21 pages, 4 figures. V2: significant changes to the second half of paper and overall clarification of argument. Discussion of geometric quantization and topological aspects of the quantum phase space added
Following up on a recent model yielding fermionic geometries, I turn to more familiar territory to address the question of statistics in purely geometric theories. Working in the gauge formulation of gravity, where geometry is characterized by a symmetry broken Cartan connection, I give strong evidence to suggest that de Sitter space itself, and a class of de Sitter-like geometries, can be consistently quantized fermionically. By this I mean that de Sitter space can be quantized such that the wavefunctional picks up an overall minus sign under a $2π$ rotational diffeomorphism. Surprisingly, the underlying mathematics is the same as that of the Skyrme model for strongly interacting baryons. This promotes the question {\it "Is geometry bosonic or fermionic?"} beyond the realm of the rhetorical and places it on uncomfortably familiar ground.
Fermions in (anti) de Sitter gravity theory in four dimensions are considered. Especially we propose new fermion actions to derive a Weyl or Majorana fermion action if we break the AdS (dS) group to the Lorentz group in curved spacetime.
We present a method to semiclassically compute the pair creation rate of bosons and fermions in de Sitter spacetime. The results in the bosonic case agree with the ones in the literature. We find that for the constant electric field the fermionic and bosonic pair creation rate are the same. This analogy of bosons and fermions in the semiclassical limit is known from several flat spacetime examples.
The quantum tunneling radiation of fermions with arbitrary spin at the event horizon of Kerr-de Sitter black hole is accurately modified by using the dispersion relation proposed in the study of string theory and quantum gravitational theory. The derived tunneling rate and temperature at the black hole horizons are analyzed and studied.
We studied the correction of the quantum tunneling radiation of fermions with spin $1/2$ in Kerr Anti-de-Sitter black hole. First, the dynamic equation of spin $1/2$ fermions was corrected using Lorentz's violation theory. Second, the new expressions of the fermions quantum tunneling rate, the Hawking temperature of the black hole and the entropy of the black hole were obtained according to the corrected fermions dynamic equation. At last, some comments are made on the results of our work.
We study two fermionic systems that have an underlying supersymmetric structure, namely a color superconductor and Dirac fermion in a Reissner-Nordström-anti-de Sitter gravitational background. In the chiral limit of the color superconductor, the localized fermionic zero modes around the vortex form an N=2 with zero central charge $d=1$ quantum algebra, with all the operators being Fredholm. We compute the Witten index of this algebra and we find an unbroken supersymmetry. The fermionic gravitational system in the chiral limit too, has two underlying unbroken N=2, $d=1$ supersymmetric algebras…
Using an exact expression for the bi-spinor of parallel transport, we construct the Feynman propagator for Dirac fermions in the vacuum state on anti-de Sitter space-time. We compute the vacuum expectation value of the stress-energy tensor by removing coincidence-limit divergences using the Hadamard method. We then use the vacuum Feynman propagator to compute thermal expectation values at finite temperature. We end with a discussion of rigidly rotating thermal states.
Making use of the symmetries of anti-de Sitter space-time, we derive an analytic expression for the bispinor of parallel transport, from which we construct in closed form the vacuum Feynman Green's function of the Dirac field on this background. Using the imaginary time anti-periodicity property of the thermal Feynman Green's function, we calculate the thermal expectation values of the fermion condensate and stress-energy tensor and highlight the effect of quantum corrections as compared to relativistic kinetic theory results.
We demonstrate that the fermions in Reissner-Nordström-anti-de Sitter black hole background in the chiral limit $m=0$, are related to an $N=4$ extended one dimensional supersymmetry with non-trivial topological charges. We also show that the $N=4$ extended supersymmetry is unbroken and we extend the two $N=2$ one dimensional supersymmetries that the system also possess, to have a trivial central charge. The implications of the trivial central charge on the Witten index are also discussed.
