[Show abstract][Hide abstract] ABSTRACT: We investigate path integral quantization of two versions of unimodular gravity. First a fully diffeomorphism-invariant theory is proposed, which does not include a unimodular condition on the metric, while still being equivalent to other unimodular gravity theories at classical level. The path integral has the same form as in general relativity (GR), except that the cosmological constant is an unspecified value of a variable, and thus unrelated to any coupling constant. When the state of the universe is a superposition of vacuum states, the path integral is extended to include an integral over the cosmological constant. Second, we analyze the standard unimodular theory of gravity, where the metric determinant is fixed by a constraint. Its path integral differs from the one of GR in two ways: the metric of spacetime satisfies the unimodular condition only in average over space, and both the Hamiltonian constraint and the associated gauge condition have zero average over space. Finally, the canonical relation between the given unimodular theories of gravity is established.
European Physical Journal C 10/2015; 75:477. DOI:10.1140/epjc/s10052-015-3683-3 · 5.08 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study modifications of the Schwarzschild solution within the
noncommutative gauge theory of gravity. In the present analysis, the deformed
solutions are obtained by solving the field equations perturbatively, up to the
second order in the noncommutativity parameter $\Theta$, for both exterior and
interior solutions of the equations of motion for $e_\mu ^a \left(x\right)$.
Remarkably, we find that this new noncommutive solution is analogous to the
Reissner-Nordstr\"om solution in the ordinary spacetime, in which the square of
electric charge is replaced by the square of the noncommutativity parameter,
but with opposite sign. This amounts to the noncommutative Schwarzschild radius
$r_{NCS}$ becoming larger than the usual radius $r_S =2M$, instead of smaller
as it happens to the Reissner-Nordstr\"om radius $r_{RN}$, implying that
$r_{NCS}>r_{S} >r_{RN}$. An intuitive interpretation of this result is
mentioned.
Physical Review D 09/2015; 92:065017. DOI:10.1103/PhysRevD.92.065017 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: By adding a neutrino mass term to the Standard Model, which is Lorentz and
$SU(2)\times U(1)$ invariant but non-local to evade $CPT$ theorem, it is shown
that non-locality within a distance scale of the Planck length, that may not be
fatal to unitarity in generic effective theory, can generate the
neutrino-antineutrino mass splitting of the order of observed neutrino mass
differences, which is tested in oscillation experiments, and non-negligible
baryon asymmetry depending on the estimate of sphaleron dynamics. The one-loop
order induced electron-positron mass splitting in the Standard Model is shown
to be finite and estimated at $\sim 10^{-20}$ eV, well below the experimental
bound $< 10^{-2}$ eV. The induced $CPT$ violation in the $K$-meson in the
Standard Model is expected to be even smaller and well below the experimental
bound $|m_{K}-m_{\bar{K}}|<0.44\times 10^{-18}$ GeV.
Modern Physics Letters A 07/2015; 30(21). DOI:10.1142/S0217732315300165 · 1.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We revisit the problem of stability of string vacua involving hyperbolic
orbifolds using methods from homotopy theory and K-homology. We propose a
definition of Type II string theory on such backgrounds that further carry
stratified systems of fiber bundles, which generalise the more conventional
orbifold and symmetric string backgrounds, together with a classification of
wrapped branes by a suitable generalized homology theory. For spaces stratified
fibered over hyperbolic orbifolds we use the algebraic K-theory of their
fundamental groups and Quinn homology to derive criteria for brane stability in
terms of an Atiyah-Hirzebruch type spectral sequence with its lift to
K-homology. Stable D-branes in this setting carry stratified charges which
induce new additive structures on the corresponding K-homology groups. We
extend these considerations to backgrounds which support H-flux, where we use
K-groups of twisted group algebras of the fundamental groups to analyse
stability of locally symmetric spaces with K-amenable isometry groups, and
derive stability conditions for branes wrapping the fibers of an
Eilenberg-MacLane spectrum functor.
[Show abstract][Hide abstract] ABSTRACT: We develop a self-consistent $Spin(4,4)$-invariant model of the unification
of gravity with weak $SU(2)$ gauge and Higgs fields in the visible and
invisible sectors of our Universe. We consider a general case of the graviweak
unification, including the higher-derivative super-renormalizable theory of
gravity, which is a unitary, asymptotically-free and perturbatively consistent
theory of the quantum gravity.
