KK States Research Articles

A gravitino distance conjecture

We conjecture that in a consistent supergravity theory with non-vanishing gravitino mass, the limit m3/2 → 0 is at infinite distance. In particular one can write Mtower ~ {m}_{3/2}^{delta } so that as the gravitino mass goes to zero, a tower of KK states as well as emergent strings becomes tensionless. This conjecture may be motivated from the Weak Gravity Conjecture as applied to strings and membranes and implies in turn the AdS Distance Conjecture. We test this proposal in classical 4d type IIA orientifold vacua in which one obtains a range of values frac{1}{3} ≤ δ ≤ 1. The parameter δ is related to the scale decoupling exponent in AdS vacua and to the α exponent in the Swampland Distance Conjecture for the type IIA complex structure. We present a general analysis of the gravitino mass in the limits of moduli space in terms of limiting Mixed Hodge Structures and study in some detail the case of two-moduli F-theory settings. Moreover, we obtain general lower bounds δ ≥ frac{1}{3},frac{1}{4} for Calabi-Yau threefolds and fourfolds, respectively. The conjecture has important phenomenological implications. In particular we argue that low-energy supersymmetry of order 1 TeV is only obtained if there is a tower of KK states at an intermediate scale, of order 108 GeV. One also has an upper bound for the Hubble constant upon inflation H ≲ {m}_{3/2}^{delta }{M}_{mathrm{P}}^{left(1-delta right)} .

Tree-level quartic for a holographic composite Higgs

We present a new class of composite Higgs models where an adjustable treelevel Higgs quartic coupling allows for a significant reduction in the tuning of the Higgs potential. Our 5D warped space implementation is the first example of a holographic composite Higgs model with a tree-level quartic. It is inspired by a 6D model where the quartic originates from the Tr[A5, A6]2 term of the gauge field strength, the same model that led to the original little Higgs construction of Arkani-Hamed, Cohen, and Georgi. Beyond the reduction of the tuning and the standard composite Higgs signatures, the model predicts a doubling of the KK states with relatively small splittings as well as a Higgs sector with two doublets in the decoupling limit.

Super-Yang-Mills and M5-branes

We uplift 5-dimensional super-Yang-Mills theory to a 6-dimensional gauge theory with the help of a space-like constant vector η M, whose norm determines the YM coupling constant. After the localization of η M the 6D gauge theory acquires Lorentzian invariance as well as scale invariance. We discuss KK states, instantons and the flux quantization. The theory admits extended solutions like 1/2 BPS ‘strings’ and monopoles.

Strings in an arbitrary constant magnetic field with arbitrary constant metric and stringy form factors

We quantize the open string in an arbitrary constant magnetic field with a non factorized metric on a torus. We then discuss carefully the vertexes which describe the emission of dipole open strings and closed strings in the non compact limit. Finally we compute various stringy form factors which in the compact case induces a Kaehler and complex structure dependence and suppression of some amplitudes with KK states.

Domain wall brane in squared curvature gravity

We suggest a thick braneworld model in the squared curvature gravity theory. Despite the appearance of higher order derivatives, the localization of gravity and various bulk matter fields is shown to be possible. The existence of the normalizable gravitational zero mode indicates that our four-dimensional gravity is reproduced. In order to localize the chiral fermions on the brane, two types of coupling between the fermions and the brane forming scalar is introduced. The first coupling leads us to a Schr\"odinger equation with a volcano potential, and the other a P\"oschl-Teller potential. In both cases, the zero mode exists only for the left-hand fermions. Several massive KK states of the fermions can be trapped on the brane, either as resonant states or as bound states.

Suppressing electroweak precision observables in 5D warped models

We elaborate on a recently proposed mechanism to suppress large contributions to the electroweak precision observables in five dimensional (5D) warped models, without the need for an extended 5D gauge sector. The main ingredient is a modification of the AdS metric in the vicinity of the infrared (IR) brane corresponding to a strong deviation from conformality in the IR of the 4D holographic dual. We compute the general low energy effective theory of the 5D warped Standard Model, emphasizing additional IR contributions to the wave function renormalization of the light Higgs mode. We also derive expressions for the S and T parameters as a function of a generic 5D metric and zero-mode wave functions. We give an approximate formula for the mass of the radion that works even for strong deviation from the AdS background. We proceed to work out the details of an explicit model and derive bounds for the first KK masses of the various bulk fields. The radion is the lightest new particle although its mass is already at about 1/3 of the mass of the lightest resonances, the KK states of the gauge bosons. We examine carefully various issues that can arise for extreme choices of parameters such as the possible reintroduction of the hierarchy problem, the onset of nonperturbative physics due to strong IR curvature or the creation of new hierarchies near the Planck scale. We conclude that a KK scale of 1 TeV is compatible with all these constraints.