The tetrad gauge invariant theory of the free Dirac field in two special moving charts of the de Sitter spacetime is investigated pointing out the operators that commute with the Dirac one. These are the generators of the symmetry transformations corresponding to isometries that give rise to conserved quantities according to the Noether theorem. With their help the plane wave spinor solutions of the Dirac equation with given momentum and helicity are derived and the final form of the quantum Dirac field is established. It is shown that the canonical quantization leads to a correct physical int…
We study the vacuum polarisation effects of the Dirac fermionic field induced by a pointlike global monopole located in the cosmological de Sitter spacetime. First we derive the four orthonormal Dirac modes in this background in a closed form. Quantising the field using these modes, we then compute the fermionic condensate, $\langle 0| \overlineΨ Ψ| 0\rangle$, as well as the vacuum expectation value of the energy-momentum tensor for a massive Dirac field, regularised in a particular way. We have used the Abel-Plana summation formula in order to extract the global monopole contribution to these…
We have studied scalar perturbations as well as fermion perturbations in pure de Sitter space-times. For scalar perturbations we have showed that well-defined quasinormal modes can exist provided that the mass of scalar field $m>\frac{d-1}{2l}$. The quasinormal frequencies of fermion perturbations in three and four dimensional cases have also been presented. We found that different from other dimensional cases, in three dimensional pure de Sitter spacetime there is no quasinormal mode for the s-wave. This interesting difference caused by the spacial dimensions is true for both scalar and fermi…
We have investigated the Unruh effect in Anti de-Sitter (AdS) spacetime by examining the response function of an Unruh-DeWitt particle detector with uniform constant acceleration. An exact expression of the detector response function for the scalar field has been obtained with different levels of non-linearity in even dimensional AdS spacetime. We also showed how the response of the accelerated Unruh detector coupled quadratically to massless Dirac field in $D$ dimensional $(D \geq 2)$ AdS spacetime is proportional to that of a detector linearly coupled to a massless scalar field in $2D$ dimen…
We have investigated the emerging conformal field theory behavior on the interior interface of the region near the cosmological event horizon on an example of massless Dirac fermions. Indeed, we have constructed and verified the emerging de Sitter/CFT correspondence for the near cosmological event horizon region. It is in this near horizon region where the infinitely thin shell of matter with the stiffest equation of state (Zeldovich's matter) is placed in the model for a thermodynamically stable `would be black hole' which is sometimes called a gravastar or a dark energy star. We put forward …
In this paper we study the charged electro-weak interactions in the de Sitter geometry. We develop the reduction formalism for the Proca field with the help of the solutions for the interacting fields. Perturbation theory is used for obtaining the definition of the transition amplitudes in the first order. We apply our formalism to the study of spontaneous vacuum emission of fermions, anti-fermions and $W^{\pm}$ bosons in the expanding de Sitter universe. Our results are generalizations of the Weinberg-Salam electro-weak theory to curved space-time, in the case of $W^{\pm}$ boson interaction w…
Based on some recent work of the authors, we focus on the relationship between the Casimir energy of a Majorana spinor field for a Euclidean Einstein universe $S^4\times R$ and for a Euclidean de Sitter brane ($S^4$) embedded in AdS(5). This is for a conformally coupled massless field. Interestingly, the one brane effective potential is zero and the results are equivalent, as for the scalar case, when evaluated on the conformally related cylinder. However, using the actual metric this equivalence no longer holds because a non-trivial contribution from the path integral measure (known as the co…
We investigate two measures of quantum correlations and entanglement, namely the violation of the Bell-Mermin-Klyshko inequalities and the quantum discord, for Dirac fermions in the cosmological de Sitter background of dimension four. The BMK violation is focussed on the vacuum for two and four mode squeezed states and it is shown to increase with the number of modes. For the quantum discord, we investigate a maximally entangled in-vacuum state. Qualitative similarities as well as differences of our results with that of different coordinatisations of de Sitter in the context of scalar and ferm…
We study the fermionic Schwinger effect in two dimensional de Sitter spacetime. To do so we first present a method to semiclassically compute the number of pairs created per momentum mode for general time dependent fields. In addition the constant electric field is studied in depth. In this case solutions for the Dirac equation can be found and the number of pairs can be computed using the standard Bogoliubov method. This result is shown to agree with the semiclassical one in the appropriate limit. The solutions are also used to compute the expectation value of the induced current. Comparing t…
Instabilities of two dimensional (1+1) de Sitter space induced by interacting fields are studied. As for the case of flat Minkowski space, several interacting fermion models can be translated into free boson ones and vice versa. It is found that interacting fermion theories do not lead to any instabilities, while the interacting bosonic sine-Gordon model does lead to a breakdown of de Sitter symmetry and to the vanishing of the vacuum expectation value of the S matrix.
