Using irreducible and reducible representations of the Dirac matrices, we study the two-and four-... more Using irreducible and reducible representations of the Dirac matrices, we study the two-and four-component quantum mechanical supersymmetric (SUSY) theories for ultrarelativistic fermions in (2+1)-dimensions ("graphinos") in a background uniform magnetic field perpendicular to their plane of motion. We then consider ordinary and parity-violating mass terms and identify the former as a soft SUSY-breaking term and the later as the hard SUSY-breaking one.
We show that though conformal symmetry can be broken by the dilaton, such can happen without brea... more We show that though conformal symmetry can be broken by the dilaton, such can happen without breaking the conformal degeneracy patterns in the spectra. Our argumentation goes as follows: We departure from the gauge-gravity duality which predicts on the boundaries of the AdS5 geometry a conformal theory, associated with QCD at high temperatures, and consider S 1 × S 3 slicing. The inverse radius, R, of S 3 relates to the temperature of the deconfinement phase transition and has to satisfy,hc/R ≫ ΛQCD. On S 3 , whose isometry group is SO(4), we then focus on the eigenvalue problem of the conformal Laplacian there, given by 1 R 2 K 2 + 1 , with K 2 standing for the Casimir invariant of the so(4) algebra. This eigenvalue problem describes the spectrum of a scalar particle, to be associated with a qq system. Such a spectrum is characterized by a (K + 1) 2 -fold degeneracy of its levels, with K ∈ [0, ∞). We then break the conformal S 3 metric, ds 2 = dχ 2 + sin 2 χ(dθ 2 + sin 2 θdϕ 2 ) -in polar χ, θ, and azimuthal ϕ coordinates-according to, d s 2 = e −bχ (1 + b 2 )dχ 2 + sin 2 χ(dθ 2 + sin 2 θdϕ 2 ) , and attribute the symmetry breaking scale bh 2 c 2 /R 2 to the dilaton. Next we show that the above metric deformation is equivalent to a breaking of the conformal curvature of S 3 by a term proportional to b cot χ, and that the perturbed conformal Laplacian is equivalent to K 2 + cK , with cK a representation constant, and K 2 being again an so(4) Casimir invariant, but this time in a representation unitarily inequivalent to the 4D rotational one. As long as the spectra before and after the symmetry breaking happen to be determined each by eigenvalues of a Casimir invariant of an so(4), no matter whether or not in a representation that generates the orthogonal group SO(4) as a subgroup of the conformal group SO(2, 4), the degeneracy patterns remain unaltered though the conformal symmetry breaks at the level of the representation of the algebra. We fit the S 3 radius and theh 2 c 2 b/R 2 scale to the high-lying excitations in the spectra of the unflavored mesons, as reported by the Crystal Barrel collaboration, and observe the correct tendency of thehc/R = 373 MeV value to notably exceed ΛQCD. The size of the symmetry breaking scale is calculated ashc √ b/R = 673.7 MeV.
We study the gauge dependence of the fermion propagator in quenched QED3, with and without dynami... more We study the gauge dependence of the fermion propagator in quenched QED3, with and without dynamical symmetry breaking, in the light of its Landau-Khalatnikov-Fradkin transformation (LKFT). In the former case, starting with the massive bare propagator in the Landau gauge, we obtain non perturbative propagator in an arbitrary covariant gauge. Carrying out a perturbative expansion of this result, it yields correct wavefunction renormalization and the mass function up to the terms independent of the gauge parameter. Also, we obtain valuable information for the higher order perturbative expansion of the propagator. As for the case of dynamical chiral symmetry breaking, we start by approximating the numerical solution in Landau gauge in the rainbow approximation in terms of analytic functions. We then use LKFT to obtain the dynamically generated fermion propagator in an arbitrary covariant gauge. We find that the results obtained have all the required qualitative features. We also go beyond the rainbow and encounter similar desirable qualitative features.
