Massless fermions on scalar domain walls are considered. Two walls are established, corresponding to 5-dimensional static spacetime asymptotically Anti de-Sitter, differentiated by the symmetry around the wall, and in each case massless chiral fermions are coupled to the wall by a Yukawa term. We identify a normalizable state associated to the migration of fermions toward the edge of the wall. This effect is generated by the competition between the Yukawa interaction and the gravitational repulsion on the matter fields, and it is independent of the $Z_2$ symmetry of the wall.
In this paper we study fermion localization and resonances on a special type of braneworld model supporting brane splitting. In such models one can construct multi-wall branes which cause considerable simplification in field equations. We use a polynomial superpotential to construct this brane. The suitable Yukawa coupling between the background scalar field and localized fermion is determined. The massive fermion resonance spectrum is obtained. The number of resonances is increased for higher values of Yukawa coupling.
The components of the position operator, at a fixed time, for a massless and spinning particle with given helicity $λ$ described in terms of bosonic degrees of freedom have an anomalous commutator proportional to $λ$. The position operator generates translations in momentum space. We show that a ray-representation for these translations emerges due to the non-commuting components of the position operators and relate this to the Berry-phase for photons. The Tomita-Chiao experiment then gives support for this relativistic and quantum mechanical description of photons in terms of non-commuting po…
We study gravity localization in the context of a six-dimensional gravity model coupled with complex scalar fields. With a supergravity-motivated scalar potential, we show that the domain wall junction solutions localize a four-dimensional massless graviton under an assumption on the wall profile. We find that unlike the global supersymmetric model, contributions to the junction tension cancel locally with gravitational contributions. The wall tension vanishes due to the metric suppression.
We study QCD with massless quarks on $\mathbb{R}^3\times S^1$ under symmetry-twisted boundary conditions with small compactification radius, i.e. at high temperatures. Under suitable boundary conditions, the theory acquires a part of the center symmetry and it is spontaneously broken at high temperatures. We show that these vacua at high temperatures can be regarded as different symmetry-protected topological orders, and the domain walls between them support nontrivial massless gauge theories as a consequence of anomaly-inflow mechanism. At sufficiently high temperatures, we can perform the se…
We study the localization properties of bulk form potentials on dilatonic domain walls. We find that bulk form potentials of any ranks can be localized as form potentials of the same ranks or one lower ranks, for any values of the dilaton coupling parameter. For large enough values of the dilaton coupling parameter, bulk form potentials of any ranks can be localized as form potentials of both the same ranks and one lower ranks.
It is important to obtain (nearly) massless localized modes for the low-energy four-dimensional effective field theory in the brane-world scenario. We propose a mechanism for bosonic zero modes using the field-dependent kinetic function in the classical field theory set-up. As a particularly simple case, we consider a domain wall in five dimensions, and show that massless states for scalar (0-form), vector (1-form), and tensor (2-form) fields appear on a domain wall, which may be called topological because of robustness of their existence (insensitive to continuous deformations of parameters).…
Massless localized vector field is obtained in five-dimensional supersymmetric (SUSY) QED coupled to tensor multiplets as a half BPS solution. The four-dimensional gauge coupling is obtained as a topological charge. We also find all the (bosonic) massive modes exactly for a particular value of a parameter, demonstrating explicitly the existence of a mass gap. The four-dimensional Coulomb law is shown to hold for sources placed on the wall.