We study the one-loop radiative corrections for massless fermions in de Sitter space induced by a Yukawa coupling to a light, nearly minimally coupled scalar field. We show that the fermions acquire a mass. Next we construct the corresponding (nonlocal) effective fermionic action, which -- in contrast to the case of a massive Dirac fermion -- preserves chirality. Nevertheless, the resulting fermion dynamics is precisely that of a Dirac fermion with a mass proportional to the expansion rate. Our finding supports the view that an observer or a test particle responds to a scalar field in inflatio…
The propagators of the Dirac fermions are studied in the configuration representation on the expanding portion of the $(1+3)$-dimensional de Sitter spacetime considering a fixed vacuum of Bunch-Davies type. In this representation the method of Koksma and Prokopec [J. F. Koksma and T. Prokopec, Class. Quant. Grav. {\bf 26}, 125003 (2009)] is applied recovering thus the form of the propagators in the massive case but obtaining a new result for the left-handed massless fermions (neutrinos).
Fermion production in an external Coulomb field on de Sitter expanding universe is studied. The amplitude and probability of pair production in an external Coulomb field are computed and the cases of large/small values of the expansion factor comparatively with the particle mass are studied. We obtain from our calculations that the modulus of the momentum is no longer a conserved quantity. We find that in the de Sitter space there are probabilities for production processes where the helicity is no longer conserved. For a vanishing expansion factor we recover the Minkowski limit where the ampli…
The effect of the electric field on the creation of spin 1/2 particles from vacuum in the (1+1) dimensional de-Sitter space-time is studied. The Dirac equation with a constant electric field is solved by introducing an unitary transformation. Then the canonical method based on Bogoliubov transformation is applied to calculate the pair creation probability and the density of created particles both for positive or negative wave vector. By doing summation over all allowed states, the number of created particles per unit of time per unit of length and the imaginary part of the Schwinger effective …
Fermionic condensate is investigated in $(D+1)$-dimensional de Sitter spacetime by using the cutoff function regularization. In order to fix the renormalization ambiguity for massive fields an additional condition is imposed, requiring the condensate to vanish in the infinite mass limit. For large values of the field mass the condensate decays exponentially in odd dimensional spacetimes and follows a power law decay in even dimensional spacetimes. For a massless field the fermionic condensate vanishes for odd values of the spatial dimension $D$ and is nonzero for even $D$. Depending on the spa…
We show that an interacting spin-0 field on a de Sitter space background will break the underlying de Sitter symmetry. This is done first for a (1+1) de Sitter space where a boson-fermion correspondence permits us to solve certain interacting theories by transforming them into free ones of opposite statistics. A massless boson interacting by a sine-Gordon potential is shown to be equivalent to a free massive fermion with the mass depending on the de Sitter time thus breaking the symmetry explicitly. We then show that for larger dimensions and any boson potential, to one loop, an anomaly develo…
Fermionic condensate and the vacuum expectation values of the energy-momentum tensor are investigated for twisted and untwisted massive spinor fields in higher-dimensional de Sitter spacetime with toroidally compactified spatial dimensions. The expectation values are presented in the form of the sum of corresponding quantities in the uncompactified de Sitter spacetime and the parts induced by non-trivial topology. The latter are finite and the renormalization is needed for the first parts only. Closed formulae are derived for the renormalized fermionic vacuum densities in uncompactified odd-di…
The propagators of the Dirac fermions on the expanding portion of the (1+3)-dimensional de Sitter spacetime are considered as mode sums in momentum representation with a fixed vacuum of Bunch-Davies type. The principal result reported here is a new integral representation of the Feynman propagators of the massive and left-handed massless Dirac fields which can be used for deriving the Feynman rules of the de Sitter QED in Coulomb gauge or of an extended QFT.
The violation of the Bell inequality for Dirac fermions is investigated in the cosmological de Sitter spacetime, in the presence of background electromagnetic fields of constant strengths. The orthonormal Dirac mode functions are obtained and the relevant in-out squeezed state expansion in terms of the Bogoliubov coefficients are found. We focus on two scenarios here : strong electric field and heavy mass limits (with respect to the Hubble constant). Using the squeezed state expansion, we then demonstrate the Bell violations for the vacuum and some maximally entangled initial states. Even thou…
We consider 1/2 BPS excitations of AdS(5)xS(5) geometries in type IIB string theory that can be mapped into free fermion configurations according to the prescription of Lin, Lunin and Maldacena (LLM). It is shown that whenever the fermionic probability density exceeds one or is negative, closed timelike curves appear in the bulk. A violation of the Pauli exclusion principle in the phase space of the fermions is thus intimately related to causality violation in the dual geometries.