We study the behavior of the dual quark condensate Σ1 in the Nambu-Jona-Lasinio (NJL) model and i... more We study the behavior of the dual quark condensate Σ1 in the Nambu-Jona-Lasinio (NJL) model and its nonlocal variant. In quantum chromodynmics Σ1 can be related to the breaking of the center symmetry and is therefore an (approximate) order parameter of confinement. The deconfinement transition is then signaled by a strong rise of Σ1 as a function of temperature. However, a similar behavior is also seen in the NJL model, which is known to have no confinement. Indeed, it was shown that in this model the rise of Σ1 is triggered by the chiral phase transition. In order to shed more light on this issue, we calculate Σ1 for several variants of the NJL model, some of which have been suggested to be confining. Switching between "confining" and "non-confining" models and parametrizations we find no qualitative difference in the behavior of Σ1, namely, it always rises in the region of the chiral phase transition. We conclude that without having established a relation to the center symmetry in a given model, Σ1 should not blindly be regarded as an order parameter of confinement.
We compute the thermo-magnetic correction to the quark-gluon vertex in the presence of a weak mag... more We compute the thermo-magnetic correction to the quark-gluon vertex in the presence of a weak magnetic field within the Hard Thermal Loop approximation. The vertex satisfies a QED-like Ward identity with the quark self-energy. The only vertex components that get modified are the longitudinal ones. The calculation provides a first principles result for the quark anomalous magnetic moment at high temperature in a weak magnetic field. We extract the effective thermo-magnetic quark-gluon coupling and show that this decreases as a function of the field strength. The result supports the idea that the properties of the effective quark-gluon coupling in the presence of a magnetic field are an important ingredient to understand the inverse magnetic catalysis phenomenon.
Monolayer graphite films, or graphene, have quasiparticle excitations that can be effectively des... more Monolayer graphite films, or graphene, have quasiparticle excitations that can be effectively described by (2+1)-dimensional quantum electrodynamics. Such a theory resembles more to quantum chromodynamics in some aspects, in particular, allowing for a non-trivial topological term in the gauge sector of the corresponding Lagrangian, the Chern-Simons term. In analogy to the chiral magnetic effect, proposed for quantum chromodynamics, we show that the presence of such topological gauge configurations associated to an external -in plane -magnetic field in a planar quantum elecrodynamical system, generates an electrical current along the magnetic field direction. This result is unexpected from the point of view of Maxwell equations and is uniquely due to the interaction of the gauge sector with the fermions.
Gauge covariance properties of the scalar propagator in spinless/scalar quantum electrodynamics (... more Gauge covariance properties of the scalar propagator in spinless/scalar quantum electrodynamics (SQED) are explored in the light of the corresponding Landau-Khalatnikov-Fradkin transformation (LKFT). These transformations are non perturbative in nature and describe how each Green function of the gauge theory changes under a variation of the gauge parameter. With a simple strategy, considering the scalar propagator at the tree level in Landau gauge, we derive a non perturbative expression for this propagator in an arbitrary covariant gauge and three as well as four space-time dimensions. Some relevant kinematical limits are discussed. Particularly, we compare our findings in the weak coupling regime with the direct one-loop calculation of the said propagator and observe perfect agreement up to an expected gauge independent term. We further notice that some of the coefficients of the all-order expansion for the propagator are fixed directly from the LKFT, a fact that makes this set of transformations appealing over ordinary perturbative calculations in gauge theories.
An interesting class of background field configurations in QED are the O(2)×O(3) symmetric fields... more An interesting class of background field configurations in QED are the O(2)×O(3) symmetric fields. Those backgrounds have some instanton-like properties and yield a one-loop effective action that is highly nontrivial but amenable to numerical calculation, for both scalar and spinor QED. Here we report on an application of the recently developed "partial-wavecutoff method" to the numerical analysis of both effective actions in the full mass range. In particular, at large mass we are able to match the asymptotic behavior of the physically renormalized effective action against the leading two mass levels of the inverse mass (or heat kernel) expansion. At small mass we obtain good numerical results even in the massless case for the appropriately (unphysically) renormalized effective action after the removal of the chiral anomaly term through a small radial cutoff factor. In particular, we show that the effective action after this removal remains finite in the massless limit, which also provides indirect support for M. Fry's hypothesis that the QED effective action in this limit is dominated by the chiral anomaly term.