We consider chiral fermion confinement in scalar thick branes, which are known to localize gravity, coupled through a Yukawa term. The conditions for the confinement and their behavior in the thin-wall limit are found for various different BPS branes, including double walls and branes interpolating between different AdS_5 spacetimes. We show that only one massless chiral mode is localized in all these walls, whenever the wall thickness is keep finite. We also show that, independently of wall's thickness, chiral fermionic modes cannot be localized in dS_4 walls embedded in a M_5 spacetime. Fina…
Combining the semi-classical localization mechanism for gauge fields with $N$ domain wall background in a simple $SU(N)$ gauge theory in five space-time dimensions we investigate the geometric Higgs mechanism, where a spontaneous breakdown of the gauge symmetry comes from splitting of domain walls. The mass spectra are investigated in detail for the phenomenologically interesting case $SU(5) \to SU(3)\times SU(2)\times U(1)$ which is realized on a split configuration of coincident triplet and doublet of domain walls. We derive a low energy effective theory in a generic background using the mod…
Volume of moduli space of non-Abelian BPS domain-walls is exactly obtained in U(N_c) gauge theory with N_f 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 s…
Localization properties of scalar single particle states are analyzed by explicit calculational examples with a focus on the massless case. Problems arising from the non-existence of relativistic particle position operators respecting the causal structure of Minkowski spacetime are illustrated by exploring the conflicts arising from localization and causal properties commonly imposed on single particle states. These topics necessitate the introduction of quantum field theoretical localization concepts and are scarcely discussed and often misinterpreted in the literature.
We continue the studies of localization of the U(1) gauge fields on domain walls. Depending on dynamics of the bulk theory the gauge field localized on the domain wall can be either in the Coulomb phase or squeezed into flux tubes implying (Abelian) confinement of probe charges on the wall along the wall surface. First, we consider a simple toy model with one flavor in the bulk at weak coupling (a minimal model) realizing the latter scenario. We then suggest a model presenting an extension of the Seiberg--Witten theory which is at strong coupling, but all theoretical constructions are under fu…
We propose a method for simultaneous localization of non-Abelian gauge fields and matter fields with minimal interaction on domain walls using $U(N)_c$ gauge theory with $SU(N)_{L}\times SU(N)_{R}\times U(1)_{A}$ flavor symmetry. Localization of non-Abelian fields is achieved using field-dependent gauge coupling. We find that effective Lagrangian up to second order of derivatives for low energy fluctuations resembles a chiral model from hadron physics with additional minimal interactions of pions with localized gauge fields together with nonlinear interactions of moduli fields. This result pro…
Generalized Wess-Zumino models which admit topologically non-trivial BPS saturated configurations along one compact, spatial dimension are investigated in various dimensions of space-time. We show that, in a representative model and for sufficiently large circumference, there are BPS configurations along the compact dimension containing an arbitrary number of equidistant, well-separated domain walls. We analyze the spectrum of the bosonic and fermionic light and massless modes that are localized on these walls. The masses of the light modes are exponentially suppressed by the ratio of the dist…
In this paper, we investigate localization of a bulk massless q-form field on codimension-one brane by using a new Kaluza-Klein (KK) decomposition, for which there are two types of KK modes for the bulk q-form field, the q-form and (q-1)-form modes. The first modes may be massive or massless while the second ones are all masselss. These two types fo KK modes satisfy twy Schrodinger-like equations. For a five-dimensional brane model with a finite dimension, the spectrum of a bulk 3-form field on the brane consists of some massive bound 3-form KK modes as well as some massless bound 2-form ones …
We study some consequences of dimensionally reducing systems with massless fermions and Abelian gauge fields from 3+1 to 2+1 dimensions. We first consider fermions in the presence of an external Abelian gauge field. In the reduced theory, obtained by compactifying one of the coordinates `a la Kaluza-Klein, magnetic flux strings are mapped into domain wall defects. Fermionic zero modes, localized around the flux strings of the 3+1 dimensional theory, become also zero modes in the reduced theory, via the Callan and Harvey mechanism, and are concentrated around the domain wall defects. We also st…
In this work, we consider the multi-wall braneworld arisen from multi-scalar fields, and investigate the localization and resonances of spin-1/2 fermion on the multi-walls. We build two analytic multi-wall solutions with a polynomial superpotential and a modified sine-Gordon superpotential respectively. The massless fermion is the only bound state and localized between the two outermost sub-branes. The factors affecting the number of massive resonant fermions are analyzed. What interesting is that all the fermion resonant states are non-degenerate for the cases of single- and two-walls, howeve…
