We consider the one loop effective action in four dimensional Euclidean space for a background chiral field coupled to a spinor field. It proves possible to find an exact expression for this action if the mass $m$ of the spinor vanishes. If $m$ does not vanish, one can make a perturbative expansion in powers of the axial field that contributes to the chiral field, while treating the contribution of the vector field exactly when it is a constant. The analogous problem in two dimensions is also discussed.
The strong-field limit for the 2-form potential on an M5-brane yields a conformal chiral 2-form electrodynamics in six dimensions, with gauge-invariant self-interactions but no adjustable coupling constant; the stress tensor is that of a null fluid. Lorentz invariance can be made manifest via an interpretation as a tensionless `space-filling M5-brane', or as a truncation of the infra-red dynamics of an M5-brane in AdS7 x S4.
In our previous article Phys. Rev. Lett. 127 (2021) 271601, we announced a novel 'democratic' Lagrangian formulation of general nonlinear electrodynamics in four dimensions that features electric and magnetic potentials on equal footing. Here, we give an expanded and more detailed account of this new formalism, and then proceed to push it significantly further by building the corresponding Lagrangian theories of higher form field interactions in arbitrary dimensions. Special attention is given to interactions of chiral 2k-forms in 4k+2 dimensions, with further details for 2-forms in 6 dimensio…
Non-linear electrodynamic models are re-assessed in this paper to pursue an investigation of the kinematics of the Compton effect in a magnetic background. Before considering specific models, we start off by presenting a general non-linear Lagrangian built up in terms of the most general Lorentz- and gauge-invariant combinations of the electric and magnetic fields. The extended Maxwell-like equations and the energy-momentum tensor conservation are presented and discussed in their generality. We next expand the fields around a uniform and time-independent electric and magnetic backgrounds up to…
Spontaneous chiral symmetry breaking in three dimensional ($d=3$) quantum electrodynamics is understood as annihilation of an infrared-stable fixed point that describes the large-N conformal phase by another unstable fixed point at a critical number of fermions $N=N_c$. We discuss the root of universality of $N_c$ in this picture, together with some features of the phase boundary in the $(d,N)$ plane. In particular, it is shown that as $d\rightarrow 4$, $N_c\rightarrow 0$ with a constant slope, our best estimate of which suggests that $N_c = 2.89$ in $d=3$.
Relations between the various formulations of nonlinear p-form electrodynamics with conformal-invariant weak-field and strong-field limits are clarified, with a focus on duality invariant (2n-1)-form electrodynamics and chiral 2n-form electrodynamics in Minkowski spacetime of dimension D=4n and D=4n+2, respectively. We exhibit a new family of chiral 2-form electrodynamics in D=6 for which these limits exhaust the possibilities for conformal invariance; the weak-field limit is related by dimensional reduction to the recently discovered ModMax generalisation of Maxwell's equations. For n>1 we sh…
Effects of Born-Infeld Electrodynamics on Chiral Symmetry Restoration and Meson Susceptibilities in Holographic QCD
Charmo Center for Research, Training, and Consultancy, Charmo University（查尔莫研究、培训与咨询中心，查尔莫大学）；Department of Physics, College of Science, Charmo University（查尔莫大学理学院物理系）
In the framework of Carrol-Field-Jackiw electrodynamics we calculate the spectral distribution of the Cherenkov radiation (CHR) produced by a charge moving at constant velocity in a chiral medium. We find zero, one or two Cherenkov angles according to the relation between the velocity of the particle and the refraction index of the medium.
In a quantum electrodynamics theory that is realized by critical scaling and anomalous dimensions, the action is not chiral invariant and there are no dynamical Goldstone or Higgs boson bound states. In the mean-field approximation to a chiral invariant four-fermion theory the associated mean-field sector action is not chiral invariant either and it also possesses no dynamical bound states, with Goldstone and Higgs bosons instead being generated by an accompanying four-fermion residual interaction. In this paper we show that if a critical scaling electrodynamics in which the dimension $d_θ$ of…
We analytically describe the properties of the s-wave holographic superconductor with the Exponential nonlinear electrodynamics in the Lifshitz black hole background in four-dimensions. Employing an assumption the scalar and gauge fields backreact on the background geometry, we calculate the critical temperature as well as the condensation operator. Based on Sturm-Liouville method, we show that the critical temperature decreases with increasing exponential nonlinear electrodynamics and Lifshitz dynamical exponent, z, indicating that condensation becomes difficult. Also we find that the effects…
The ground state of quantum chromodynamics in sufficiently strong external magnetic fields and at moderate baryon chemical potential is a chiral soliton lattice (CSL) of neutral pions. We investigate the interplay between the CSL structure and dynamical electromagnetic fields. Our main result is that in presence of the CSL background, the two physical photon polarizations and the neutral pion mix, giving rise to two gapped excitations and one gapless mode with a nonrelativistic dispersion relation. The nature of this mode depends on the direction of its propagation, interpolating between a cir…
The least action principle is established for the dynamics of a test particle in a dilaton-Maxwell background. These dynamics and background are invariant under the action of the dilatation transformation; explicit form of the corresponding generalization of the Lorentz force is established for the considered model. On a stationary background, we have found the integral of motion of the energy type. This integral is used to resolve the radial dynamics of test particles in a spherically symmetric electrostatic background.