Theories that support dynamical generation of a fermion mass gap are of widespread interest. The ... more Theories that support dynamical generation of a fermion mass gap are of widespread interest. The phenomenon is often studied via the Dyson-Schwinger equation (DSE) for the fermion self energy; i.e., the gap equation. When the rainbow truncation of that equation supports dynamical mass generation, it typically also possesses a countable infinity of simultaneous solutions for the dressed-fermion mass function, solutions which may be ordered by the number of zeros they exhibit. These features can be understood via the theory of nonlinear Hammerstein integral equations. Using QED3 as an example, we demonstrate the existence of a large class of gap equation truncations that possess solutions with damped oscillations. We suggest that there is a larger class, quite probably including the exact theory, which does not. The structure of the dressed-fermion-gauge-boson vertex is an important factor in deciding the issue.
Journal of Physics A: Mathematical and Theoretical, 2015
We carry out an explicit calculation of the vacuum polarization tensor for an effective low-energ... more We carry out an explicit calculation of the vacuum polarization tensor for an effective low-energy model of monolayer graphene in the presence of a weak magnetic field of intensity B perpendicularly aligned to the membrane. By expanding the quasiparticle propagator in the Schwinger proper time representation up to order (eB) 2 , where e is the unit charge, we find an explicitly transverse tensor, consistent with gauge invariance. Furthermore, assuming that graphene is radiated with monochromatic light of frequency ω along the external field direction, from the modified Maxwell's equations we derive the intensity of transmitted light and the angle of polarization rotation in terms of the longitudinal (σxx) and transverse (σxy) conductivities. Corrections to these quantities, both calculated and measured, are of order (eB) 2 /ω 4 . Our findings generalize and complement previously known results reported in literature regarding the light absorption problem in graphene from the experimental and theoretical points of view, with and without external magnetic fields.
Using irreducible and reducible representations of the Dirac matrices, we study the two-and four-... more Using irreducible and reducible representations of the Dirac matrices, we study the two-and four-component quantum mechanical supersymmetric (SUSY) theories for ultrarelativistic fermions in (2+1)-dimensions ("graphinos") in a background uniform magnetic field perpendicular to their plane of motion. We then consider ordinary and parity-violating mass terms and identify the former as a soft SUSY-breaking term and the later as the hard SUSY-breaking one.
We show that though conformal symmetry can be broken by the dilaton, such can happen without brea... more We show that though conformal symmetry can be broken by the dilaton, such can happen without breaking the conformal degeneracy patterns in the spectra. Our argumentation goes as follows: We departure from the gauge-gravity duality which predicts on the boundaries of the AdS5 geometry a conformal theory, associated with QCD at high temperatures, and consider S 1 × S 3 slicing. The inverse radius, R, of S 3 relates to the temperature of the deconfinement phase transition and has to satisfy,hc/R ≫ ΛQCD. On S 3 , whose isometry group is SO(4), we then focus on the eigenvalue problem of the conformal Laplacian there, given by 1 R 2 K 2 + 1 , with K 2 standing for the Casimir invariant of the so(4) algebra. This eigenvalue problem describes the spectrum of a scalar particle, to be associated with a qq system. Such a spectrum is characterized by a (K + 1) 2 -fold degeneracy of its levels, with K ∈ [0, ∞). We then break the conformal S 3 metric, ds 2 = dχ 2 + sin 2 χ(dθ 2 + sin 2 θdϕ 2 ) -in polar χ, θ, and azimuthal ϕ coordinates-according to, d s 2 = e −bχ (1 + b 2 )dχ 2 + sin 2 χ(dθ 2 + sin 2 θdϕ 2 ) , and attribute the symmetry breaking scale bh 2 c 2 /R 2 to the dilaton. Next we show that the above metric deformation is equivalent to a breaking of the conformal curvature of S 3 by a term proportional to b cot χ, and that the perturbed conformal Laplacian is equivalent to K 2 + cK , with cK a representation constant, and K 2 being again an so(4) Casimir invariant, but this time in a representation unitarily inequivalent to the 4D rotational one. As long as the spectra before and after the symmetry breaking happen to be determined each by eigenvalues of a Casimir invariant of an so(4), no matter whether or not in a representation that generates the orthogonal group SO(4) as a subgroup of the conformal group SO(2, 4), the degeneracy patterns remain unaltered though the conformal symmetry breaks at the level of the representation of the algebra. We fit the S 3 radius and theh 2 c 2 b/R 2 scale to the high-lying excitations in the spectra of the unflavored mesons, as reported by the Crystal Barrel collaboration, and observe the correct tendency of thehc/R = 373 MeV value to notably exceed ΛQCD. The size of the symmetry breaking scale is calculated ashc √ b/R = 673.7 MeV.
