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 full control if we base our analysis on a dual effective action. Finally, we compare our findings with the wall in a "nonminimal" theory with two distinct quark flavors that had been studied previously. In this case the U(1) gauge field trapped on the wall is exactly massless because it is the Goldstone boson of a U(1) symmetry in the bulk spontaneously broken on the wall. The theory on the wall is in the Coulomb phase. We explain why the mechanism of confinement discussed in the first part of the paper does not work in this case, and strings are not formed on the walls.
We consider D-branes at orientifold singularities and discuss two properties of the corresponding low energy four-dimensional effective theories which are not shared, generically, by other Calabi-Yau singularities. The first property is that duality cascades are finite and, unlike ordinary ones, do not require an infinite number of degrees of freedom to be UV-completed. The second is that orientifolds tend to stabilize runaway directions. These two properties can have interesting implications and widen in an intriguing way the variety of gauge theories one can describe using D-branes.
We study confinement-deconfinement phase transition in a holographic soft-wall QCD model. By solving the Einstein-Maxwell-scalar system analytically, we obtain the phase structure of the black hole backgrounds. We then impose probe open strings in such background to investigate the confinement-deconfinement phase transition from different open string configurations under various temperatures and chemical potentials. Furthermore, we study the Wilson loop by calculating the minimal surface of the probing open string world-sheet and obtain the Cornell potential in confinement phase analytically.
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.
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.
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.
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…
We consider a brane generated by a scalar field domain wall configuration in 4+1 dimensions, interpolating, in most cases, between two vacua of the field. We study the cosmology of such a system in the cases where the effective four-dimensional brane metric is de Sitter or anti de Sitter, including a discussion of the bulk coordinate singularities present in the de-Sitter case. We demonstrate that a scalar field kink configuration can support a brane with dS$_4$ cosmology, despite the presence of coordinate singularities in the metric. We examine the trapping of fermion fields on the domain wa…
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…
In a spontaneously dimerized quantum antiferromagnet, spin-1/2 excitations (spinons) are confined in pairs by strings akin to those confining quarks in non-abelian gauge theories. The system has multiple degenerate ground states (vacua) and domain walls between regions of different vacua. For two vacua, we demonstrate that spinons on a domain wall are liberated, in a mechanism strikingly similar to domain-wall deconfinement of quarks in variants of quantum chromodynamics. This observation not only establishes a novel phenomenon in quantum magnetism, but also provides a new direct link between …
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…
We study the thermodynamics of the hard wall model, which consists in the introduction of an infrared cut-off in asymptotically AdS spaces. This is a toy model for confining backgrounds in the context of the gauge/gravity correspondence. We use holographic renormalization and reproduce the existence of a Hawking Page phase transition recently discussed by Herzog. We also show that the entropy jumps from $N^0$ to $N^2$, which reinforces the interpretation of this transition as the gravity dual of confinement/deconfinement. We also show that similar results hold for the phenomenologically motiva…
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…
We study BPS saturated domain walls in the supersymmetric SU(2) gauge theory. For a theory with a very light adjoint scalar (mass <~ Lambda/400) we use the perturbed N=2 Seiberg-Witten theory to calculate the actual field configuration of the domain wall. The wall has a sandwich-like five-layer structure of three distinct phases -- electric confinement, Coulomb and oblique confinement -- separated by two separate transition regions. For larger scalar masses, the three-phase structure disappears and the Seiberg-Witten theory becomes inadequate because of two major problems: First, the higher-de…
We consider a higher-dimensional hard wall model with an infrared (IR) cut-off in asymptotically AdS space and investigate its thermodynamics via the holographic renormalization method. We find a relation between the confinement temperature and the IR cut-off for any dimension. It is also shown that the entropy of $p$-branes with the number of coincident branes (the number of the gauge group) $N$ jumps from leading order in $\cal O$($N^0$) at the confining low temperature phase to $\cal O$($N^{\frac{p+1}{2}}$) at the deconfining high temperature phase like $D3$-branes ($p=3$) case. On the othe…
We derive and analyze the confinement potential of the Cornell type within the framework of the generalized Soft Wall holographic model that includes a parameter controlling the intercept of the linear Regge spectrum. In the phenomenology of Regge trajectories, this parameter is very important for the quantitative description of experimental data. Our analysis shows that the ''linear plus Coulomb'' confinement potential obtained in the scalar channel is quantitatively consistent with the phenomenology and lattice simulations while the agreement in the vector channel is qualitative only. This r…
We present a quantum field theoretic description on the t$-$J model on a square lattice with dilute holes (i.e. near half-filling), based on the compact mutual Chern-Simons gauge theory. We show that, due to the presence of non-perturbative monopole plasma configuration from the antiferromagnetic background, holons (carrying electric charge) are linearly confined and strongly localized even without extrinsic disorder taken into account. Accordingly, the translation symmetry is spontaneously broken at ground state. Such an exotic localization is distinct from Anderson localization and essential…
We study quark confinement in a system of two parallel domain walls interpolating different color dielectric media. We use the phenomenological approach in which the confinement of quarks appears considering the QCD vacuum as a color dielectric medium. We explore this phenomenon in QCD_2, where the confinement of the color flux between the domain walls manifests, in a scenario where two 0-branes (representing external quark and antiquark) are connected by a QCD string. We obtain solutions of the equations of motion via first-order differential equations. We find a new color confining potential…
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.