A vector-like fourth generation with a discrete symmetry from Split-UED

Split-UED allows for the possibility that the lowest lying KK excitations of the Standard Model fermions can be much lighter than the corresponding gauge or Higgs KK states. This can happen provided the fermion bulk masses are chosen to be large, in units of the inverse compactification radius, 1/R, and negative. In this setup, all of the other KK states would be effectively decoupled from low energy physics. Such a scenario would then lead to an apparent vector-like fourth generation with an associated discrete symmetry that allows us to accommodate a dark matter candidate. In this paper the rather unique phenomenology presented by this picture will be examined.

Randall-Sundrum and strings

We investigate stringy excitations in Randall-Sundrum effective theories for electroweak symmetry breaking arising from embedding in string theory. RS is dual to a confining gauge theory, which we expect to have “QCD strings”, or color flux tubes. Stringy constructions of RS-like theories allow us to investigate the mass of these string states, which typically grows with a small fractional power of the number of colors N of the dual gauge theory. There are two known strong constraints on N for RS-like theories. The first arises from demanding that the Standard Model gauge couplings do not have a Landau pole at low scales. The second arises from demanding that the first-order confining phase transition in the early universe is able to proceed without leaving an empty universe, i.e. that the rate of bubble nucleation is not too small. We find that these constraints on N imply that string states are generically at most a factor of a few heavier than the lightest KK states, and we cannot self-consistently remain in the limit N,λ ≫ 1. We examine various string constructions of AdS or RS-like backgrounds, including orbifolds, theories on M5-branes, theories on D4-branes, and the recent F-theory construction of Polchinski and Silverstein. In every case we find that there are strong bounds on the mass of new stringy states. We briefly discuss important phenomenological implications due to the presence of such light stringy excitations, such as precision electroweak and flavor observables, as well as collider signals.

Testing extra dimensions below the production threshold of Kaluza-Klein excitations

We consider a stabilized RS1 model in the energy range below the direct production of KK states. In this range we work out the effective Lagrangian due to exchange of heavy KK tensor graviton and scalar radion states and compute explicitly the corresponding effective coupling constants. As an example, the Drell-Yan lepton pair production at the Tevatron and the LHC is analyzed in two situations, when the first KK resonance is too heavy to be directly detected at the colliders, and when the first KK resonance is visible but other states are still too heavy. It is shown that in both cases the contribution from the KK invisible tower leads to a modification of final particles distributions. In particular, for the second case a nontrivial interference between the first KK mode and the rest KK tower takes place. Expected 95% CL limits for model parameters for the Tevatron and the LHC are given. In the Appendix useful formulas for the cross sections and distributions of various new $2\to2$ processes via heavy KK tower exchange are presented, the new formulas containing nonzero particle masses for final state fermions and bosons. The formulas and numerical results are obtained by means of the CompHEP code, in which all new effective interactions are implemented providing a tool for simulation of corresponding events and a more detailed analysis.

CERN LHC signals from warped extra dimensions

We study production of Kaluza-Klein gluons (KKG) at the Large Hadron Collider (LHC) in the framework of a warped extra dimension with the Standard Model (SM) fields propagating in the bulk. We show that the detection of KK gluon is challenging since its production is suppressed by small couplings to the proton's constituents. Moreover, the KK gluon decays mostly to top pairs due to an enhanced coupling and hence is broad. Nevertheless, we demonstrate that for m_{KKG} \lesssim 4 TeV, 100 fb^{-1} of data at the LHC can provide discovery of the KK gluon. We utilize a sizeable left-right polarization asymmetry from the KK gluon resonance to maximize the signal significance, and we explore the novel feature of extremely highly energetic "top-jets". We briefly discuss how the detection of electroweak gauge KK states (Z/W) faces a similar challenge since their leptonic decays (``golden'' modes) are suppressed. Our analysis suggests that other frameworks, for example little Higgs, which rely on UV completion via strong dynamics might face similar challenges, namely (1) Suppressed production rates for the new particles (such as Z'), due to their ``light-fermion-phobic'' nature, and (2) Difficulties in detection since the new particles are broad and decay predominantly to third generation quarks and longitudinal gauge bosons.

