Localized gravity in string theory

We propose a string realization of the AdS4 brane in AdS5 that is known to localize gravity. Our theory is M D5 branes in the near horizon geometry of N D3 branes, where M and N are appropriately tuned.     

Anyonic strings and membranes in anti-de Sitter space and dual Aharonov-Bohm effects

It is observed that strings in AdS(5) x S(5) and membranes in AdS(7) x S(4) exhibit long range phase interactions. Two well separated membranes dragged around one another in anti-de Sitter space (AdS) acquire phases of 2 pi/N. The same phases are acquired by a well separated F and D string dragged around one another. The phases are shown to correspond to both the standard and a novel type of Aharonov-Bohm effect in the dual field theory.     

M‐theory solutions invariant under D(2,1; γ) ⊕ D(2,1;γ)

We simplify and extend the construction of half‐BPS solutions to 11‐dimensional supergravity, with isometry superalgebra D(2,1;γ) ⊕ D(2,1;γ). Their space‐time has the form AdS₃× S³× S³ warped over a Riemann surface Σ. It describes near‐horizon geometries of M2 branes ending on, or intersecting with, M5 branes along a common string. The general solution to the BPS equations is specified by a reduced set of data (γ, h, G), where γ is the real parameter of the isometry superalgebra, and h and G are functions on Σ whose differential equations and regularity conditions depend only on the sign of γ. The magnitude of γ enters only through the map of h,G onto the supergravity fields, thereby promoting all solutions into families parametrized by |γ|. By analyzing the regularity conditions for the supergravity fields, we prove two general theorems: (i) that the only solution with a 2‐dimensional CFT dual is AdS₃× S³× S³× ℝ², modulo discrete identifications of the flat ℝ², and (ii) that solutions with γ < 0 cannot have more than one asymptotic higher‐dimensional AdS region. We classify the allowed singularities of h and G near the boundary of Σ, and identify four local solutions: asymptotic AdS₄/Z₂ or AdS₇^′ regions; highly‐curved M5‐branes; and a coordinate singularity called the “cap”. By putting these “Lego” pieces together we recover all known global regular solutions with the above symmetry, including the self‐dual strings on M5 for γ <0, and the Janus solution for γ > 0, but now promoted to families parametrized by |γ|. We also construct exactly new regular solutions which are asymptotic to AdS₄/Z₂ for γ < 0, and conjecture that they are a different superconformal limit of the self‐dual string. Finally, we construct exactly γ > 0 solutions with highly curved M5‐brane regions, which are the formal continuation of the self‐dual string solutions across the decompactification point at γ = 0.     

Unification and hierarchy from 5D anti-de Sitter space

We show that perturbative high scale unification and a solution to the hierarchy problem are possible with extra dimensions in the context of the warped geometry of 5D anti-de Sitter space ( AdS(5)). This is possible because the couplings for bulk gauge bosons run logarithmically below the AdS(5) curvature scale. The calculation is done in five dimensions, rather than in the effective theory, which is strongly coupled above the TeV scale.     

QCD axion from a higher dimensional gauge field theory

We point out that a QCD axion solving the strong CP problem can arise naturally from a parity-odd gauge field in five-dimensional (5D) orbifold field theory. The required axion coupling to the QCD anomaly comes from the 5D Chern-Simons coupling, and all other unwanted U(1)PQ breaking axion couplings can be avoided naturally by the 5D gauge symmetry and locality. If the fifth dimension is warped, the resulting axion scale is suppressed by a small warp factor compared to the Planck scale, thereby the model can generate naturally an intermediate axion scale fa = 10(10)-10(12) GeV.     

Branes wrapping black holes

We examine the dynamics of extended branes, carrying lower-dimensional brane charges, wrapping black holes and black hole microstates in M and type II string theory. We show that they have a universal dispersion relation typical of threshold bound states with a total energy equal to the sum of the contributions from the charges. In near-horizon geometries of black holes, these are BPS states, and the dispersion relation follows from supersymmetry as well as properties of the conformal algebra. However they break all supersymmetries of the full asymptotic geometries of black holes and microstates. We comment on a recent proposal which uses these states to explain black hole entropy.     

Towards a realistic model of Higgsless electroweak symmetry breaking

We present a 5D gauge theory in warped space based on a bulk SU(2)L x SU(2)R x U(1)(B-L) gauge group where the gauge symmetry is broken by boundary conditions. The symmetry breaking pattern and the mass spectrum resemble that in the standard model (SM). To leading order in the warp factor the rho parameter and the coupling of the Z (S parameter) are as in the SM, while corrections are expected at the level of a percent. From the anti-de Sitter (AdS) conformal field theory point of view the model presented here can be viewed as the AdS dual of a (walking) technicolorlike theory, in the sense that it is the presence of the IR brane itself that breaks electroweak symmetry, and not a localized Higgs on the IR brane (which should be interpreted as a composite Higgs model). This model predicts the lightest W, Z, and gamma resonances to be at around 1.2 TeV, and no fundamental (or composite) Higgs particles.     