International Journal of Modern Physics A 11/2014; 30(09). DOI:10.1142/S0217751X1550044X · 1.70 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: On the basis of a previously proposed mechanism of neutrino-antineutrino mass
splitting in the Standard Model, which is Lorentz and $SU(2)\times U(1)$
invariant but non-local to evade $CPT$ theorem, we discuss the possible
implications of neutrino-antineutrino mass splitting on neutrino physics and
baryogenesis. It is shown that non-locality within a distance scale of the
Planck length, that may not be fatal to unitarity in generic effective theory,
can generate the neutrino-antineutrino mass splitting of the order of observed
neutrino mass differences, which is tested in oscillation experiments, and
non-negligible baryon asymmetry depending on the estimate of sphaleron
dynamics. The one-loop order induced electron-positron mass splitting in the
Standard Model is shown to be finite and estimated at $\sim 10^{-20}$ eV, well
below the experimental bound $< 10^{-2}$ eV. The induced $CPT$ violation in the
$K$-meson in the Standard Model is expected to be even smaller and well below
the experimental bound $|m_{K}-m_{\bar{K}}|<0.44\times 10^{-18}$ GeV.
Physics Letters B 09/2014; 743. DOI:10.1016/j.physletb.2015.01.053 · 6.13 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Recently modified gravitational theories which mimic the behaviour of dark
matter, the so-called "Mimetic Dark Matter", have been proposed. We study the
consistency of such theories with respect to the absence of ghost instability
and propose a new tensor-vector-scalar theory of gravity, which is a
generalization of the previous models of mimetic dark matter with additional
desirable features. In the light of these observations, the idea of mimetic
matter is a promising approach to the problem of dark matter.
Journal of High Energy Physics 04/2014; 2014(12). DOI:10.1007/JHEP12(2014)102 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Among modified gravitational theories, the Tensor-Vector-Scalar (TeVeS)
occupies a special place -- it is a covariant theory of gravity that produces
the modified Newtonian dynamics (MOND) in the nonrelativistic weak field limit
and explains the astrophysical data by all means better than the GR, at scales
larger than that of the Solar System. We show that, in contrast with other
modified theories, TeVeS is free from ghosts. These achievements make TeVeS
(and its nonrelativistic limit) a viable theory of gravity. A speculative
outlook on the emergence of TeVeS from a quantum theory is presented.
Physics Letters B 02/2014; 735. DOI:10.1016/j.physletb.2014.06.036 · 6.13 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Life sciences are among the most interesting fields of contemporary scientific research. The biological world has such a wide range of complexities that any attempt to present it in any depth would take us outside the scope of the present book. In the present chapter, we shall thus only refer to a few specific physical problems in the biological world.
[Show abstract][Hide abstract] ABSTRACT: In the previous chapter we saw that an electric charge at rest creates a surrounding static field. A charge moving with constant velocity creates a constant electromagnetic field displacing with the charge. However, an accelerated charge produces a field of a different nature: a radiation field, which propagates far from its source and becomes independent of it. A charge moving at constant velocity is displaced with its field, but does not emit radiation. Charge acceleration is a necessary and sufficient condition for the generation of electromagnetic radiation. We shall see later that radiation behaves in dual form, as waves and as particles (photons), but this chapter will deal mainly with the wave behaviour of radiation.
[Show abstract][Hide abstract] ABSTRACT: We construct a model unifying gravity with weak $SU(2)$ gauge and "Higgs"
scalar fields. We assume the existence of a visible and an invisible (hidden)
sector of the Universe. We used the extension of Plebanski's 4-dimensional
gravitational theory, in which the fundamental fields are two-forms containing
tetrads, spin connections and additional auxiliary fields. Considering a
$Spin(4,4)$ invariant extended Plebanski action, we recover the actions in both
(visible and invisible) sectors of the Universe. After symmetry breaking of the
graviweak (GW) unification, its physical constants (Newton's constants,
cosmological constants, YM-couplings, etc.), are determined by a parameter
$g_{uni}$ of the GW unification. It is discussed that if this "Higgs" field
coming in the GW unification could be the Higgs of the Standard Model, then the
idea that its vacuum value could be, according to the Multiple Point Principle,
a second minimum of the Higgs field effective potential, turns out not to be
viable. Then other scalar "Higgs" field, giving the inflation and axion fields,
has a Planck scale expectation value, and could have a better chance of being
the scalar field unified with gravity.
