scholarly journals ModMax meets Susy

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Igor Bandos ◽  
Kurt Lechner ◽  
Dmitri Sorokin ◽  
Paul K. Townsend
Keyword(s):  
Conformal Invariance ◽  
Lagrangian Density ◽  
Nonlinear Electrodynamics ◽  
Convexity Condition ◽  
Higher Derivative ◽  
Maxwell Electrodynamics ◽  
The One

Abstract We give a prescription for $$ \mathcal{N} $$ N = 1 supersymmetrization of any (four-dimensional) nonlinear electrodynamics theory with a Lagrangian density satisfying a convexity condition that we relate to semi-classical unitarity. We apply it to the one-parameter ModMax extension of Maxwell electrodynamics that preserves both electromagnetic duality and conformal invariance, and its Born-Infeld-like generalization, proving that duality invariance is preserved. We also establish superconformal invariance of the superModMax theory by showing that its coupling to supergravity is super-Weyl invariant. The higher-derivative photino-field interactions that appear in any supersymmetric nonlinear electrodynamics theory are removed by an invertible nonlinear superfield redefinition.

scholarly journals Separation of variables in AdS/CFT: functional approach for the fishnet CFT

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Andrea Cavaglià ◽  
Nikolay Gromov ◽  
Fedor Levkovich-Maslyuk
Keyword(s):  
Integrable Systems ◽  
Density Operator ◽  
Numerical Evaluation ◽  
Lagrangian Density ◽  
Separation Of Variables ◽  
Functional Approach ◽  
Quantum Integrable Systems ◽  
Arbitrary State ◽  
Nontrivial Coupling ◽  
The One

Abstract The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV) remains unknown in $$ \mathcal{N} $$ N = 4 SYM and similar models, even though it is widely believed they are integrable. In this paper we initiate the SoV approach for observables with nontrivial coupling dependence in a close cousin of $$ \mathcal{N} $$ N = 4 SYM — the fishnet 4D CFT. We develop the functional SoV formalism in this theory, which allows us to compute non-perturbatively some nontrivial observables in a form suitable for numerical evaluation. We present some applications of these methods. In particular, we discuss the possible SoV structure of the one-point correlators in presence of a defect, and write down a SoV-type expression for diagonal OPE coefficients involving an arbitrary state and the Lagrangian density operator. We believe that many of the findings of this paper can be applied in the $$ \mathcal{N} $$ N = 4 SYM case, as we speculate in the last part of the article.

scholarly journals Supergraph calculation of one-loop divergences in higher-derivative 6D SYM theory

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
B. S. Merzlikin ◽  
K. V. Stepanyantz
Keyword(s):  
Effective Action ◽  
A Priori ◽  
Coupling Constant ◽  
Harmonic Superspace ◽  
Classical Action ◽  
Higher Derivative ◽  
Component Approach ◽  
Dimensionless Coupling ◽  
The One ◽  
Dimensionless Coupling Constant

Abstract We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of renormalizable 6D, $$ \mathcal{N} $$ N = (1, 0) supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and $$ \mathcal{N} $$ N = (1, 0) supersymmetric way. We exploit the regularization by dimensional reduction, in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant β-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed a priori. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations.

Planar generalized electrodynamics for one-loop amplitude in the Heisenberg picture

2021 ◽  
pp. 2150142
Author(s):  
David Montenegro ◽  
B. M. Pimentel
Keyword(s):  
Gauge Invariance ◽  
Quantum Electrodynamics ◽  
Mass Shell ◽  
Natural Extension ◽  
Quantum Model ◽  
Covariant Quantization ◽  
Heisenberg Picture ◽  
Maxwell Electrodynamics ◽  
Loop Amplitude ◽  
The One