We demonstrate explicitly that the vacuum expectation values (vevs) of BPS line operators in 4d N=2 super Yang-Mills theory compactified on a circle, computed by localization techniques, can be expanded in terms of Darboux coordinates as proposed by Gaiotto, Moore, and Neitzke [arXiv:1006.0146]. However, we need to refine the expansion by including additional novel monopole bubbling contributions to obtain a precise match. Using D-brane realization of these singular BPS line operators, we derive and incorporate the monopole bubbling contributions as well as predict the degeneracies of framed B…
Domain wall solitons are the simplest topological objects in field theories. The conventional translational symmetry in a field theory is the generator of a one-parameter family of domain wall solutions, and induces a massless moduli field which propagates along a domain wall. We study similar issues in braided noncommutative field theories possessing Hopf algebraic translational symmetries. As a concrete example, we discuss a domain wall soliton in the scalar phi^4 braided noncommutative field theory in Lie-algebraic noncommutative spacetime, [x^i,x^j]=2i kappa epsilon^{ijk}x_k (i,j,k=1,2,3),…
Massless matter fields and non-Abelian gauge fields are localized on domain walls in a (4+1)-dimensional $U(N)_c$ gauge theory with $SU(N)_{L}\times SU(N)_{R}\times U(1)_{A}$ flavor symmetry. We also introduce $SU(N)_{L+R}$ flavor gauge fields and a scalar-field-dependent gauge coupling, which provides massless non-Abelian gauge fields localized on the wall. We find a chiral Lagrangian interacting minimally with the non-Abelian gauge field together with nonlinear interactions of moduli fields as the (3+1)-dimensional effective field theory up to the second order of derivatives. Our result prov…
Building on our previous results, we study D-brane/string prototypes in weakly coupled (3+1)-dimensional supersymmetric field theory engineered to support (2+1)-dimensional domain walls, "non-Abelian" strings and various junctions. Our main but not exclusive task is the study of localization of non-Abelian gauge fields on the walls. The model we work with is N=2 QCD, with the gauge group SU(2)x$U(1) and N_f=4 flavors of fundamental hypermultiplets (referred to as quarks), perturbed by the Fayet-Iliopoulos term of the U(1) factor. In the limit of large but almost equal quark mass terms a set of…
Based on the previous works (arXiv:1202.5375 and 1402.1346), we investigate the localization of the fields on the dynamical domain wall, where the four dimensional FRW universe is realized on the domain wall in the five dimensional space-time. Especially we show that the chiral spinor can localize on the domain wall, which has not been succeeded in the past works as the seminal work in arXiv:0810.3746.
We supplement the discussion on localization of gravity on dilatonic domain walls in ``Solitons in Brane Worlds'' (Nucl. Phys. B576, 106, hep-th/9911218) by giving unified and coherent discussion which combines the result of this paper and the expanded results in the author's subsequent papers in an attempt to avoid misleading readers. We also discuss the possible string theory embeddings of the Randall-Sundrum type brane world scenarios through non-dilatonic and dilatonic domain walls, which straightforwardly follows from the author's previous works but was not elaborated explicitly.
In the literatures, several types of thick smooth brane configurations in a pure geometric Weyl integrable 5-dimensional space time have been presented. The Weyl geometry is a non-Riemannian modification of 5-dimensional Kaluza--Klein (KK) theory. All these thick brane solutions preserve 4-dimensional Poincaré invariance, and some of them break $Z_2$--symmetry along the extra dimension. In this paper, we study localization of various matter fields on these pure geometrical thick branes, which also localize the graviton. We present the shape of the potential of the corresponding Schr$\mathrm{\d…
Localization of fermions is studied in different gravitational domain wall models. These are generalizations of the brane-world models considered by Randall and Sundrum, but which also allow gravitational localization. Therefore, they might be considered as possible realistic scenarios for phenomenology.
We consider the algebraic effective couplings for open superstring massless modes in the framework of the $A_\infty$ theory in the small Hilbert space. Focusing on quartic algebraic couplings, we reduce the effective action of the $A_\infty$ theory to the Berkovits one where we have already shown that such couplings are fully computed from contributions at the boundary of moduli space, when the massless fields under consideration are appropriately charged under an ${\cal N}\!=\!2$ $R$-symmetry. Here we offer a proof of localization which is in the small Hilbert space. We also discuss the flat …
The Casimir forces on two parallel plates in conformally flat domain wall background due to conformally coupled massless scalar field satisfying mixed boundary conditions on the plates is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy-momentum tensor and vacuum forces acting on boundaries.