[Show abstract][Hide abstract] ABSTRACT: We analyze gravitational theories with quadratic curvature terms, including
the case of conformally invariant Weyl gravity, motivated by the intention to
find a renormalizable theory of gravity in the ultraviolet region, yet yielding
general relativity at long distances. In the Hamiltonian formulation of Weyl
gravity, the number of local constraints is equal to the number of unstable
directions in phase space, which in principle could be sufficient for
eliminating the unstable degrees of freedom in the full nonlinear theory. All
the other theories of quadratic type are unstable -- a problem appearing as
ghost modes in the linearized theory.
We find that the full projection of the Weyl tensor onto a three-dimensional
hypersurface contains an additional fully traceless component, given by a
quadratic extrinsic curvature tensor. A certain inconsistency in the literature
is found and resolved: when the conformal invariance of Weyl gravity is broken
by a cosmological constant term, the theory becomes pathological, since a
constraint required by the Hamiltonian analysis imposes the determinant of the
metric of spacetime to be zero. In order to resolve this problem by restoring
the conformal invariance, we introduce a new scalar field that couples to the
curvature of spacetime, reminiscent of the introduction of vector fields for
ensuring the gauge invariance.
Physical Review D 11/2013; 89(6). DOI:10.1103/PhysRevD.89.064043 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The CPT theorem in quantum field theory, its validity, breaking and
consequences are reviewed. One can show that for CPT theorem to hold,
Lorentz invariance is not always needed. Also one can have CPT
violation, while there is Lorentz invariance. Field theoretical examples
for both cases are given and mass differences between
particle-antiparticle are discussed as well. Unambiguous tests of CPT
violation, unrelated to the breaking of Lorentz invariance, are
suggested.
Journal of Physics Conference Series 11/2013; 474(1):2031-. DOI:10.1088/1742-6596/474/1/012031
[Show abstract][Hide abstract] ABSTRACT: We study M-theory and D-brane quantum partition functions for microscopic
black hole ensembles within the context of the AdS/CFT correspondence in terms
of highest weight representations of infinite-dimensional Lie algebras,
elliptic genera, and Hilbert schemes, and describe their relations to elliptic
modular forms. The common feature in our examples lie in the modular properties
of the characters of certain representations of the pertinent affine Lie
algebras, and in the role of spectral functions of hyperbolic three-geometry
associated with q-series in the calculation of elliptic genera. We present new
calculations of supergravity elliptic genera on local Calabi-Yau threefolds in
terms of BPS invariants and spectral functions, and also of equivariant D-brane
elliptic genera on generic toric singularities. We use these examples to
conjecture a link between the black hole partition functions and elliptic
cohomology.
International Journal of Geometric Methods in Modern Physics 08/2013; 11(5). DOI:10.1142/S0219887814500480 · 0.44 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We consider a Graviweak Unification model with the assumption of the
existence of the hidden (invisible) sector of our Universe parallel to the
visible world. This Hidden World (HW) is assumed to be a Mirror World (MW) with
broken mirror parity. We start with a diffeomorphism invariant theory of a
gauge field valued in a Lie algebra g, which is broken spontaneously to the
direct sum of the spacetime Lorentz algebra and the Yang-Mills algebra: $\tilde
{\mathfrak g} = {\mathfrak su}(2)^{(grav)}_L \oplus {\mathfrak su}(2)_L$ -- in
the ordinary world, and $\tilde {\mathfrak g}' = {{\mathfrak
su}(2)'}^{(grav)}_R \oplus {\mathfrak su}(2)'_R$ -- in the hidden world. Using
an extension of the Plebanski action for general relativity, we recover the
actions for gravity, SU(2) Yang-Mills and Higgs fields in both (visible and
invisible) sectors of the Universe, and also the total action. After symmetry
breaking, all physical constants, including the Newton's constants,
cosmological constants, Yang-Mills couplings, and other parameters, are
determined by a single parameter $g$ presented in the initial action, and by
the Higgs VEVs. The Dark Energy problem of this model predicts a too large
supersymmetric breaking scale ($\sim 10^{10}-10^{12}$ GeV), which is not within
the reach of the LHC experiments.
