arXiv subjects

Unai D. M. Sarraga

Publications and source records attributed to Unai D. M. Sarraga.

6 recordsLinked to original sources

arXiv2026

Towards a complete description of multiple D$p$-brane systems: Multiple D$0$ Story

In this thesis, we address the problem of constructing the complete supersymmetric description of systems of $N$ nearly coincident Dirichlet $p$-branes (multiple D$p$-brane or mD$p$). A particularly important result is a completely nonlinear action for the 10-dimensional dynamical system of nearly coincident multiple D$0$-branes (mD$0$) which is doubly supersymmetric, i.e. it is invariant under both spacetime (target superspace) supersymmetry and the worldline supersymmetry; the latter is a counterpart of the local fermionic $κ$-symmetry characteristic of a single D$0$-brane (Dirichlet superparticle). This problem is approached in flat superspace using the (spinor) moving frame formalism, which provides us with a geometric framework to the treatment of supersymmetric particles and extended objects ($p$-branes) in higher dimensions. Furthermore, we have initiated the quantization program aimed at development of a field theory of multiple D$0$-branes. This quantization in its complete form is expected to lead to a novel supersymmetric field theory formulated on a superspace extended by additional bosonic and fermionic matrix coordinates, whose development may offer significant insights into the deeper structure of String/M-theory.

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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

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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arXiv2024

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 $κ-$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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arXiv2023

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 $κ$-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 $κ$-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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