We study the gauge dependence of the fermion propagator in quenched QED3, with and without dynami... more We study the gauge dependence of the fermion propagator in quenched QED3, with and without dynamical symmetry breaking, in the light of its Landau-Khalatnikov-Fradkin transformation (LKFT). In the former case, starting with the massive bare propagator in the Landau gauge, we obtain non perturbative propagator in an arbitrary covariant gauge. Carrying out a perturbative expansion of this result, it yields correct wavefunction renormalization and the mass function up to the terms independent of the gauge parameter. Also, we obtain valuable information for the higher order perturbative expansion of the propagator. As for the case of dynamical chiral symmetry breaking, we start by approximating the numerical solution in Landau gauge in the rainbow approximation in terms of analytic functions. We then use LKFT to obtain the dynamically generated fermion propagator in an arbitrary covariant gauge. We find that the results obtained have all the required qualitative features. We also go beyond the rainbow and encounter similar desirable qualitative features.
We study the behavior of the dual quark condensate Σ1 in the Nambu-Jona-Lasinio (NJL) model and i... more We study the behavior of the dual quark condensate Σ1 in the Nambu-Jona-Lasinio (NJL) model and its nonlocal variant. In quantum chromodynmics Σ1 can be related to the breaking of the center symmetry and is therefore an (approximate) order parameter of confinement. The deconfinement transition is then signaled by a strong rise of Σ1 as a function of temperature. However, a similar behavior is also seen in the NJL model, which is known to have no confinement. Indeed, it was shown that in this model the rise of Σ1 is triggered by the chiral phase transition. In order to shed more light on this issue, we calculate Σ1 for several variants of the NJL model, some of which have been suggested to be confining. Switching between "confining" and "non-confining" models and parametrizations we find no qualitative difference in the behavior of Σ1, namely, it always rises in the region of the chiral phase transition. We conclude that without having established a relation to the center symmetry in a given model, Σ1 should not blindly be regarded as an order parameter of confinement.
We compute the thermo-magnetic correction to the quark-gluon vertex in the presence of a weak mag... more We compute the thermo-magnetic correction to the quark-gluon vertex in the presence of a weak magnetic field within the Hard Thermal Loop approximation. The vertex satisfies a QED-like Ward identity with the quark self-energy. The only vertex components that get modified are the longitudinal ones. The calculation provides a first principles result for the quark anomalous magnetic moment at high temperature in a weak magnetic field. We extract the effective thermo-magnetic quark-gluon coupling and show that this decreases as a function of the field strength. The result supports the idea that the properties of the effective quark-gluon coupling in the presence of a magnetic field are an important ingredient to understand the inverse magnetic catalysis phenomenon.
Monolayer graphite films, or graphene, have quasiparticle excitations that can be effectively des... more Monolayer graphite films, or graphene, have quasiparticle excitations that can be effectively described by (2+1)-dimensional quantum electrodynamics. Such a theory resembles more to quantum chromodynamics in some aspects, in particular, allowing for a non-trivial topological term in the gauge sector of the corresponding Lagrangian, the Chern-Simons term. In analogy to the chiral magnetic effect, proposed for quantum chromodynamics, we show that the presence of such topological gauge configurations associated to an external -in plane -magnetic field in a planar quantum elecrodynamical system, generates an electrical current along the magnetic field direction. This result is unexpected from the point of view of Maxwell equations and is uniquely due to the interaction of the gauge sector with the fermions.