We investigate the vacuum properties of a massless scalar field theory in constrained spatial geometry, namely, the instantaneous appearance of a thick Dirichlet boundary inside a one-dimensional (1D) Dirichlet cavity and divides it into two parts. Our work presents the calculations for the energy density and particle number density created. The expression of the energy density is found to be dependent on the size nature of the appearing wall, more precisely, it depends on whether the length of the wall is rational or irrational.
We point out that gravity on dS_n gives rise to a localized graviton on dS_{n-1}. This way one can derive a recursion relation for the entropy of dS spaces, which might have interesting implications for dS holography. In the same spirit we study domain walls interpolating between dS spaces with different cosmological constant. Our observation gives an easy way to calculate what fraction of the total entropy can be accessed by an observer stuck on the bubble wall.
We calculate the four-dimensional low-energy effective action for the perturbations of a two-scalar domain wall model in five dimensions. Comparison of the effective action to the Nambu-Goto action reveals the presence of an additional coupling between the light scalar field and the massless translation mode (branon excitation), which can be written in terms of the curvature scalar of the induced metric. We comment on the impact of this interaction to branon physics.
This is the first of two papers studying localization of massive bulk fields on a bane in 5D anti-de Sitter spacetime, and some of their cosmological consequences. Here we focus on a massive 5D scalar, which is known to lack a localized mode, and discuss how a seeming discontinuity between this theory and the massless theory - known to support a localized zero mode - is resolved thanks to peculiar analytic properties of the massive two-point amplitude. Furthermore, we propose a boundary term that leads to the emergence of a massless localized mode in the massive theory. Last but not least, we …
A series of exact BPS solutions are found for single and double domain walls in N=2 supersymmetric (SUSY) QED for finite gauge coupling constants. Vector fields are found to be massive, although it is localized on the wall. Massless modes can be assembled into a chiral scalar multiplet of the preserved N=1 SUSY, after an appropriate gauge choice. The low-energy effective Lagrangian for the massless fields is obtained for the finite gauge coupling. The inter-wall force is found to be much stronger than the known infinite coupling case. The previously proposed expansion in inverse powers of the …
We study singular, supersymmetric domain-wall solutions supported by the massive breathing mode scalars of, for example, sphere reductions in M-theory or string theory. The space-time on one side of such a wall is asymptotic to the Cauchy horizon of the anti-de Sitter (AdS) space-time. However, on the other side there is a naked singularity. The higher-dimensional embedding of these solutions has the novel interpretation of (sphere compactified) brane configurations in the domain ``inside the horizon region,'' with the singularity corresponding to the sphere shrinking to zero volume. The naked…
The Casimir forces on two parallel plates in conformally flat de Sitter background due to conformally coupled massless scalar field satisfying mixed boundary conditions on the plates is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy-momentum tensor and vacuum forces acting on boundaries. Different cosmological constants are assumed for the space between and outside of the plates to have general results applicable to the case of domain wall formations in the early universe.
We provide complete and self-contained formulas about localization of massless/massive Abelian gauge fields on topological solitons in generic $D$ dimensions via a field dependent gauge kinetic term. The localization takes place when a stabilizer (a scalar field) is condensed in the topological soliton. We show that the localized gauge bosons are massless when the stabilizer is neutral. On the other hand, they become massive for the charged stabilizer as a consequence of interplay between the localization mechanism and the Higgs mechanism. For concreteness, we give two examples in six dimensio…
Both non-Abelian gauge fields and minimally interacting massless matter fields are localized on a domain wall in the five-dimensional spacetime. Field-dependent gauge coupling naturally gives a position-dependent coupling to localize non-Abelian gauge fields on the domain wall. An economical field content allows us to eliminate a moduli for a instability, and to demonstrate the positivity of the position-dependent coupling in the entire moduli space. Effective Lagrangian similar to the chiral Lagrangian is found with a new feature of different coupling strengths for adjoint and singlet matter …
We discuss the problem of localization of 4D massless states in Randall-Sundrum 2 (one-brane) models. A Randall-Sundrum 2 construction starting from N=8 gauged supergravity in 5D Anti de Sitter space gives rise to an N=4 supergravity-matter system. We explicitly show that only the modes of the N=4 graviton supermultiplet localize on the 4D brane, streamlining and generalizing previous works. We also point out that while charged 1/4 BPS black holes do exist in the 4D theory, they are always produced in sets of total charge zero. This zero-charge configuration uplifts to a 5D metric without nake…
A brief survey of fermion localization mechanism on a domain wall ("thick brane") generated by a topologically nontrivial vacuum configuration of scalar fields is given. The extension of scalar fields interaction with fermions which supplies fermions with an axial mass is proposed. For several flavors and generations of fermions this extension can entail the Cabibbo-Kobayashi-Maskawa matrix of the Standard Model. As well the model with two scalar doublets which provide a supplementary CP violation mechanism is considered.