Based on the motivation that some quantum gravity theories predicts the Lorentz Invariance Violation (LIV) around Planck-scale energy levels, this paper proposes a new formalism that addresses the possible effects of LIV in the electrodynamics. This formalism is capable of changing the usual electrodynamics through high derivative arbitrary mass dimension terms that includes a constant background field controlling the intensity of LIV in the models, producing modifications in the dispersion relations in a manner that is similar to the Myers-Pospelov approach. With this framework, it was possib…
We study the impact of Lorentz violating terms on a physical observable for both electrodynamics of chiral matter and an Abelian Higgs-like model in $3+1$ dimensions. Our calculation is done within the framework of the gauge-invariant, but path-dependent, variables formalism. Interestingly enough, for electrodynamics of chiral matter we obtain a logarithmic correction to the usual static Coulomb potential. Whereas for a Abelian Higgs model with a Lorentz-breaking term, our result displays new corrections to the Yukawa potential.
We explore the properties of a new Maxwell electrodynamics coupled to a Lorentz-violating background through the presence of higher-derivative terms. Physical implications of this alternative effective theory modified by Lorentz-violating operators of mass dimension-$5$ are considered, such as modified dispersion relations which exhibit the vacuum birefringence phenomenon. Subsequently, we analyze the energy-momentum tensor in the case we reproduce the Gambini-Pullin electrodynamics. We explicitly show that for a background time-like four-vector, $n^μ$, the equations of motion indeed reproduce…
We explore the effects of Power-Maxwell nonlinear electrodynamics on the properties of holographic s-wave paramagnetic-ferromagnetic phase transition in the background of Schwarzchild Anti-de Sitter (AdS) black hole. For this purpose, we introduce a massive 2-form coupled to the Power-Maxwell field. We perform the numerical shooting method in the probe limit by assuming the Power-Maxwell and the 2-form fields do not back react on the background geometry. We observe that increasing the strength of the power parameter causes the formation of magnetic moment in the black hole background harder an…
We investigate holographic s-wave superconductors with nonlinear arcsin-electrodynamics in the background of Schwarzschild anti-de Sitter black holes. The analytical Sturm-Liouville eigenvalue problem is explored and we assume that the scalar and electromagnetic fields do not influence on the background metric (the probe limit). The critical temperatures of phase transitions depending on the parameter of the model is obtained. We show that in our case the condensation formation becomes easier compared to Born-Infeld nonlinear electrodynamics. The critical exponent near the critical temperature…
We study higher-form global symmetries and a higher-group structure of a low-energy limit of $(3+1)$-dimensional axion electrodynamics in a gapped phase described by a topological action. We argue that the higher-form symmetries should have a semi-strict 4-group (3-crossed module) structure by consistency conditions of couplings of the topological action to background gauge fields for the higher-form symmetries. We find possible 't Hooft anomalies for the 4-group global symmetry, and discuss physical consequences.
Based on the Sturm-Liouville (SL) eigenvalue problem, we analytically study several properties of holographic $s$-wave superconductors with exponential nonlinear electrodynamics in the background of Schwarzschild anti-de Sitter (AdS) black holes. We assume the probe limit in which the scalar and gauge fields do not back react on the background metric. We show that for this system, one can still obtain an analytical relation between the critical temperature and the charge density. Interestingly enough, we find that logarithmic nonlinear electrodynamics decreases the critical temperature, $T_c$,…
It is shown how operator regularization can be used to obtain an expansion of the effective action in powers of derivatives of the background field. This is applied to massless scalar electrodynamics to find the one-loop corrections to the kinetic terms associated with both the scalar and vector fields in arbitrary gauge. This allows us to examine the radiatively induced masses arising in this model.
The aims of this letter are three-fold: First is to show that nonlinear generalizations of electrodynamics support various types of knotted solutions in vacuum. The solutions are universal in the sense that they do not depend on the specific Lagrangian density, at least if the latter gives rise to a well-posed theory. Second is to describe the interaction between probe waves and knotted background configurations. We show that the qualitative behaviour of this interaction may be described in terms of Robinson congruences, which appear explicitly in the causal structure of the theory. Finally, w…
Holographic s-wave superconductors in the framework of nonlinear Born - Infeld-type electrodynamics is investigated in the background of Schwarzschild anti-de Sitter black holes. As particular cases, at some model parameters, we obtain results for Born - Infeld and exponential electrodynamics. We explore the analytical Sturm-Liouville eigenvalue problem in the probe limit where the scalar and electromagnetic fields do not effect on the background metric. The critical temperatures of phase transitions and the order parameter are calculated which depend on the model parameters. We show that the …
In this paper, we investigate an electrodynamics in which the physical modes are coupled to a Lorentz-violating (LV) background by means of a higher-derivative term. We analyze the modes associated with the dispersion relations (DRs) obtained from the poles of the propagator. More specifically, we study Maxwell's electrodynamics modified by a LV operator of mass dimension 6. The modification has the form ${D_{βα}}\partial_σF^{σβ}\partial_λ F^{λα}$, i.e., it possesses two additional derivatives coupled to a \textit{CPT}-even tensor $D_{βα}$ that plays the role of the fixed background. We first …