Fermion production by the electric field of a charge on de Sitter expanding universe is analyzed. The amplitude and probability of pair production are computed. We obtain from our calculations that the modulus of the momentum is no longer conserved and that there are probabilities for production processes where the helicity is no longer conserved. The rate of pair production in an electric field is found to be important in the early universe when the expansion factor was large comparatively with the particle mass.
Fermionic fields of higher spin in de Sitter space
King’s College London（伦敦国王学院）；KU Leuven（荷语鲁汶大学）；UMONS（蒙斯大学）；Instituto de Física de La Plata - CONICET（拉普拉塔物理研究所-阿根廷国家科学研究委员会）；Universidad Nacional de La Plata（拉普拉塔国立大学）
We point out that the transition probabilities used in a recent perturbative calculation of pair creation in an external magnetic field in the expanding de Sitter space with the $in$ and $out$ fermion states defined by the Bunch-Davies modes [C. Crucean et al., Phys. Rev. D 73 044019 (20016)] are gauge dependent quantities. We examine the gauge variations of these amplitudes assuming a decoupling of the interaction at infinite times, which allows to conclude that the source of the problem lies in the nonoscillatory behavior of the fermion current in the infinite future.
According to a corrected dispersion relation proposed in the study on string theory and quantum gravity theory, Rarita-Schwinger equation has been precisely modified, which results in a Rarita-Schwinger-Hamilton-Jacobi equation, and through which, the characteristics of arbitrary spin fermions quantum tunneling radiation from non-stationary Kerr-de Sitter black hole are researched. A series of accurately corrected physical quantities such as surface gravity, chemical potential, tunneling probability and Hawking temperature that describe the properties of the black hole are derived. This resear…
The fermionic projector state is a distinguished quasi-free state for the algebra of Dirac fields in a globally hyperbolic spacetime. We construct and analyze it in the four-dimensional de Sitter spacetime, both in the closed and in the flat slicing. In the latter case we show that the mass oscillation properties do not hold due to boundary effects. This is taken into account in a so-called mass decomposition. The involved fermionic signature operator defines a fermionic projector state. In the case of a closed slicing, we construct the fermionic signature operator and show that the ensuing st…
We investigate the fermionic condensate and the vacuum expectation values of the energy-momentum tensor for a massive spinor field in de Sitter spacetime with spatial topology $\mathrm{R}^{p}\times (\mathrm{S}^{1})^{q}$. Both cases of periodicity and antiperiodicity conditions along the compactified dimensions are considered. By using the Abel-Plana formula, the topological parts are explicitly extracted from the vacuum expectation values. In this way the renormalization is reduced to the renormalization procedure in uncompactified de Sitter spacetime. It is shown that in the uncompactified su…
The Casimir densities are investigated for a massive spinor field in de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions. The vacuum expectation value of the energy-momentum tensor is presented in the form of the sum of corresponding quantity in the uncompactified de Sitter spacetime and the part induced by the non-trivial topology. The latter is finite and the renormalization is needed for the first part only. The asymptotic behavior of the topological term is investigated in the early and late stages of the cosmological expansion. When the comoving leng…
Starting with a new theory of symmetries generated by isometries in field theories with spin, one finds the generators of the spinor representation in backgrounds with a given symmetry. In this manner one obtains a collection of conserved operators from which one can chose the complete sets of commuting operators defining quantum modes. In this framework, the quantum modes of the free Dirac field on de Sitter or anti-de Sitter spacetimes can be completely derived in static or moving charts. One presents the discrete quantum modes, in the central static charts of the anti-de Sitter spacetime, w…
In this work we show how the criterion of asymptotic Hamiltonian diagonalization originated in hybrid quantum cosmology serves to pick out a unique vacuum for the Dirac field in de Sitter, in the context of quantum field theory in curved spacetimes. This criterion is based on the dynamical definition of annihilation and creationlike variables for the fermionic field, which obey the linearized dynamics of a Hamiltonian that has been diagonalized in a way that is adapted to its local spatial structure. This leads to fermionic variables that possess a precise asymptotic expansion in the ultraviol…
The most prominent realization of gravity as a gauge theory similar to the gauge theories of the standard model comes from enlarging the gauge group from the Lorentz group to the de Sitter group. To regain ordinary Einstein-Cartan gravity the symmetry must be broken, which can be accomplished by known quasi-dynamic mechanisms. Motivated by symmetry breaking models in particle physics and condensed matter systems, we propose that the symmetry can naturally be broken by a homogenous and isotropic fermionic condensate of ordinary spinors. We demonstrate that the condensate is compatible with the …
