23 research outputs found
Higher derivatives and brane-localised kinetic terms in gauge theories on orbifolds
We perform a detailed analysis of one-loop corrections to the self-energy of
the (off-shell) gauge bosons in six-dimensional N=1 supersymmetric gauge
theories on orbifolds. After discussing the Abelian case in the standard
Feynman diagram approach, we extend the analysis to the non-Abelian case by
employing the method of an orbifold-compatible one-loop effective action for a
classical background gauge field. We find that bulk higher derivative and
brane-localised gauge kinetic terms are required to cancel one-loop divergences
of the gauge boson self energy. After their renormalisation we study the
momentum dependence of both the higher derivative coupling h(k^2) and the {\it
effective} gauge coupling g_eff(k^2). For momenta smaller than the
compactification scales, we obtain the 4D logarithmic running of g_eff(k^2),
with suppressed power-like corrections, while the higher derivative coupling is
constant. We present in detail the threshold corrections to the low energy
gauge coupling, due to the massive bulk modes. At momentum scales above the
compactification scales, the higher derivative operator becomes important and
leads to a power-like running of g_eff(k^2) with respect to the momentum scale.
The coefficient of this running is at all scales equal to the renormalised
coupling of the higher derivative operator which ensures the quantum
consistency of the model. We discuss the relation to the similar one-loop
correction in the heterotic string, to show that the higher derivative
operators are relevant in that case too, since the field theory limit of the
one-loop string correction does not commute with the infrared regularisation of
the (on-shell) string result.Comment: 1+45 pages, 2 figures, JHEP style file, version to be published in
JHE
Higher Derivative Operators as Counterterms in Orbifold Compactifications
In the context of 5D N=1 supersymmetric models compactified on S_1/Z_2 or
S_1/(Z_2 x Z_2') orbifolds and with brane-localised superpotential, higher
derivative operators are generated radiatively as one-loop counterterms to the
mass of the (brane or zero mode of the bulk) scalar field. It is shown that the
presence of such operators which are brane-localised is not related to the
mechanism of supersymmetry breaking considered (F-term, discrete or continuous
Scherk-Schwarz breaking) and initial supersymmetry does not protect against the
dynamical generation of such operators. Since in many realistic models the
scalar field is commonly regarded as the Higgs field, and the higher derivative
operators seem a generic presence in orbifold compactifications, we stress the
importance of these operators for solving the hierarchy problem.Comment: Contribution to the Conference "Supersymmetry 2005", Durham; 13
pages, LaTe
On gauge unification in Type I/I' models
We discuss whether the (MSSM) unification of gauge couplings can be
accommodated in string theories with a low (TeV) string scale. This requires
either power law running of the couplings or logarithmic running extremely far
above the string scale. In both cases it is difficult to arrange for the
multiplet structure to give the MSSM result. For the case of power law running
there is also enhanced sensitivity to the spectrum at the unification scale.
For the case of logarithmic running there is a fine tuning problem associated
with the light closed string Kaluza Klein spectrum which requires gauge
mediated supersymmetry breaking on the ``visible'' brane with a dangerously low
scale of supersymmetry breaking. Evading these problems in low string scale
models requires a departure from the MSSM structure, which would imply that the
success of gauge unification in the MSSM is just an accident.Comment: 10 pages, LaTeX, 2 figures; minor change
Quantum scale invariance in gauge theories and applications to muon production
We discuss quantum scale invariance in (scale invariant) gauge theories with
both ultraviolet (UV) and infrared (IR) divergences. Firstly, their BRST
invariance is checked in two apparently unrelated approaches using a scale
invariant regularisation (SIR). These approaches are then shown to be
equivalent. Secondly, for the Abelian case we discuss both UV and IR quantum
corrections present in such theories. We present the Feynman rules in a form
suitable for offshell Green functions calculations, together with their
one-loop renormalisation. This information is then used for the muon production
cross section at one-loop in a quantum scale invariant theory. Such a theory
contains not only new UV poles but also IR poles. While the UV poles bring new
quantum corrections (in the form of counterterms), finite or divergent, that we
compute, it is shown that the IR poles do not bring new physics. The IR quantum
corrections, both finite and divergent, cancel out similarly to the way the IR
poles themselves cancel in the traditional approach to IR divergences (in the
cross section, after summing over virtual and real corrections). Hence, the
evanescent interactions induced by the scale-invariant analytical continuation
of the SIR scheme do not affect IR physics, as illustrated at one-loop for the
muon production () cross section.Comment: 20 page
Quadratic Divergences in Kaluza-Klein Theories
We investigate the so-called ``Kaluza-Klein regularisation'' procedure in
supersymmetric extensions of the standard model with additional compact
dimensions and Scherk-Schwarz mechanism for supersymmetry breaking. This
procedure uses a specific mathematical manipulation to obtain a finite result
for the scalar potential. By performing the full calculation, we show that the
finiteness of this result is not only a consequence of the underlying
supersymmetry, but also the result of an implicit fine-tuning of the
coefficients of the terms that control the ultraviolet behaviour. The
finiteness of the Higgs mass at one-loop level seems therefore to be an
artefact of the regularisation scheme, and quadratic divergences are expected
to reappear in higher orders of perturbation theory.Comment: 10 pages, LaTe
