arXiv subjects

Igor Bandos

Publications and source records attributed to Igor Bandos.

At least 19 recordsLinked to original sources

arXiv2026

Tensionless limit of M5-brane and conformal symmetry of its bosonic body

We obtain a tensionless limit of the M-theory 5-brane action and discuss its properties. The consistency of this limit requires that the field strength of the worldvolume 2-form gauge field on the M5 brane worldvolume is non-degenerate and never vanishes. Also the induced $6d$ worldvolume metric of this theory is non-degenerate in contrast to conventional tensionless (null) $p$-branes. We find that the tensionless M5-brane action is invariant under a super-Weyl symmetry acting on the bulk supergeometry, while in the purely bosonic case the action is invariant under an 11D target-space conformal symmetry, a property which is characteristic for the tensionless bosonic branes. Upon imposing a static gauge, which fixes worldvolume diffeomorphisms, this 11D conformal symmetry becomes a deformed 6d worldovolume conformal symmetry whose action on the worldvolume coordinates involves field dependent terms. When the transversal fluctuations of the 5-brane in the bulk are zero, the model reduces to the conformal non-linear chiral 2-form electrodynamics considered earlier by Gibbons and West, and by Townsend.

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arXiv2026

Twistor approach to classical and quantum D0-brane

We develop the (super)twistor approach to D$0$-brane, which is the massive type IIA superparticle in ten dimensional spacetime. The basic variables are hexadecuplet of constrained $OSp(32|1)$ supertwistors similar but not identical to the ones which have been used for the description of 11D massless superparticle, also known as M$0$-brane. We show how the constrained supertwistor formulation is related to the spinor moving frame approach to D$0$-brane. We perform the quantization of the model by two different methods and discuss the relation of the results with the quantization of the spinor moving frame formulation of D$0$-brane. The quantum state spectrum describes the massive counterpart of the linearized type IIA supergravity.

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arXiv2026

Spinor moving frame, type II superparticle quantization, hidden $SU(8)$ symmetry of linearized 10D supergravity, and superamplitudes

A covariant quantization of type IIB and type IIA superparticles in their spinor moving frame formulation reveals the hidden $SU(8)$ symmetry of the linearized type II supergravity. It acts on auxiliary variables parameterizing the possible choices of complex structures which is necessary to arrive at the realization of the quantum state vector as an analytic on-shell superfield, the one-particle counterpart of analytical superamplitudes for type IIB and type IIA supergravity multiplets. The description of the type IIA supergraity multiplet in terms of an analytic on-shell superfield is then identical to that for type IIB supermultiplet; the difference is in spacetime interpretation. However, the definition of suitable auxiliary variables in type IIA case requires introduction of covariantly constant $SO(8)$ vector which can be related to T-duality transform between type IIA and type IIB superspaces. The simplest analytic IIB superamplitudes discussed in the literature thus also describe type IIA processes. We elaborate on these using the spinor moving frame (Lorentz harmonic) formalism and point out the restrictions on computation of many particle type IIA amplitudes in this approach. We also briefly discuss the initial steps towards type IIA superamplitudes involving, besides supergravity multiplets, also D$0$-branes (Dirichlet superparticles), which was recently quantized in the similar formalism, and indicate some problems which appear are to be solved to proceed on this way.

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arXiv2025

Quantum state spectrum and field theory of D$0$-brane

We quantize D$0$-brane, the simplest representative of the family of supersymmetric Dirichlet p-branes, in its spinor moving frame formulation and analyze its quantum state spectrum. Besides being a preparatory stage for quantization of the complete supersymmetric multiple D$0$-brane (mD$0$) model, which is presently known only in the frame of spinor moving frame formalism, this is interesting as its own: despite the covariant quantization of D=10 D$0$-brane was discussed before, its quantum state spectrum was not analyzed and its field theory, describing that, was not studied. We show that the quantum state vector of the D$0$-brane is described by an on-shell superfield that collects the fields of the massive counterpart of the linearized type IIA supergravity supermultiplet which can be obtained as massive Kaluza-Klein mode of the dimensional reduction of the eleven dimensional supergravity down to ten dimensions. In conclusion, we briefly discuss a spinor helicity formalism for D$0$-brane which can be used as one of the basic elements for developing type IIA string theory amplitude calculus based on multiparticle generalizations of the on-shell superfields.

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arXiv2024

Komar charge of N = 2 supergravity and its superspace generalization

We find the defining equations for a Killing vector and its superpartner (called the generalized Killing spinor) and use them to construct the generalized Komar superform of minimal N=2, d=4 supergravity using the superspace formulation. The superspace procedure presented here can be used for the construction of generalized Komar forms in more general supergravity theories. We also present the (more cumbersome) calculation of the generalized Komar 2-form and of the on-shell closed 2-form used to prove the first law in the component formalism, as an independent confirmation of our main result.