In this work we study a scenario with a warped 5D smooth braneworld with 4D Minkowski geometry builded from bulk scalar matter non-minimally coupled to gravity with an additional Gauss-Bonnet term. We present exact solutions for the full braneworld configuration in contrast to previous results where only approximate solutions were constructed due to the highly non-linear character of the relevant differential equations. These solutions allow us to study the necessary conditions for the finiteness of the 4D Planck mass and additionally, enables us to perform a more rigorous analysis of 4D gravi…
In the previous works (arXiv:1202.5375 and 1402.1346), the dynamical domain wall, where the four dimensional FRW universe is embedded in the five imensional space-time, has been realized by using two scalar fields. In this paper, we consider the localization of vector field in three formulations. The first formulation was investigated in the previous paper (arXiv:1510.01099) for the $U(1)$ gauge field. In the second formulation, we investigate the Dvali-Shifman mechanism (hep-th/9612128), where the non-abelian gauge field is confined in the bulk but the gauge symmetry is spontaneously broken o…
Spin 1/2 fields localization on an asymmetric dS${}_4$ scenario, where the brane interpolates between two spacetimes dS${}_5$ and AdS${}_5$, is determined. The bulk spinor is coupled to scalar field of the brane by a nonminimal Yukawa term compatible with the scenario's geometry. We show that, independently of wall's thickness, only one massless chiral mode is localized on the wall. The massive chiral modes follow a Schrödinger equation, whose potential has a mass gap determined by Yukawa constant, which is a generic property of this system. The fermions spectrum is defined bellow the gap, by …
We construct a four-dimensional domain wall universe by using the Brans-Dicke type gravity with two scalar field. We give a formulation where for arbitrarily given warp factor and scale factor, we construct an action which reproduces both of the warp and scale factors as a solution of the Einstein equation and the field equations given by the action. This formulation could be called as reconstruction. We show that the model does not contain ghost with negative kinetic term and there occur the localization of gravity as in the Randall-Sundrum model. It should be noted that in the equation of th…
We study the Kaluza-Klein zero modes of massless bulk fields with various spins in the background of dilatonic and self-tuning flat domain walls. We find that the zero modes of all the massless bulk fields in such domain wall backgrounds are normalizable, unlike those in the background of the non-dilatonic domain wall with infinite extra space of Randall and Sundrum. In particular, gravity in the bulk of dilatonic domain walls is effectively compactified to the Einstein gravity with vanishing cosmological constant and nonzero gravitational constant in one lower dimensions for any values of dil…
We show that the thin wall limit of the thick domain wall associated with a sine-Gordon soliton in a single non-compactified patch of 5-dimensional spacetime explicitly yields the Randall-Sundrum localized gravity two patch brane, with its discrete $Z_2$ symmetry arising from the discrete symmetry of the potential, and with the thin Minkowski brane $Λ_5+κ^2_5Λ^2_b/6=0$ relation between bulk and brane cosmological constants arising naturally without any need for fine tuning. Additionally we show that for an embedded thin de Sitter brane, localization of gravity is again possible provided the 5-…
N=2 Seiberg-Witten theories allow an interesting interplay between the Argyres-Douglas loci, singularity structures and wall-crossing formulae. In this paper we investigate this connection by first studying the singularity structures of hyper-elliptic Seiberg-Witten curves for pure N=2 gauge theories with SU(r+1) and Sp(2r) gauge groups, and propose new methods to locate the Argyres-Douglas loci in the moduli space, where multiple mutually non-local BPS states become massless. In a region of the moduli space, we compute dyon charges for all 2r+2 and 2r+1 massless dyons for SU(r+1) and Sp(2r) g…
We consider a class of higher order corrections in the form of Euler densities of arbitrary rank $n$ to the standard gravity action in $D$ dimensions. We have previously shown that this class of corrections allows for domain wall solutions despite the presence of higher powers of the curvature. In the present paper we explicitly solve the linearized equation of motion for gravity fluctuations around the domain wall background and show that there always exist one massless state (graviton) propagating on the wall and a continuous tower of massive states propagating in the bulk.