Light neutrinos from a mini-seesaw mechanism in warped space

The seesaw mechanism provides a simple explanation for the lightness of the known neutrinos. Under the standard assumption of a weak scale Dirac mass and a heavy sterile Majorana scale the neutrino mass is naturally suppressed below the weak scale. However, Nature may employ Dirac and Majorana scales that are much less than typically assumed, possibly even far below the weak scale. In this case the seesaw mechanism alone would not completely explain the lightness of the neutrinos. In this work we consider a warped framework that realizes this possibility by combining naturally suppressed Dirac and Majorana scales together in a mini-seesaw mechanism to generate light neutrino masses. Via the AdS/CFT correspondence the model is dual to a 4D theory with a hidden strongly coupled sector containing light composite right-handed neutrinos.     

Branes, geometry and N = 1 duality with product gauge groups of SO and Sp

We study N = 1 dualities in four-dimensional supersymmetric gauge theories as the world volume theory of D4 branes with one compact direction in type IIA string theory. We generalize the previous work for SO(N_c1) × Sp(N_c2) with the superpotential W = TrX⁴ to the case of W = TrX^4(k+1) in terms of brane configuration. We conjecture that the new dualities for the product gauge groups of SO(N_c1) × Sp(N_c2) × SO(N_c3), SO(N_c1) × Sp(N_c2) × SO(N_c3) × Sp(N_c4) and higher multiple product gauge groups can be obtained by reversing the ordering of NS5 branes and D6 branes while preserving the linking numbers. We also describe the above dualities in terms of wrapping D6 branes around 3-cycles of Calabi-Yau threefolds in type IIA string theory. The theory with adjoint matter can be regarded as taking multiple copies of NS5 brane in the configuration of brane or geometric approaches.     

Aspects of stability and phenomenology in type IIA orientifolds with intersecting D6‐branes

Intersecting branes have been the subject of an elaborate string model building for several years. After a general introduction into string theory, this work introduces in detail the toroidal and $\mathbb{Z}_N$‐orientifolds. The picture involving D9‐branes with B‐fluxes is shortly reviewed, but the main discussion employs the T‐dual picture of intersecting D6‐branes. The derivation of the R‐R and NS‐NS tadpole cancellation conditions in the conformal field theory is shown in great detail. Various aspects of the open and closed chiral and non‐chiral massless spectrum are discussed, involving spacetime anomalies and the generalized Green‐Schwarz mechanism. An introduction into possible gauge breaking mechanisms is given, too. Afterwards, both 𝒩 = 1 supersymmetric and non‐supersymmetric approaches to low energy model building are treated. Firstly, the problem of complex structure instabilities in toroidal ΩR‐orientifolds is approached by a $\mathbb{Z}_3$‐orbifolded model. In particular, a stable non‐supersymmetric standard‐like model with three fermion generations is discussed. This model features the standard model gauge groups at the same time as having a massless hypercharge, but possessing an additional global B‐L symmetry. The electroweak Higgs mechanism and the Yukawa couplings are not realized in the usual way. It is shown that this model descends naturally from a flipped SU(5) GUT model, where the string scale has to be at least of the order of the GUT scale. Secondly, supersymmetric models on the $\mathbb{Z}_4$‐orbifold are discussed, involving exceptional 3‐cycles and the explicit construction of fractional D‐branes. A three generation Pati‐Salam model is constructed as a particular example, where several brane recombination mechanisms are used, yielding non‐flat and non‐factorizable branes. This model even can be broken down to a MSSM‐like model with a massless hypercharge. Finally, the possibility that unstable closed and open string moduli could have played the role of the inflaton in the evolution of the universe is being explored. In the closed string sector, the important slow‐rolling requirement can only be fulfilled for very specific cases, where some moduli are frozen and a special choice of coordinates is taken. In the open string sector, inflation does not seem to be possible at all.     

Evaporation of microscopic black holes in string theory and the bound on species

We address the question how string compactifications with D‐branes are consistent with the black hole bound, which arises in any theory with number of particle species to which the black holes can evaporate. For the Kaluza‐Klein particles, both longitudinal and transversal to the D‐branes, it is relatively easy to see that the black hole bound is saturated, and the geometric relations can be understood in the language of species‐counting. We next address the question of the black hole evaporation into the higher string states and discover, that contrary to the naive intuition, the exponentially growing number of Regge states does not preclude the existence of semi‐classical black holes of sub‐stringy size. Our analysis indicates that the effective number of string resonances to which such micro black holes evaporate is not exponentially large but is bounded by N = 1/g_s², which suggests the interpretation of the well‐known relation between the Planck and string scales as the saturation of the black hole bound on the species number. In addition, we also discuss some other issues in D‐brane compactifications with a low string scale of order TeV, such as the masses of light moduli fields.     