We examine the generalized quantum electrodynamics as a natural extension of the Maxwell electrodynamics to cure the one-loop divergence. We establish a precise scenario to discuss the underlying features between photon and fermion where the perturbative Maxwell electrodynamics fails. Our quantum model combines stability, unitarity, and gauge invariance as the central properties. To interpret the quantum fluctuations without suffering from the physical conflicts proved by Haag’s theorem, we construct the covariant quantization in the Heisenberg picture instead of the Interaction one. Furthermore, we discuss the absence of anomalous magnetic moment and mass-shell singularity.

scholarly journals Emergent GUP from modified Hawking radiation in Einstein–NED theory

2020 ◽  
Vol 98 (8) ◽  
pp. 801-809
Author(s):  
S. Hamid Mehdipour
Keyword(s):  
Hawking Radiation ◽  
Lagrangian Density ◽  
General Procedure ◽  
Generalized Uncertainty Principle ◽  
Energy Condition ◽  
Intrinsic Property ◽  
Hawking Temperature ◽  
Nonlinear Electrodynamics ◽  
Uncertainty Relations ◽  
Schwarzschild Solution

We present a general procedure for constructing exact black hole (BH) solutions with a magnetic charge in the context of nonlinear electrodynamics (NED) theory as well as in the coherent state approach to noncommutative geometry (NCG). In this framework, the Lagrangian density for a noncommutative Hayward BH is obtained and the weak energy condition is satisfied. The noncommutative Hayward solution depends on two kind of charges, without which the Schwarzschild solution is applicable. Moreover, to find a link between the BH evaporation and uncertainty relations, we may calculate the Hawking temperature and find the effect of the Lagrangian density of BHs on the Hawking radiation. Therefore, a generalized uncertainty principle (GUP) emerges from the modified Hawking temperature in Einstein–NED theory. The origin of this GUP is the combined influence of a nonlinear magnetic source and an intrinsic property of the manifold associated with a fictitious charge. Finally, we find that there is an upper bound on the Lagrangian uncertainty of the BHs that is caused by the NED field and (or) the fictitious charge.

scholarly journals Lorentz-violating effects in three-dimensional QED

2014 ◽  
Vol 29 (22) ◽  
pp. 1450112 ◽  
Author(s):  
R. Bufalo
Keyword(s):  
Quantum Electrodynamics ◽  
Lagrangian Density ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Space Time ◽  
Nonminimal Coupling ◽  
Coupling Term ◽  
Interaction Terms ◽  
Higher Derivative ◽  
Dimensional Space Time

Inspired in discussions presented lately regarding Lorentz-violating interaction terms in B. Charneski, M. Gomes, R. V. Maluf and A. J. da Silva, Phys. Rev. D86, 045003 (2012); R. Casana, M. M. Ferreira Jr., R. V. Maluf and F. E. P. dos Santos, Phys. Lett. B726, 815 (2013); R. Casana, M. M. Ferreira Jr., E. Passos, F. E. P. dos Santos and E. O. Silva, Phys. Rev. D87, 047701 (2013), we propose here a slightly different version for the coupling term. We will consider a modified quantum electrodynamics with violation of Lorentz symmetry defined in a (2+1)-dimensional space–time. We define the Lagrangian density with a Lorentz-violating interaction, where the space–time dimensionality is explicitly taken into account in its definition. The work encompasses an analysis of this model at both zero and finite-temperature, where very interesting features are known to occur due to the space–time dimensionality. With that in mind, we expect that the space–time dimensionality may provide new insights about the radiative generation of higher-derivative terms into the action, implying in a new Lorentz-violating electrodynamics, as well the nonminimal coupling may provide interesting implications on the thermodynamical quantities.

scholarly journals RADIATIVE DAMPING AND FUNCTIONAL DIFFERENTIAL EQUATIONS

2011 ◽  
Vol 26 (35) ◽  
pp. 2627-2638 ◽  
Author(s):  
SUVRAT RAJU ◽  
C. K. RAJU
Keyword(s):  
Differential Equations ◽  
Body Problem ◽  
Equations Of Motion ◽  
Functional Differential Equations ◽  
General Technique ◽  
Covariant Model ◽  
Maxwell Electrodynamics ◽  
Functional Differential ◽  
The One ◽  
Radiative Damping