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.
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.
Domain Walls From Confining Bubbles: $SU(N_{c})$ Yang Mills at Finite $θ$
SISSA, International School for Advanced Studies（国际高等研究院）；INFN Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；IFPU, Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；Dipartimento di Fisica, Università di Trieste（的里雅斯特大学物理系）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）
We study confining strings in ${\cal{N}}=1$ supersymmetric $SU(N_c)$ Yang-Mills theory in the semiclassical regime on $\mathbb{R}^{1,2} \times \mathbb{S}^1$. Static quarks are expected to be confined by double strings composed of two domain walls - which are lines in $\mathbb{R}^2$ - rather than by a single flux tube. Each domain wall carries part of the quarks' chromoelectric flux. We numerically study this mechanism and find that double-string confinement holds for strings of all $N$-alities, except for those between fundamental quarks. We show that, for $N_c \ge 5$, the two domain walls con…
We study the dynamical localization of a massless gauge field on a lower-dimensional surface (2-brane). In flat space, the necessary and sufficient condition for this phenomenon is the existence of confinement in the bulk. The resulting configuration is equivalent to a dual Josephson junction. This duality leads to an interesting puzzle, as it implies that a localized massless theory, even in the Abelian case, must become confining at exponentially large distances. Through the use of topological arguments we clarify the physics behind this large-distance confinement and identify the instantons…
We consider the Abelian-Higgs model in 2+1 dimensions with instanton-monopole defects. This model is closely related to the phases of quantum anti-ferromagnets. In the presence of $\mathbb{Z}_2$ preserving monopole operators, there are two confining ground states in the monopole phase, corresponding to the Valence Bond Solid (VBS) phase of quantum magnets. We show that the domain-wall carries a 't Hooft anomaly in this case. The anomaly can be saturated by, e.g., charge-conjugation breaking on the wall or by the domain wall theory becoming gapless (a gapless model that saturates the anomaly is…
We study thermal transitions in a Domain Wall AdS/QCD model. The model is based on the D5/probe D7 system with a discontinuous mass profile which restricts chiral fermions to 3+1 dimensional domain walls. Fluctuations on the domain wall are dual to the quark mass and condensate and reveal the relation between domain wall separation and the quark mass. The massive quarks exhibit a second order thermal, meson melting transition. Witten's multi-trace prescription can be used to interpret these configurations as having a dynamical mass from a Nambu-Jona-Lasinio interaction - here the transition is…
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 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…
Wave functions and form factors of vector mesons are investigated in the holographic dual model of QCD with a smooth oscillator-like wall. We introduce wave functions conjugate to solutions of the 5D equation of motion and develop a formalism based on these wave functions, which are very similar to those of a quantum-mechanical oscillator. For the lowest bound state (rho-meson), we show that, in this model, the basic elastic form factor exhibits the perfect vector meson dominance, i.e., it is given by the rho-pole contribution alone. The electric radius of the rho-meson is calculated, <r^2_rho…
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 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.
In this manuscript, we discuss the confinement of the spin $\frac{1}{2}$ field on a plethora of branewords models. Recently, in (Eur.Phys.J.C 80 (2020) 5, 432), we studied the consistency of the Standard Model (SM) fields localization on braneworlds with the Einstein equation. In that paper, we discussed the consistency of the spinor field confinement and, by using a Yukawa-like interaction given by $\mathcal{L}_{int}\propto f(y)\barΨΨ$, we obtained that the function must be defined as $f(y)\propto e^{-A}A'$. This shape of the scalar function emerge from the requirement that the spin $\frac{1}…