Non-threshold (F, Dp) bound states

In the previous paper [hep-th/9904112], we argued that there exist BPS bound states of Dp branes carrying certain units of quantized constant electric field for every p (with 1 p 8). Each of these bound states preserves one half of the spacetime supersymmetries. In this paper, we construct these bound state configurations explicitly for 2 p 7 from Schwarz's (m, n)-string or (F, D1) bound state in type IIB string theory by T-dualities along the transverse directions. We calculate the charge per of (p − 1)-dimensional area for F-strings in (F,Dp) and the tension for each of these bound states. The results agree precisely with those obtained previously from the worldvolume study. We study the decoupling limit for the (F, D3) bound state and find that Maldacena's AdS₅/CFT₄ correspondence may hold true even with respect to this bound state but now with an effective string coupling rather than the usual string coupling. This coupling is quantized and can be independent of the usual string coupling in a certain limit.     

Warped electroweak breaking without custodial symmetry

We propose an alternative to the introduction of an extra gauge (custodial) symmetry to suppress the contribution of KK modes to the T   parameter in warped theories of electroweak breaking. The mechanism is based on a general class of warped 5D metrics and a Higgs propagating in the bulk. The metrics are nearly AdS in the UV region but depart from AdS in the IR region, towards where KK fluctuations are mainly localized, and have a singularity outside the slice between the UV and IR branes. This gravitational background is generated by a bulk stabilizing scalar field which triggers a natural solution to the hierarchy problem. Depending on the model parameters, gauge-boson KK modes can be consistent with present bounds on EWPT for mKK?1 TeV$m_{\mathit{KK}}?1\text{TeV}$ at 95% CL. The model contains a light Higgs mode which unitarizes the four-dimensional theory. The reduction in the precision observables can be traced back to a large wave function renormalization for this mode.     

Hadronic spectrum of a holographic dual of QCD

We compute the spectrum of light hadrons in a holographic dual of QCD defined on AdS5 x S5 which has conformal behavior at short distances and confinement at large interquark separation. Specific hadrons are identified by the correspondence of string modes with the dimension of the interpolating operator of the hadron's valence Fock state. Higher orbital excitations are matched quanta to quanta with fluctuations about the AdS background. Since only one parameter, the QCD scale Lambda(QCD), is used, the agreement with the pattern of physical states is remarkable. In particular, the ratio of delta to nucleon trajectories is determined by the ratio of zeros of Bessel functions.     

Crystal Melting and Toric Calabi-Yau Manifolds

We construct a statistical model of crystal melting to count BPS bound states of D0 and D2 branes on a single D6 brane wrapping an arbitrary toric Calabi-Yau threefold. The three-dimensional crystalline structure is determined by the quiver diagram and the brane tiling which characterize the low energy effective theory of D branes. The crystal is composed of atoms of different colors, each of which corresponds to a node of the quiver diagram, and the chemical bond is dictated by the arrows of the quiver diagram. BPS states are constructed by removing atoms from the crystal. This generalizes the earlier results on the BPS state counting to an arbitrary non-compact toric Calabi-Yau manifold. We point out that a proper understanding of the relation between the topological string theory and the crystal melting involves the wall crossing in the Donaldson-Thomas theory.     

Gauge threshold corrections in intersecting brane world models

We calculate the one‐loop corrections to gauge couplings in N = 1 supersymmetric brane world models, which are realized in an type IIA orbifold/orientifold background with several stacks of D6 branes wrapped on 3‐cycles with non‐vanishing intersections. Contributions arise from both N = 1 and N = 2 open string subsectors. In contrast to what is known from ordinary orbifold theories, N = 1 subsectors do give rise to moduli‐dependent one‐loop corrections.     

New Einstein-Sasaki spaces in five and higher dimensions

We obtain infinite classes of new Einstein-Sasaki metrics on complete and nonsingular manifolds. They arise, after Euclideanization, from BPS limits of the rotating Kerr-de Sitter black hole metrics. The new Einstein-Sasaki spaces L(p,q,r) in five dimensions have cohomogeneity 2 and U(1) x U(1) x U(1) isometry group. They are topologically S(2) x S(3). Their AdS/CFT duals describe quiver theories on the four-dimensional boundary of AdS(5). We also obtain new Einstein-Sasaki spaces of cohomogeneity n in all odd dimensions D = 2n + 1 > or = 5, with U(1)(n + 1) isometry.