We investigate the fermionic condensate and the vacuum expectation value of the energy-momentum tensor for a massive spinor field in the geometry of a straight cosmic string on background of de Sitter spacetime. By using the Abel-Plana summation formula, we explicitly extract form the expectation values the contribution associated with purely de Sitter space, remaining the expectation values induced by the cosmic string. The latter presents information about de Sitter gravity as well. Because the investigation of the fermionic quantum fluctuations in de Sitter space have been investigated in l…
In Vaidya-Bonner de Sitter Black hole space-time, the tunneling radiation characteristics of fermions and bosons are corrected by taking Lorentz symmetry breaking theory into account. The corresponding gamma matrices and ether-like field vectors of the black hole are constructed, then the new modified form of Dirac equation for the fermion with spin 1/2 and the new modified form of Klein-Gordon equation for boson in the curved space-time of the black hole are obtained. Through solving the two equations, new and corrected expressions of surface gravity, Hawking temperature and tunneling rate of…
The process of fermion production in the field of a magnetic dipole on a de Sitter expanding universe is analyzed. The amplitude and probability for production of massive fermions are obtained using the exact solution of the Dirac equation written in the momentum-helicity basis. We found that the most probable transitions are those that generate the fermion pair perpendicular to the direction of the magnetic field. The behavior of the probability is graphically studied for large/small values of the expansion factor, and a detailed analysis of the probability in terms of the angle between the m…
We study Hawking radiation as a phenomenon of tunneling through event horizons of charged torus-like as well as dilaton black holes involving cosmological constant based on Kerner and Mann's formulation. We obtain tunneling probabilities as well as Hawking's emission temperature of outgoing charged particles by applying the semiclassical WKB approximation to the general covariant Dirac equation. The graphical behavior of Hawking temperature and horizon radius is investigated. We find results consistent with those already given in literature.
We investigate the vacuum fermionic currents in the geometry of a compactified cosmic string on background of de Sitter spacetime. The currents are induced by magnetic fluxes running along the cosmic string and enclosed by the compact dimension. We show that the vacuum charge and the radial component of the current density vanish. By using the Abel-Plana summation formula, the azimuthal and axial currents are explicitly decomposed into two parts: the first one corresponds to the geometry of a straight cosmic string and the second one is induced by the compactification of the string along its a…
In this paper we study the problem of gauge invariance of the first order transition amplitudes in de Sitter QED in Coulomb gauge. We consider the gauge transformations which preserve the Coulomb gauge, that contain the gradient of the gauge function. The final results prove that the first order transition amplitudes do not change at a gradient transformation of the vector potential because the only allowed transformation is $Λ=0$. Our results suggest that the remarks made in the comment by Nicolaevici and Farkas {\em Phys. Rev. D} \textbf{95}, are not directly applicable to the results in our…
In this paper we investigate the fermionic condensate (FC) and the vacuum expectation value (VEV) of the energy-momentum tensor, associated with a massive fermionic field, induced by the presence of a cosmic string in the anti-de Sitter (AdS) spacetime. In order to develop this analysis we construct the complete set of normalized eigenfunctions in the corresponding spacetime. We consider a special case of boundary conditions on the AdS boundary, when the MIT bag boundary condition is imposed on the field operator at a finite distance from the boundary, which is then taken to zero. The FC and t…
In this paper we are discussing the problem of low-energy greybody factors for fermions emitted by a Schwarzschild-de Sitter black hole. In our study we are using the analytical methods proposed by Unruh some time ago for determining the greybody factors. We have found that at low energies the greybody factors are constant for a given total angular momentum (similar to what happens in the case of scalar particles reported before in the literature). Also our results are indicating an enhancement in the energy spectrum if one is increasing the value of the cosmological constant. These results ar…
The fermionic condensate and vacuum expectation value of the energy-momentum tensor, for a massive fermionic field on the background of anti-de Sitter spacetime, in the geometry of two parallel boundaries with bag boundary conditions, are investigated. Vacuum expectation values, expressed as series involving the eigenvalues of the radial quantum number, are neatly decomposed into boundary-free, single-boundary-induced, and second-boundary-induced parts, with the help of the generalized Abel-Plana summation formula. In this way, the renormalization procedure is very conveniently reduced to the …
Magnetic Catalysis and Fermion Mass Generation in de Sitter Spacetime
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Graduate School of Arts and Sciences, University of Tokyo（东京大学大学院人文社会系研究科）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心）
The main objective of this comment is to correct the density number of created fermions by an electric field in the (1+1) dimensional de-Sitter space-time communicated by V. M. Villalba in Phys. Rev. D 52, 3742 (1995). It is shown how the positive and negative energy solutions are connected to one another by the charge conjugation. Some concluding remarks are made.
