1,720,975 research outputs found
Wick rotation and fermion doubling in noncommutative geometry
No full textIn 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
Emergent spontaneous symmetry breaking and emergent symmetry restoration in rippling gravitational background
No full textWe study effects of a rippling gravitational background on a scalar field with a double well potential, focusing on the analogy with the well known dynamics of the Kapitza’s pendulum. The ripples are rendered as infinitesimal but rapidly oscillating perturbations of the scale factor. We find that the resulting dynamics crucially depends on a value of the parameter in the vertex. For the time-dependent perturbations of a proper form the resulting effective action is generally covariant, and at a high enough frequency at the effective potential has a single minimum at zero, thereby restoring spontaneously broken symmetry of the ground state. On the other side, at spontaneous symmetry breaking emerges even when it is absent in the unperturbed case
The Gribov problem in noncommutative QED
Full text linkIt 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
Spectral action with zeta function regularization
Full text linkIn this paper we propose a novel definition of the bosonic spectral action using zeta function regularization, in order to address the issues of renormalizability and spectral dimensions. We compare the zeta spectral action with the usual (cutoff-based) spectral action and discuss its origin and predictive power, stressing the importance of the issue of the three dimensionful fundamental constants, namely the cosmological constant, the Higgs vacuum expectation value, and the gravitational constant. We emphasize the fundamental role of the neutrino Majorana mass term for the structure of the bosonic action
Universal Landau Pole
Full text linkAbstract: 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 an unification of all fundamental interactions at the Planck scale in the form of a Universal Landau Pole (ULP), 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 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 SM vacuum
Spectral action, Weyl anomaly and the Higgs-Dilaton potential.
No full textWe show how the bosonic spectral action emerges from the fermionic action by the renormalization group flow in the presence of a dilaton and the Weyl anomaly. The induced action comes out to be basically the Chamseddine-Connes spectral action introduced in the context of noncommutative geometry. The entire spectral action describes gauge and Higgs fields coupled with gravity. We then consider the effective potential and show, that it has the desired features of a broken and an unbroken phase, with the roll down
Spectral Action from Anomalies
No full textStarting from a theory of fermions moving in a fixed gauge and gravitational background we implement the scale invariance of the theory. Upon quantization the theory is anomalous but the anomaly can be cancelled by the addition of another term to the action. This term comes out to be basically the Chamseddine Connes spectral action introduced in the context of noncommutative geometry. An alternative realization of the dilaton may involve a collective scalar mode of all fermions accumulated in a {scale-noninvariant} dilaton action. The entire spectral action describes gauge and Higgs fields coupled with gravity. Here this action is coupled with a dilaton and we discuss how it relates to the transition from the radiation to the electroweak broken phase via condensation of Higgs fields
SU(N) multi-Skyrmions at finite volume
Full text linkWe study multi-soliton solutions of the four-dimensional SU(N) Skyrme model by combining the hedgehog ansatz for SU(N) based on the harmonic maps of into and a geometrical trick which allows to analyze explicitly finite-volume effects without breaking the relevant symmetries of the ansatz. The geometric set-up allows to introduce a parameter which is related to the ’t Hooft coupling of a suitable large N limit, in which and the curvature of the background metric approaches zero, in such a way that their product is constant. The relevance of such a parameter to the physics of the system is pointed out. In particular, we discuss how the discrete symmetries of the configurations depend on it
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