Radiative corrections to the lightest KK states in theT2/(Z2×Z2′) orbifold

We study radiative corrections localized at the fixed points of the orbifold for the field theory in six dimensions with two dimensions compactified on the T2/(Z2 × Z2') orbifold in a specific realistic model for low energy physics that solves the proton decay and neutrino mass problem. We calculate corrections to the masses of the lightest stable KK modes, which could be the candidates for dark matter.

4D gravity localized in non Bbb Z2-symmetric thick branes

We present a comparative analysis of localization of 4D gravity on a non Z_2-symmetric scalar thick brane in both a 5-dimensional Riemannian space time and a pure geometric Weyl integrable manifold. This work was mainly motivated by the hypothesis which claims that Weyl geometries mimic quantum behaviour classically. We start by obtaining a classical 4-dimensional Poincare invariant thick brane solution which does not respect Z_2-symmetry along the (non-)compact extra dimension. The scalar energy density of our field configuration represents several series of thick branes with positive and negative energy densities centered at y_0. The only qualitative difference we have encountered when comparing both frames is that the scalar curvature of the Riemannian manifold turns out to be singular for the found solution, whereas its Weylian counterpart presents a regular behaviour. By studying the transverse traceless modes of the fluctuations of the classical backgrounds, we recast their equations into a Schroedinger's equation form with a volcano potential of finite bottom (in both frames). By solving the Schroedinger equation for the massless zero mode m^2=0 we obtain a single bound state which represents a stable 4-dimensional graviton in both frames. We also get a continuum gapless spectrum of KK states with positive m^2>0 that are suppressed at y_0, turning into continuum plane wave modes as "y" approaches spatial infinity. We show that for the considered solution to our setup, the potential is always bounded and cannot adopt the form of a well with infinite walls; thus, we do not get a discrete spectrum of KK states, and we conclude that the claim that Weylian structures mimic, classically, quantum behaviour does not constitute a generic feature of these geometric manifolds.

LOW ENERGY GAUGE UNIFICATION THEORY

Because of the problems arising from the fermion unification in the traditional grand unified theory and the mass hierarchy between the four-dimensional Planck scale and weak scale, we suggest the low energy gauge unification theory with low high-dimensional Planck scale. We discuss the nonsupersymmetric SU(5) model on M4 × S1/Z2 × S1/Z2 and the supersymmetric SU(5) model on M4 × S1/(Z2 × Z2′) × S1/(Z2 × Z2′). The SU(5) gauge symmetry is broken by the orbifold projection for the zero modes, and the gauge unification is accelerated due to the SU(5) asymmetric light KK states. In our models, we forbid the proton decay, still keep the charge quantization, and automatically solve the fermion mass problem. We also comment on the anomaly cancellation and other possible scenarios for low energy gauge unification.

Local discrete symmetry in the brane neighborhood

With the ansatz that there exist local or global discrete symmetries in the special branes' neighborhoods, we can construct the extra dimension models with only zero modes, or the models which have large extra dimensions and arbitrarily heavy KK modes because there is no simple relation between the mass scales of extra dimensions and the masses of KK states. In addition, the bulk gauge symmetry and supersymmetry can be broken on the special branes for all the modes, and in the bulk for the zero modes by local and global discrete symmetries. To be explicit, we discuss the supersymmetric SU(5) model on $M^4\times S^1/Z_2$ in which there is a local $Z_2'$ symmetry in the special 3-brane neighborhood along the fifth dimension.

Discrete symmetry and GUT breaking

We study the supersymmetric GUT models where the supersymmetry and GUT gauge symmetry can be broken by the discrete symmetry. First, with the ansatz that there exist discrete symmetries in the branes' neighborhoods, we discuss the general reflection $Z_2$ symmetries and GUT breaking on $M^4\times M^1$ and $M^4\times M^1\times M^1$. In those models, the extra dimensions can be large and the KK states can be set arbitrarily heavy. Second, considering the extra space manifold is the annulus $A^2$ or disc $D^2$, we can define any $Z_n$ symmetry and break any 6-dimensional N=2 supersymmetric SU(M) models down to the 4-dimensional N=1 supersymmetric $SU(3)\times SU(2)\times U(1)^{M-4}$ models for the zero modes. In particular, there might exist the interesting scenario on $M^4\times A^2$ where just a few KK states are light, while the others are relatively heavy. Third, we discuss the complete global discrete symmetries on $M^4\times T^2$ and study the GUT breaking.