We discuss the field quantisation of a free massive Dirac fermion in the two causally disconnected static patches of the de Sitter spacetime, by using mode functions that are normalisable on the cosmological event horizon. Using this, we compute the entanglement entropy of the vacuum state corresponding to these two regions, for a given fermionic mode. Further extensions of this result to more general static spherically symmetric and stationary axisymmetric spacetimes are discussed. For the stationary axisymmetric Kerr-de Sitter spacetime in particular, the variations of the entanglement entro…
It was recently shown that the Strong Cosmic Censorship conjecture might be violated for near-extremally-charged black holes in de Sitter space. Here, we extend our study to charged fermionic fields in the exterior of Reissner-Nordström-de Sitter black holes. We identify three families of modes; one related to the photon sphere, a second related to the de Sitter horizon and a third which dominates near extremality. We show that for near-extremally-charged black holes there is a critical fermionic charge below which Strong Cosmic Censorship may potentially be violated. Surprisingly enough, as o…
Vacuum expectation values (VEVs) of the current densities for charged scalar and Dirac spinor fields are investigated in (D+1)-dimensional de Sitter (dS) spacetime with toroidally compactified spatial dimensions. Along compact dimensions we impose quasiperiodicity conditions with arbitrary phases. In addition, the presence of a classical constant gauge field is assumed. The VEVs of the charge density and of the components for the current density along noncompact dimensions vanish. The gauge field leads to Aharonov-Bohm-like oscillations of the components along compact dimensions as functions o…
We report a non-trivial feature of the vacuum structure of free massive or massless Dirac fields in the hyperbolic de Sitter spacetime. Here we have two causally disconnected regions, say $R$ and $L$ separated by another region, $C$. We are interested in the field theory in $R\cup L$ to understand the long range quantum correlations between $R$ and $L$. There are local modes of the Dirac field having supports individually either in $R$ or $L$, as well as global modes found via analytically continuing the $R$ modes to $L$ and vice versa. However, we show that unlike the case of a scalar field, …
We study the quantum correlation and quantum communication channel of both free scalar and fermionic fields in de Sitter space, while the Planckian modification presented by the choice of a particular $α$-vacuum has been considered. We show that the occurrence of degradation of quantum entanglement between field modes for an inertial observer in curved space, due to the radiation associated with its cosmological horizon. Comparing with standard Bunch-Davies choice, the possible Planckian physics causes some extra decrement on the quantum correlation, which may provide the means to detect quant…
We construct the Wightman function for symmetric traceless tensors and Dirac fermions in dS$_{d+1}$ in a coordinate and index free formalism using a $d+2$ dimensional ambient space. We expand the embedding space formalism to cover spinor and tensor fields in any even or odd dimension. Our goal is to furnish a self-contained toolkit for the study of fields of arbitrary spin in de Sitter, with applications to cosmological perturbation theory. The construction for spinors is shown in extensive detail. Concise expressions for the action of isometry generators on generic bulk fields, the 2-point fu…
We study massive spinor fields in the geometry of a straight cosmic string in a de Sitter background. We find a hidden N=2 supersymmetry in the fermionic solutions of the equations of motion. We connect the zero mode solutions to the heat-kernel regularized Witten index of the supersymmetric algebra.
We compute the one loop graviton contribution to the self-energy of a very light fermion on a locally de Sitter background. This result can be used to study the effect that a small mass has on the propagation of fermions through the sea of infrared gravitons generated by inflation. We employ dimensional regularization and obtain a fully renormalized result by absorbing all divergences with BPHZ counterterms. An interesting technical aspect of this computation is the need for two noninvariant counterterms owing to the breaking of de Sitter invariance by our gauge condition.