The problem of accounting for the quantum degrees of freedom in passing from massive higher-spin potentials to massless ones and its inverse, the "fattening" of massless tensor potentials of helicity $\pm h$ to their massive $s = |h|$ counterparts, are solved - in a perfectly ghost-free approach - using "string-localized fields". This approach allows to overcome the Weinberg-Witten impediment against the existence of massless $|h| \geq 2$ energy-momentum tensors, and to qualitatively and quantitatively resolve the van Dam-Veltman-Zakharov discontinuity concerning, e.g., very light gravitons, i…
We study $SU(N)$ Quantum Chromodynamics (QCD) in 3+1 dimensions with $N_f$ degenerate fundamental quarks with mass $m$ and a $θ$-parameter. For generic $m$ and $θ$ the theory has a single gapped vacuum. However, as $θ$ is varied through $θ=π$ for large $m$ there is a first order transition. For $N_f=1$ the first order transition line ends at a point with a massless $η'$ particle (for all $N$) and for $N_f>1$ the first order transition ends at $m=0$, where, depending on the value of $N_f$, the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theo…
A class of exactly solvable models of domain walls are worked out in D=4 ${\cal N}=1$ supergravity. We develop a method to embed globally supersymmetric theories with exact BPS domain wall solutions into supergravity, by introducing a gravitationally deformed superpotential. The gravitational deformation is natural in the spirit of maintaining the Kähler invariance. The solutions of the warp factor and the Killing spinor are also obtained. We find that three distinct behaviors of warp factors arise depending on the value of a constant term in the superpotential : exponentially decreasing in bo…
In ordinary QCD with light, degenerate, fundamental flavors, $CP$ symmetry is spontaneously broken at $θ=π$, and domain wall solutions connecting the vacua can be constructed in chiral perturbation theory. In some cases the breaking of $CP$ saturates an 't Hooft anomaly, and anomaly inflow requires nontrivial massless excitations on the domain walls. Analogously, $CP$ can be spontaneously broken in supersymmetric QCD with light flavors and small soft breaking parameters. We study $CP$ breaking and domain walls in softly broken SQCD with $N_f<N$ flavors. Relative to ordinary QCD, the supersymme…
We study some properties of a dimensional reduction mechanism for fermions in an odd number D+1 of spacetime dimensions. A fermionic field is equipped with a mass term with domain wall like defects along one of the spacelike dimensions, which is moreover compactified. We show that there is a regime such that the only relevant degrees of freedom are massless fermionic fields in D dimensions. For any fixed gauge field configuration, the extra modes may be decoupled, since they can be made arbitrarily heavy. This decoupling combines the usual Kaluza-Klein one, due to the compactification, with a …
The mean square fluctuation and the expectation value of the stress-energy-momentum tensor of a neutral massive scalar field at finite temperature are determined near an infinite plane Dirichlet wall, and also near an infinite plane Neumann wall. The flat background has an arbitrary number of dimensions and the field is arbitrarily coupled to the vanishing curvature. It is shown that, unlike vacuum contributions, thermal contributions are free from boundary divergences, and that the thermal behaviour of the scalar field near a Dirichlet wall differs considerably from that near a Neumann wall. …