Compactified NCOS and duality

We study four-dimensional U(1) on a non-commutative T^2 with rational Theta. This theory has dual descriptions as ordinary SYM or as NCOS. We identify a set of massive non-interacting KK states in the SYM theory and track them through the various dualities. They appear as stretched strings in the non-commutative U(1) providing another example of the IR/UV mixing in non-commutative field theories. In the NCOS these states appear as D-strings with winding and momentum. They form an unconventional type of 1/4 BPS state with the 3-brane. To obtain a consistent picture of S-duality for compactified theories it is essential to keep track of both the NS and the RR B-fields.

Bulk fermions in multi-brane worlds

We study bulk fermion fields in various multi-brane models with localized gravity. The chiral zero mode that these models support can be identified as a right-handed sterile neutrino. In this case small neutrino Dirac masses can naturally appear due to a localization of the bulk fermion zero mode wavefunction, in an analogous way to graviton, without invoking the see-saw mechanism. The conditions and the options for localization are discussed in detail. It is shown that, considering a well motivated five dimensional mass term, the localization behaviour of this mode can resemble the graviton's at least in a region of the parameter space. As a result, the ''+-+'', ''++'' models can support, in addition to the ultralight graviton KK state, an ultralight localized and strongly coupled bulk fermion KK mode. We find that there are severe constraints on the parameter space of ''+-+'' and ''++'' models if the neutrino properties resulting from this light fermion state are to be reasonable. Furthermore, in the case that also the Bigravity scenario is realized the above special KK mode can induce too large mixing between the neutrino and the KK tower sterile modes restricting even more the allowed parameter space.

A Note on Gaugino Masses in Kaluza-Klein/Radion Mediated SUSY Breaking

We review the equivalence of two approaches to study theories with gauge fields in extra spatial dimensions, namely the ``4D'' approach (with KK states) and the ``5D'' approach (with matching to the 4D theory at the compactification scale). In particular, we reiterate that there are two different power-law scalings of ``effective'' gauge couplings. In a supersymmetric framework with SUSY breaking in the radius modulus, i.e., the field which fixes the size of the extra dimensions, these two approaches seem to give gaugino masses at loop-level (with a possible enhancement due to large number of Kaluza-Klein states) (hep-ph/0008069), and tree-level (hep-ph/0008103), respectively. We show explicitly how this discrepancy can be resolved.

Intersecting brane worlds

It is known that chiral fermions naturally appear at certain intersections of branes at angles. Motivated by this fact, we propose a string scenario in which different standard model gauge interactions propagate on different (intersecting) brane worlds, partially wrapped in the extra dimensions. Quarks and leptons live at brane intersections, and are thus located at different positions in the extra dimensions. Replication of families follows naturally from the fact that the branes generically intersect at several points. Gauge and Yukawa couplings can be computed in terms of the compactification radii. Hierarchical Yukawa couplings appear naturally, since amplitudes involving three different intersections are proportional to exp{-A_{ijk}}, where A_{ijk} is the area of a string world-sheet extending among the intersections. The models are non-supersymmetric but the string scale may be lowered down to 1-10 TeV. The proton is however stable due to a set of discrete symmetries arising from world-sheet selection rules, exact to all orders in perturbation theory. The scenario has some distinctive features like the presence of KK, winding and other new excited states (`gonions'), with masses below the string scale and accessible to accelerators. The models contain scalar tachyons with the quantum numbers of standard SU(2) x U(1) Higgs doublets, and we propose that they induce electroweak symmetry breaking in a somewhat novel way. Specific string models with D4-branes wrapping on T^2 x (T^2)^2/Z_N, leading to three-family semirealistic spectra, are presented, in which the above properties are exemplified.

Multibrane worlds and modification of gravity at large scales

We discuss the implications of multibrane constructions involving combinations of positive and negative tension brane and show how anomalously light KK states emerge when negative tension “ − ” branes are sandwiched between “ + ” branes. We present a detailed study of a “ +−−+ ” brane assignment which interpolates between two models that have been previously proposed in which gravity is modified at large scales due to the anomalously light states. We show that it has the peculiar characteristic that gravity changes from four-dimensional (4D) to 5D at large distances and returns to 4D at even larger scales. We also consider a crystalline universe which leads to a similar structure for gravity. The problems associated with intermediate negative tension branes are discussed and a possible resolution suggested.