Gauge covariance properties of the scalar propagator in spinless/scalar quantum electrodynamics (... more Gauge covariance properties of the scalar propagator in spinless/scalar quantum electrodynamics (SQED) are explored in the light of the corresponding Landau-Khalatnikov-Fradkin transformation (LKFT). These transformations are non perturbative in nature and describe how each Green function of the gauge theory changes under a variation of the gauge parameter. With a simple strategy, considering the scalar propagator at the tree level in Landau gauge, we derive a non perturbative expression for this propagator in an arbitrary covariant gauge and three as well as four space-time dimensions. Some relevant kinematical limits are discussed. Particularly, we compare our findings in the weak coupling regime with the direct one-loop calculation of the said propagator and observe perfect agreement up to an expected gauge independent term. We further notice that some of the coefficients of the all-order expansion for the propagator are fixed directly from the LKFT, a fact that makes this set of transformations appealing over ordinary perturbative calculations in gauge theories.
An interesting class of background field configurations in QED are the O(2)×O(3) symmetric fields... more An interesting class of background field configurations in QED are the O(2)×O(3) symmetric fields. Those backgrounds have some instanton-like properties and yield a one-loop effective action that is highly nontrivial but amenable to numerical calculation, for both scalar and spinor QED. Here we report on an application of the recently developed "partial-wavecutoff method" to the numerical analysis of both effective actions in the full mass range. In particular, at large mass we are able to match the asymptotic behavior of the physically renormalized effective action against the leading two mass levels of the inverse mass (or heat kernel) expansion. At small mass we obtain good numerical results even in the massless case for the appropriately (unphysically) renormalized effective action after the removal of the chiral anomaly term through a small radial cutoff factor. In particular, we show that the effective action after this removal remains finite in the massless limit, which also provides indirect support for M. Fry's hypothesis that the QED effective action in this limit is dominated by the chiral anomaly term.
Theories that support dynamical generation of a fermion mass gap are of widespread interest. The ... more Theories that support dynamical generation of a fermion mass gap are of widespread interest. The phenomenon is often studied via the Dyson-Schwinger equation (DSE) for the fermion self energy; i.e., the gap equation. When the rainbow truncation of that equation supports dynamical mass generation, it typically also possesses a countable infinity of simultaneous solutions for the dressed-fermion mass function, solutions which may be ordered by the number of zeros they exhibit. These features can be understood via the theory of nonlinear Hammerstein integral equations. Using QED3 as an example, we demonstrate the existence of a large class of gap equation truncations that possess solutions with damped oscillations. We suggest that there is a larger class, quite probably including the exact theory, which does not. The structure of the dressed-fermion-gauge-boson vertex is an important factor in deciding the issue.
Journal of Physics A: Mathematical and Theoretical, 2015
We carry out an explicit calculation of the vacuum polarization tensor for an effective low-energ... more We carry out an explicit calculation of the vacuum polarization tensor for an effective low-energy model of monolayer graphene in the presence of a weak magnetic field of intensity B perpendicularly aligned to the membrane. By expanding the quasiparticle propagator in the Schwinger proper time representation up to order (eB) 2 , where e is the unit charge, we find an explicitly transverse tensor, consistent with gauge invariance. Furthermore, assuming that graphene is radiated with monochromatic light of frequency ω along the external field direction, from the modified Maxwell's equations we derive the intensity of transmitted light and the angle of polarization rotation in terms of the longitudinal (σxx) and transverse (σxy) conductivities. Corrections to these quantities, both calculated and measured, are of order (eB) 2 /ω 4 . Our findings generalize and complement previously known results reported in literature regarding the light absorption problem in graphene from the experimental and theoretical points of view, with and without external magnetic fields.
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Papers by Alfredo Raya