International Journal of Modern Physics A 07/2013; 28(18):1350085. DOI:10.1142/S0217751X13500851 · 1.70 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study a Lie algebra of formal vector fields $W_n$ with its application to
the perturbative deformed holomorphic symplectic structure in the A-model, and
a Calabi-Yau manifold with boundaries in the B-model. A relevant concept in the
vertex operator algebra and the BRST cohomology is that of the elliptic genera
(the one-loop string partition function). We show that the elliptic genera can
be written in terms of spectral functions of the hyperbolic three-geometry
(which inherits the cohomology structure of BRST-like operator). We show that
equivalence classes of deformations are described by a Hochschild cohomology
theory of the DG-algebra ${\mathfrak A} = (A, Q)$, $Q
=\bar{\partial}+\partial_{\rm deform}$, which is defined to be the cohomology
of $(-1)^n Q +d_{\rm Hoch}$. Here $\bar{\partial}$ is the initial non-deformed
BRST operator while $\partial_{\rm deform}$ is the deformed part whose algebra
is a Lie algebra of linear vector fields ${\rm gl}_n$. We discuss the
identification of the harmonic structure $(HT^\bullet(X); H\Omega_\bullet(X))$
of affine space $X$ and the group ${\rm Ext}_{X}^n({\cal O}_{\triangle}, {\cal
O}_{\triangle})$ (the HKR isomorphism), and bulk-boundary deformation pairing.
International Journal of Modern Physics A 06/2013; 28(16). DOI:10.1142/S0217751X13500693 · 1.70 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Algebraic aspects of the computation of partition functions for quantum
gravity and black holes in $AdS_3$ are discussed. We compute the sub-leading
quantum corrections to the Bekenstein-Hawking entropy. It is shown that the
quantum corrections to the classical result can be included systematically by
making use of the comparison with conformal field theory partition functions,
via the $AdS_3/CFT_2$ correspondence. This leads to a better understanding of
the role of modular and spectral functions, from the point of view of the
representation theory of infinite-dimensional Lie algebras. Besides, the sum of
known quantum contributions to the partition function can be presented in a
closed form, involving the Patterson-Selberg spectral function. These
contributions can be reproduced in a holomorphically factorized theory whose
partition functions are associated with the formal characters of the Virasoro
modules. We propose a spectral function formulation for quantum corrections to
the elliptic genus from supergravity states.
Nuclear Physics B 04/2013; 873(3). DOI:10.1016/j.nuclphysb.2013.05.001 · 3.93 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: An attempt is made to incorporate the electromagnetic interaction in a
Lorentz invariant but CPT violating non-local model with particle-antiparticle
mass-splitting, which is regarded as a modified QED. The gauge invariance is
maintained by the Schwinger non-integrable phase factor but the electromagnetic
interaction breaks C, CP and CPT symmetries. Implications of the present CPT
breaking scheme on the electromagnetic transitions and particle-antiparticle
pair creation are discussed. The CPT violation such as the one suggested here
may open a new path to the analysis of baryon asymmetry since some of the
Sakharov constraints are expected to be modified.
[Show abstract][Hide abstract] ABSTRACT: The Lorentz invariant $CPT$ violation by using non-local interactions is
naturally incorporated in the Higgs coupling to neutrinos in the Standard
Model, without spoiling the basic $SU(2)_{L}\times U(1)$ gauge symmetry. The
neutrino--antineutrino mass splitting is thus realized by the mechanism which
was proposed recently, assuming the neutrino masses to be predominantly
Dirac-type in the Standard Model.
Physics Letters B 08/2012; 718(1). DOI:10.1016/j.physletb.2012.09.071 · 6.13 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In order to explore some general features of modified theories of gravity
which involve higher derivatives and spontaneous Lorentz and/or diffeomorphism
symmetry breaking, we study the recently proposed new version of covariant
renormalizable gravity (CRG). CRG attains power-counting renormalizability via
higher derivatives and introduction of a constrained scalar field and
spontaneous symmetry breaking. We obtain an Arnowitt-Deser-Misner
representation of the CRG action in four-dimensional spacetime with respect to
a foliation of spacetime adapted to the constrained scalar field. The resulting
action is analyzed by using Hamiltonian formalism. We discover that CRG
contains two extra degrees of freedom. One of them carries negative energy (a
ghost) and it will destabilize the theory due to its interactions. This result
is in contrast with the original paper [Phys. Lett. B 701, 117 (2011),
arXiv:1104.4286 [hep-th]], where it was concluded that the theory is free of
ghosts and renormalizable when we analyze fluctuations on the flat background.