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arXiv2024

Noether-Wald and Komar charges in supergravity, fermions, and Killing supervectors in superspace

The supersymmetry properties of Killing vectors and spinors in supergravity theory can be clarified by relating them to Killing supervectors in the supergravity superspace. In the superspace approach it is manifest that supersymmetry 'mixes' a Killing vector with its fermionic spinor 'superpartner' and the Killing equations with the generalization of the Killing spinor equations. The latter reduces to the standard Killing spinor equation, albeit with a fermionic spinor, when the fermionic fields are set to zero. Using these supersymmetry transformations in the spacetime component approach, we construct a Noether-Wald charge of ${\cal N}=1$, $D=4$ supergravity with fermionic contributions which is diff-, Lorentz- and supersymmetry-invariant (up to a total derivative). The Killing supervector formalism for the maximal $D=11$ supergravity and some related issues are also discussed.

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arXiv2024

Towards field theory of multiple D0-branes. Hamiltonian mechanics and quantization of simplest 3D prototype of multiple D0-brane system

Recently we have constructed a completely supersymmetric nonlinear action possessing the properties expected from multiple D0-brane system. Its quantization should result in an interesting supersymmetric field theory in the (super)space with additional matrix coordinates which can provide an important insights in the study of String Theory. As a first stage toward this aim, in this paper we construct the Hamiltonian mechanics and perform covariant quantization of the simplest three dimensional counterpart of the ten dimensional multiple D0-brane model. We obtain a supersymmetric system of equations in super-spacetime enlarged by bosonic and fermionic matrix coordinates which appears as a result of such quantization and discuss some of its properties.

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arXiv2023

Brane Nucleation in Supersymmetric Models

This paper explores the process of vacuum decay in supersymmetric models related to flux compactifications. In particular, we describe these instabilities within supersymmetric Lagrangians for a single three-form multiplet. This multiplet combines scalar fields, representing the moduli fields in four dimensions, with 3-form fields that influence the potential for these moduli via the integer flux of their associated 4-form field strength. Furthermore, using supersymmetry as a guide we obtain the form of the couplings of these fields to the membranes that act as sources to the 3-form potentials. Adding small supersymmetry breaking terms to these Lagrangians one can obtain instanton solutions describing the decay of the vacua in these models by the formation of a membrane bubble. These instantons combine the usual Coleman-de Luccia and the Brown-Teitelboim formalisms in a single unified model. We study simple numerical examples of theories with and without gravity in this new framework and generalize known Euclidean methods to accomodate the simulataneous inclusion of scalar fields and charged membranes to these instanton solutions. Moreover, we show explicitly in these examples how one recovers the static supersymmetric solutions in the limiting case where the supersymmetry breaking terms vanish. In this limit, the bubble becomes infinite and flat and represents a hybrid between the usual supersymmetric domain walls of field theory models and the brane solutions interpolating between the supersymmetric vacua; a sort of dressed supermembrane BPS solution. Finally, we briefly comment on the implications of these solutions in cosmological models based on the String Theory Landscape where these type of 4d effective theories could be relevant in inflationary scenarios.

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arXiv2023

Noether-Wald charge in supergravity: the fermionic contribution

We study the invariance of N=1,d=4 supergravity solutions under diffeormophisms and show that, in order to obtain consistent conditions (``Killing equations'') invariant under local supersymmetry transformations, one has to perform supersymmetry transformations generated by the superpartner of the vector that generates standard diffeomorphisms, just as a superspace analysis indicates. Using these transformations, we construct a Noether-Wald charge of N=1,d=4 supergravity with fermionic contributions which is diff- Lorentz- and supersymmetry-invariant (up to a total derivative).

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arXiv2023

Trirefringence and the M5-brane

The Hamiltonian formulation for nonlinear chiral 2-form electrodynamics in six-dimensional Minkowski spacetime is used to show that small-amplitude plane-wave perturbations of a generic uniform constant `magnetic' background exhibit trirefringence: all three independent wave-polarisations have distinct dispersion relations. While two coincide for Lorentz invariant theories, all three coincide uniquely for the chiral 2-form theory on the worldvolume of the M5-brane of M-theory. We argue that this is because, in this M-theory context, the waves propagate in a planar M5-M2-M2 bound-state preserving 16 supersymmetries. We also show how our results imply analogous results for nonlinear electrodynamics in a Minkowski spacetime of five and four dimensions.

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arXiv2022

Properties of multiple D0-brane system: 11D origin, equations of motion and their solutions

We study the properties of 10D multiple D0-brane (mD0) system described by recently proposed complete supersymmetric and $\kappa$-symmetric nonlinear action which includes an arbitrary positive definite function ${\cal M}({\cal H})$ of the relative motion Hamiltonian ${\cal H}$. First we show how the action with a particular nonlinear ${\cal M}({\cal H})$ can be obtained from the action for 11D multiple M-wave (multiple M0-brane or mM0) system. Then we obtain the complete set of equations of motion of mD0 system with arbitrary positive definite ${\cal M}({\cal H})$, perform a convenient gauge fixing, solve the center of energy equations and establish an interesting correspondence between the relative motion mD0 equations and the equations of maximal supersymmetric SU(N) Yang-Mills theory (SYM). We show that this correspondence does not imply a gauge equivalence but establishes a relation between solutions of the system. In particular, it implies that all the supersymmetric solutions of mD0 equations in its relative motion part coincide with supersymmetric solutions of the SYM equations.

