetry further implies that gradient flows of BPS equations controlled by a holomorphic superpotential and the Kähler geometry are unstable near local maximum of the scalar potential, whereas they are stable around local minimum and saddles of the scalar potential. However, the analysis using renormalization group flows shows that such gradient flows do not always exist particularly in infrared region.

Central charges of wrapped M5-brane backgrounds

We study the central charges of the supersymmetry algebra of branes in backgrounds corresponding to wrapped M5-branes. In the case of M5-branes wrapping a holomorphic 2-cycle in two complex-dimensional space, we find this allows for a supersymmetric M5-brane probe which is related to the M2-brane probe which describes the BPS spectra of the corresponding N=2 worldvolume gauge theory. For the case of M5-branes wrapping a holomorphic 2-cycle in three complex-dimensional space, we find that the central charges allow for a supersymmetric M5-brane probe wrapping a Cayley calibrated 4-cycle, which has an intersecting BPS domain wall interpretation in the corresponding N=1 MQCD gauge theory. The domain wall is constructed explicitly as an M5-brane wrapping an associative 3-cycle. The tension is found to be the integral of a calibrating form. These wrapped M5-brane backgrounds provide a clear and interesting geometrical realisation of structure groups of M-theory vacua with fluxes.

D-branes on general Script N = 1 backgrounds: superpotentials and D-terms

We study the dynamics governing space-time filling D-branes on Type II flux backgrounds preserving four-dimensional = 1 supersymmetry. The four-dimensional superpotentials and D-terms are derived. The analysis is kept on completely general grounds thanks to the use of recently proposed generalized calibrations, which also allow one to show the direct link of the superpotentials and D-terms with BPS domain walls and cosmic strings respectively. In particular, our D-brane setting reproduces the tension of D-term strings found from purely four-dimensional analysis. The holomorphicity of the superpotentials is also studied and a moment map associated to the D-terms is proposed. Among different examples, we discuss an application to the study of D7-branes on SU(3)-structure backgrounds, which reproduces and generalizes some previous results.

Massive hyper-Kähler sigma models and BPS domain walls

With the non-Abelian Hyper-Kahler quotient by U(M) and SU(M) gauge groups, we give the massive Hyper-Kahler sigma models that are not toric in the N=1 superfield formalism. The U(M) quotient gives N!/[M! (N-M)!] (N is a number of flavors) discrete vacua that may allow various types of domain walls, whereas the SU(M) quotient gives no discrete vacua. We derive BPS domain wall solution in the case of N=2 and M=1 in the U(M) quotient model.