21 research outputs found
Wick Rotation and Fermion Doubling in Noncommutative Geometry
In this paper, we discuss two features of the noncommmutative geometry and
spectral action approach to the Standard Model: the fact that the model is
inherently Euclidean, and that it requires a quadrupling of the fermionic
degrees of freedom. We show how the two issues are intimately related. We give
a precise prescription for the Wick rotation from the Euclidean theory to the
Lorentzian one, eliminating the extra degrees of freedom. This requires not
only projecting out mirror fermions, as has been done so far, and which leads
to the correct Pfaffian, but also the elimination of the remaining extra
degrees of freedom. The remaining doubling has to be removed in order to
recover the correct Fock space of the physical (Lorentzian) theory. In order to
get a Spin(1,3) invariant Lorentzian theory from a Spin(4) invariant Euclidean
theory such an elimination must be performed after the Wick rotation.
Differences between the Euclidean and Lorentzian case are described in detail,
in a pedagogical way.Comment: Minor changes. To appear in PRD. 25 page
The Gribov problem in Noncommutative QED
It is shown that in the noncommutative version of QED (NCQED) Gribov copies
induced by the noncommutativity of space-time appear in the Landau gauge. This
is a genuine effect of noncommutative geometry which disappears when the
noncommutative parameter vanishes.Comment: 19 pages, 3 figures. Published. The paper has been shortened and many
references have been judged unnecessary or not suitable during the reviewing
proces
Gravitational parity anomaly with and without boundaries
In this paper we consider gravitational parity anomaly in three and four
dimensions. We start with a re-computation of this anomaly on a 3D manifold
without boundaries and with a critical comparison of our results to the
previous calculations. Then we compute the anomaly on 4D manifolds with
boundaries with local bag boundary conditions. We find, that gravitational
parity anomaly is localized on the boundary and contains a gravitational
Chern-Simons terms together with a term depending of the extrinsic curvature.
We also discuss the main properties of the anomaly, as the conformal
invariance, relations between 3D and 4D anomalies, etc.Comment: 16 pages, final version, accepted for publication in JHE
How many surface modes does one see on the boundary of a Dirac material?
We present full expressions for the surface part of polarization tensor of a
Dirac fermion confined in a half-space in dimensions. We compare this
tensor to the polarization tensor of eventual surface mode (which is a
dimensional Dirac fermion) and find essential differences in the conductivities
in both Hall and normal sectors. Thus, the interaction with electromagnetic
field near the boundary differs significantly in the full model and in the
effective theory for the surface mode.Comment: 5 pages, 4 figures; slightly improved version, published in Physical
Review Letter
The Gribov problem in Noncommutative gauge theory
After reviewing Gribov ambiguity of non-Abelian gauge theories, a phenomenon
related to the topology of the bundle of gauge connections, we show that there
is a similar feature for noncommutative QED over Moyal space, despite the
structure group being Abelian, and we exhibit an infinite number of solutions
for the equation of Gribov copies. This is a genuine effect of noncommutative
geometry which disappears when the noncommutative parameter vanishes.Comment: 14 pages. Prepared for the XXV International Fall Workshop on
Geometry and Physics, Instituto de Estructura de la Materia (CSIC) Madrid,
Spain August 29 - September 02, 201
Clifford Structures in Noncommutative Geometry and the Extended Scalar Sector
We consider aspects of the noncommutative approach to the standard model
based on the spectral action principle. We show that as a consequence of the
incorporation of the Clifford structures in the formalism, the spectral action
contains an extended scalar sector, with respect to the minimal Standard Model.
This may have interesting phenomenological consequences. Some of these new
scalar fields carry both weak isospin and colour indexes. We calculate the new
terms in spectral action due to the presence of these fields. Our analysis
demonstrates that the fermionic doubling in the noncommutative geometry is not
just a presence of spurious degrees of freedom, but it is an interesting and
peculiar property of the formalism, which leads to physically valuable
conclusions. Some of the new fields do not contribute to the physical fermionic
action, but they appear in the bosonic spectral action. Their contributions to
the Dirac operator correspond to couplings with the spurious fermions, which
are projected out.Comment: 24 pages, no figures, final version, accepted for publication in PRD,
references adde
Noncommutative field theory from angular twist
We consider a noncommutative field theory with space-time -commutators
based on an angular noncommutativity, namely a solvable Lie algebra: the
Euclidean in two dimension. The -product can be derived from a twist
operator and it is shown to be invariant under twisted Poincar\'e
transformations. In momentum space the noncommutativity manifests itself as a
noncommutative -deformed sum for the momenta, which allows for an
equivalent definition of the -product in terms of twisted convolution of
plane waves. As an application, we analyze the field theory at
one-loop and discuss its UV/IR behaviour. We also analyze the kinematics of
particle decay for two different situations: the first one corresponds to a
splitting of space-time where only space is deformed, whereas the second one
entails a non-trivial -multiplication for the time variable, while one
of the three spatial coordinates stays commutative.Comment: 23 pages 1 figur
Universal Landau Pole at the Planck scale
The concept of quantum gravity entails that the usual geometry loses its meaning at very small distances and therefore the grand unification of all gauge interactions with the property of asymptotic freedom happens to be questionable. We propose an unification of all gauge interactions in the form of an "Universal Landau Pole" (ULP), at which all gauge couplings diverge (or, better to say, become very strong). We show that the Higgs quartic coupling also substantially increases whereas the Yukawa couplings tend to zero. Such a singular (or strong coupling) unification is obtained after adding to the Standard Model matter more fermions with vector gauge couplings and hypercharges identical to the SM fermions. The influence of new particles also may prevent the Higgs quartic coupling from crossing zero, thus avoiding the instability (or metastability) of the SM vacuum. As well this fermion pattern opens a way to partially solve the hierarchy problem between masses of quarks and leptons
Universal Landau Pole
Our understanding of quantum gravity suggests that at the Planck scale the usual geometry loses its meaning. If so, the quest for grand unification in a large non-Abelian group naturally endowed with the property of asymptotic freedom may also lose its motivation. Instead, we propose a unification of all fundamental interactions at the Planck scale in the form of a universal Landau pole, at which all gauge couplings diverge. The Higgs quartic coupling also diverges while the Yukawa couplings vanish. The unification is achieved with the addition of fermions with vector gauge couplings coming in multiplets and with hypercharges identical to those of the standard model. The presence of these particles also prevents the Higgs quartic coupling from becoming negative, thus avoiding the instability (or metastability) of the standard model vacuum