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arXiv2022

Complete nonlinear action for supersymmetric multiple D$0$-brane system

We present a complete nonlinear action for the dynamical system of nearly coincident multiple D$0$-branes (mD$0$) which possesses, besides manifest spacetime (target superspace) supersymmetry, also the worldline supersymmetry, a counterpart of the local fermionic $\kappa$-symmetry of single D$0$-brane (Dirichlet superparticle). The action contains an arbitrary non-vanishing function ${\cal M}({\cal H})$ of the relative motion Hamiltonian ${\cal H}$. The $D=10$ mD$0$ model with particular form of ${\cal M}({\cal H})$ can be obtained by dimensional reduction from the action of eleven-dimensional ($D=11$) multiple M-wave (mM$0$) system.

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arXiv2021

3D supersymmetric nonlinear multiple D$0$-brane action and 4D counterpart of multiple M-wave system

Found is the complete nonlinear action of multiple D$0$-brane system (mD$0$) in three dimensional type II superspace which is invariant under rigid $D=3$ ${\cal N}=2$ spacetime supersymmetry and under local worldline supersymmetry generalizing the $\kappa-$symmetry of single D$0$-brane action. We show that a particular representative of this family of actions can be obtained by dimensional reduction of the action of $D=4$ non-Abelian multiwaves (nAmW), the $D=4$ counterpart of 11D multiple M-wave (mM0) action, that we have also constructed in this paper. This reduction results in an action with is nonlinear due to the presence of a certain function ${\cal M}({\cal H})$ of the relative motion Hamiltonian ${\cal H}$, the counterpart of which enters the 4D nAmW action linearly. Curiously, the action possesses double supersymmetry also for an arbitrary function ${\cal M}({\cal H})$. In particular for ${\cal M}=\text{const}$ we find a dynamical system describing the sum of single D$0$ action and the action of 1d dimensional reduction of the $D=3$ ${\cal N}=2$ SYM coupled to the worldline supergravity induced by the embedding of the center of energy motion into the $D=3$ ${\cal N}=2$ superspace.

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arXiv2021

ModMax meets Susy

We give a prescription for 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.

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arXiv2020

On p-form gauge theories and their conformal limits

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 show that the chiral `strong-field' 2n-form electrodynamics is related by dimensional reduction to a new Sl(2;R)-duality invariant theory of (2n-1)-form electrodynamics.

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arXiv2020

A non-linear duality-invariant conformal extension of Maxwell's equations

All nonlinear extensions of the source-free Maxwell equations preserving both SO(2) electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalisation of Born-Infeld electrodynamics. The strong-field limit is the same as that found by Bialynicki-Birula from Born-Infeld theory but the weak-field limit is a new one-parameter extension of Maxwell electrodynamics, which is interacting but admits exact light-velocity plane-wave solutions of arbitrary polarisation. Small-amplitude waves on a constant uniform electromagnetic background exhibit birefringence, but one polarisation mode remains lightlike.

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arXiv2020

How $\mathcal N=1$, $D=4$ SYM domain walls look like

We review main features of the pure $\mathcal N=1$, $D=4$ SYM and its effective description by the Veneziano-Yankielowicz generalized sigma-model. We then indicate that the construction of BPS domain walls interpolating between different SYM vacua requires the presence of a dynamical membrane source. We will show how such a membrane is coupled to the SYM and present the explicit form of BPS domain walls which it creates in the Veneziano-Yankielowicz effective theory. In particular, we will describe 1/2 BPS domain wall configurations with $|k|\leq N/3$, where $k$ is the membrane charge that sets the "distance" between two distinct SUSY vacua.

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arXiv2019

On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring

We revisited the formalism of 11D polarized scattering equation by Geyer and Mason from the perspective of spinor frame approach and spinor moving frame formulation of the 11D ambitwistor superstring action. In particular, we rigorously obtain the equation for the spinor function on Riemann sphere from the supertwistor form of the ambitwistor superstring action, write its general solution and use it to derive the polarized scattering equation. We show that the expression used by Geyer and Mason to motivate their ansatz for the solution of polarized scattering equation can be obtained from our solution after a suitable gauge fixing. To this end we use the hidden gauge symmetries of the 11D ambitwistor superstring, including $SO(16)$, and the description of ambitwistor superstring as a dynamical system in an 11D superspace enlarged by bosonic directions parametrized by 517 tensorial central charge coordinates $Z^{\underline{\mu} \underline{\nu}}$ and $Z^{\underline{\mu}\underline{\nu}\underline{\rho}\underline{\sigma}\underline{\kappa}}$. We have also found the fermionic superpartner of the polarized scattering equation. This happens to be a differential equation in fermionic variables imposed on the superamplitude, rather then just a condition on the scattering data as the bosonic polarized scattering equation is. D=10 case is also discussed stressing the similarities and differences with 11D systems. The useful formulation of 10D ambitwistor superstring considers it as a dynamical system in superspace enlarged with 126 tensorial central charge coordinates $Z^{\mu\nu\rho\sigma\kappa}$.

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