We propose a general technique to solve the classical many-body problem with radiative damping. We modify the short-distance structure of Maxwell electrodynamics. This allows us to avoid runaway solutions as if we had a covariant model of extended particles. The resulting equations of motion are functional differential equations (FDEs) rather than ordinary differential equations (ODEs). Using recently developed numerical techniques for stiff, retarded FDEs, we solve these equations for the one-body central force problem with radiative damping. Our results indicate that locally the magnitude of radiation damping may be well approximated by the standard third-order expression but the global properties of our solutions are dramatically different. We comment on the two-body problem and applications to quantum field theory and quantum mechanics.

An analytical investigation of the cylindrical capacitor in the framework of a two-parameter modification of Born–Infeld electrodynamics

2018 ◽  
Vol 15 (07) ◽  
pp. 1850118 ◽  
Author(s):  
F. Fathi ◽  
S. K. Moayedi
Keyword(s):  
Electric Fields ◽  
Weak Field ◽  
Analytical Investigation ◽  
Nonlinear Electrodynamics ◽  
Self Energy ◽  
Maxwell Electrodynamics ◽  
Parameter Modification ◽  
Cylindrical Capacitor ◽  
Electrostatic Potential Energy ◽  
Two Parameter

Iacopini and Zavattini [Vacuum polarization effects in the [Formula: see text] atom and the Born–Infeld electromagnetic theory, Nuovo Cimento B 78 (1983) 38–52] proposed a [Formula: see text]-two-parameter modification of Born–Infeld electrodynamics, in which the classical self-energy for an electron takes a finite value for [Formula: see text]. In this paper, we want to study a cylindrical capacitor from the viewpoint of Iacopini–Zavattini nonlinear electrodynamics analytically. The capacitance, the electrostatic potential energy, and the potential difference between the plates of a cylindrical capacitor are calculated in the framework of Iacopini–Zavattini electrodynamics for two specific values of [Formula: see text] and [Formula: see text]. The study of the behavior of a nonlinear cylindrical capacitor in the weak electric fields shows that our results are compatible with the correspondence principle, i.e. we recover the results of Maxwell electrodynamics in the weak field regime. Finally, the invariance of Iacopini–Zavattini nonlinear electrodynamics under the duality transformation is investigated.

scholarly journals EXPONENTIAL LAGRANGIAN FOR THE GRAVITATIONAL FIELD AND THE PROBLEM OF VACUUM ENERGY

2008 ◽  
Vol 23 (08) ◽  
pp. 1286-1289 ◽  
Author(s):  
ORCHIDEA MARIA LECIAN ◽  
GIOVANNI MONTANI
Keyword(s):  
Gravitational Field ◽  
Cosmological Constant ◽  
Lagrangian Density ◽  
Vacuum Energy ◽  
The Other ◽  
Present Value ◽  
Other Hand ◽  
Free Parameters ◽  
The One

We will analyze two particular features of an exponential gravitational Lagrangian. On the one hand, while this choice of the Lagrangian density allows for two free parameters, only one scale, the cosmological constant, arises as fundamental when the proper Einsteinian limit is to be recovered. On the other hand, the vacuum energy arising from f(R) theories such that f(0) ≠ 0 needs a cancellation mechanism, by which the present value of the cosmological constant can be recast.

ON THE HIGHER-DERIVATIVE CONFORMAL GRAVITY

1989 ◽  
Vol 04 (10) ◽  
pp. 893-899 ◽  
Author(s):  
HYUN KUK SHIN ◽  
PONG YOUL PAC ◽  
HAE WON LEE
Keyword(s):  
Heat Kernel ◽  
Fourth Order ◽  
Kernel Method ◽  
Gravity Theory ◽  
Conformal Anomaly ◽  
Conformal Gravity ◽  
Higher Derivative ◽  
The One

We consider the fourth-order conformal gravity theory. The quantization of the theory is presented in detail. We also calculate, using the heat kernel method, the one-loop divergence and conformal anomaly.

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