Higher Derivative Operators from Scherk-Schwarz Supersymmetry Breaking on T^2/Z_2
In orbifold compactifications on T^2/Z_2 with Scherk-Schwarz supersymmetry
breaking, it is shown that (brane-localised) superpotential interactions and
(bulk) gauge interactions generate at one-loop higher derivative counterterms
to the mass of the brane (or zero-mode of the bulk) scalar field. These
brane-localised operators are generated by integrating out the bulk modes of
the initial theory which, although supersymmetric, is nevertheless
non-renormalisable. It is argued that such operators, of non-perturbative
origin and not protected by non-renormalisation theorems, are generic in
orbifold compactifications and play a crucial role in the UV behaviour of the
two-point Green function of the scalar field self-energy. Their presence in the
action with unknown coefficients prevents one from making predictions about
physics at (momentum) scales close to/above the compactification scale(s). Our
results extend to the case of two dimensional orbifolds, previous findings for
S^1/Z_2 and S^1/(Z_2 x Z_2') compactifications where brane-localised higher
derivative operators are also dynamically generated at loop level, regardless
of the details of the supersymmetry breaking mechanism. We stress the
importance of these operators for the hierarchy and the cosmological constant
problems in compactified theories.Comment: 23 pages, LaTeX, one figure, published version in JHE
Higher Derivative Operators from Transmission of Supersymmetry Breaking on S_1/Z_2
We discuss the role that higher derivative operators play in field theory
orbifold compactifications on S_1/Z_2 with local and non-local (Scherk-Schwarz)
breaking of supersymmetry. Integrating out the bulk fields generates
brane-localised higher derivative counterterms to the mass of the brane (or
zero-mode of the bulk) scalar field, identified with the Higgs field in many
realistic models. Both Yukawa and gauge interactions are considered and the
one-loop results found can be used to study the ``running'' of the scalar field
mass with respect to the momentum scale in 5D orbifolds. In particular this
allows the study of the behaviour of the mass under UV scaling of the momentum.
The relation between supersymmetry breaking and the presence of higher
derivative counterterms to the mass of the scalar field is investigated. This
shows that, regardless of the breaking mechanism, (initial) supersymmetry
cannot, in general, prevent the emergence of such operators. Some implications
for phenomenology of the higher derivative operators are also presented.Comment: 29 pages, LaTeX. Added Section 4 ("Phenomenological implications:
living with ghosts?") and Appendix
TeV-Scale Z' Bosons from D-branes
Generic D-brane string models of particle physics predict the existence of
extra U(1) gauge symmetries beyond hypercharge. These symmetries are not of the
E_6 class but rather include the gauging of Baryon and Lepton numbers as well
as certain Peccei-Quinn-like symmetries. Some of the U(1)'s have triangle
anomalies, but they are cancelled by a Green-Schwarz mechanism. The
corresponding gauge bosons typically acquire a mass of order the string scale
M_S by combining with two-index antisymmetric fields coming from the closed
string sector of the theory. We argue that in string models with a low string
scale M_S proportional to 1-10 TeV, the presence of these generic U(1)'s may be
amenable to experimental test. Present constraints from electroweak precision
data already set important bounds on the mass of these extra gauge bosons. In
particular, for large classes of models, rho-parameter constraints imply M_S >=
1.5 TeV. In the present scheme some fraction of the experimentally measured Z^0
mass would be due not to the Higgs mechanism, but rather to the mixing with
these closed string fields. We give explicit formulae for recently constructed
classes of intersecting D6- and D5-brane models yielding the Standard Model
(SM) fermion spectrum.Comment: 46 pages, LaTeX, JHEP.cls, 21 Figures. minor correction
Unification through extra dimensions at two loops
The presence of an extra dimension of size R\equiv M_c^{-1} introduces
corrections of order (\mu/M_c)\alpha to the gauge and Yukawa couplings and
accelerates their running at scales \mu larger than M_c. This could result in a
grand unification scale M_X\approx 20 M_c. We study the corrections at the
two-loop level. We find corrections of order (\mu/M_c)\alpha^2 for the gauge
couplings and of order (\mu/M_c)^2\alpha^2 for the Yukawa couplings. Therefore,
in the Yukawa sector one and two-loop contributions can be of the same order
below M_X. We show that in the usual scenarios the dominant gauge and Yukawa
couplings are decreasing functions of the scale, in such a way that
(\mu/M_c)\alpha becomes approximately constant and two-loop contributions
introduce just a 30% correction which does not increase with the scale.Comment: 14 pages, added references, corrected typo
Adjoint bulk scalars and supersymmetric unification in the presence of extra dimensions
There are several advantages of introducing adjoint superfields at
intermediate energies around GeV. Such as (i) gauge couplings still
unify (ii) neutrino masses and mixings are produced (iii) primordial lepton
asymmetry can be produced. We point out that if adjoint scalars have bulk
excitations along with gauge bosons whereas fermions and the doublet scalar
live on boundary then N=2 supersymmetric beta functions vanish.
Thus even if extra dimensions open up at an intermediate scale and all
N=2 Yang-Mills fields as well as N=2 matter fields in the adjoint
representation propagate in the bulk, still gauge couplings renormalize beyond
just like they do in 4-dimensions with adjoint scalars. Consequently
unification is achieved in the presence to extra dimensions, mass scales are
determined uniquely via Renormalization Group Equations(RGE) and unification
scale remains high enough to suppress proton decay. This scenario can be
falsified if we get signatures of extra dimensions at low energy.Comment: New references added. This version will appear in Phys. Rev.