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Branislav Sazdovic

Publications and source records attributed to Branislav Sazdovic.

18 recordsLinked to original sources
arXiv2025

From Poincare Invariance to Gauge Theories: Yang-Mills and General Relativity

This article is founded on two fundamental principles: the principle field equations introduced in Refs. \cite{S, S1, S2} and the Fock-Ivanenko covariant derivatives \cite{FI, F}. The former yields the equations of motion for free fields of arbitrary spin and helicity. In the massless case, it also dictates that Lorentz transformations for tensor fields acquire an additional term, which takes the form of a gauge transformation \cite{W, S1}. The latter principle, the Fock-Ivanenko derivative, introduces interactions based on the intrinsic and Poincare groups. This framework allows us to recover a complete Yang-Mills theory, as well as general relativity in the connection-based formulations of Palatini and Ashtekar, both of which are theories with local gauge symmetries. While the standard approach begins with the symmetries of a matter action, we will instead derive dynamics directly from Poincare invariance. This perspective reveals that for free fields, Lorentz invariance induces the gauge symmetry of massless tensors. A proper definition of these gauge transformations, in turn, requires the covariant derivatives provided by the Fock-Ivanenko approach. Considering matter fields, we derive the interacting Dirac equation in the presence of Yang-Mills and gravitational fields from its free counterpart.

physics.gen-ph↗
arXiv2024

Rarita-Schwinger equation from principle equation for all spins

In previous two articles we postulated that field equations for arbitrary spin and helicity are Casimir eigenvalue equations. In massive case, from such principle equation, we derived spin-$0$ Klein-Gordon, spin-$\frac{1}{2}$ Dirac and spin-$1$ vector equations. In the present article we will derived spin-$\frac{3}{2}$ Rarita-Schwinger equation, which is nontrivial combination of vector and spinor case. We will also show that vector-spinor field contains two spin-$\frac{1}{2}$ Dirac fields.

hep-th↗
arXiv2022

Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field

In this paper we will consider noncommutativity that arises from bosonic T-dualization of type II superstring in presence of Ramond-Ramond (RR) field, which linearly depends on the bosonic coordinates $x^μ$. The derivative of the RR field $C^{αβ}_μ$ is infinitesimal. We will employ generalized Buscher procedure that can be applied to cases that have coordinate dependent background fields. Bosonic part of newly obtained T-dual theory is non-local. It is defined in non-geometric space spanned by Lagrange multipliers $y_μ$. We will apply generalized Buscher procedure once more on T-dual theory and prove that original theory can be salvaged. Finally, we will use T-dual transformation laws along with Poisson brackets of original theory to derive Poisson bracket structure of T-dual theory and nonassociativity relation. Noncommutativity parameter depends on the supercoordinates $x^μ$, $θ^α$ and $\barθ^α$, while nonassociativity parameter is a constant tensor containing infinitesimal $C^{αβ}_μ$.

hep-th↗
arXiv2021

Courant bracket as T-dual invariant extension of Lie bracket

We consider the symmetries of a closed bosonic string, starting with the general coordinate transformations. Their generator takes vector components $ξ^μ$ as its parameter and its Poisson bracket algebra gives rise to the Lie bracket of its parameters. We are going to extend this generator in order for it to be invariant upon self T-duality, i.e. T-duality realized in the same phase space. The new generator is a function of a $2D$ double symmetry parameter $Λ$, that is a direct sum of vector components $ξ^μ$, and 1-form components $λ_μ$. The Poisson bracket algebra of a new generator produces the Courant bracket in a same way that the algebra of the general coordinate transformations produces Lie bracket. In that sense, the Courant bracket is T-dual invariant extension of the Lie bracket. When the Kalb-Ramond field is introduced to the model, the generator governing both general coordinate and local gauge symmetries is constructed. It is no longer self T-dual and its algebra gives rise to the $B$-twisted Courant bracket, while in its self T-dual description, the relevant bracket becomes the $θ$-twisted Courant bracket. Next, we consider the T-duality and the symmetry parameters that depend on both the initial coordinates $x^μ$ and T-dual coordinates $y_μ$. The generator of these transformations is defined as an inner product in a double space and its algebra gives rise to the C-bracket.

hep-th↗
arXiv2018

Simultaneous T-dualization of type II pure spinor superstring

In this article we consider simultaneous T-dualization of type II superstring action in pure spinor formulation. Simultaneous T-dualization means that we make T-dualization at the same time along some subset of initial coordinates marked by $x^a$. The only imposed assumption stems from the applicability of the Buscher T-dualization procedure - background fields do not depend on dualized directions $x^a$. In this way we obtain the full form of the T-dual background fields and T-dual transformation laws. Because two chiral sectors transform differently, there are two sets of vielbeins and gamma matrices connected by the local Lorentz transformation. Its spinorial representation is the same as in the constant background case. We also found the full expression for T-dual dilaton field.

hep-th↗
arXiv2018

From geometry to non-geometry via T-duality

Reconsideration of the T-duality of the open string allows us to introduce some geometric features in non-geometric theories. First, we have found what symmetry is T-dual to the local gauge transformations. It includes transformations of background fields but does not include transformations of the coordinates. According to this we have introduced a new, up to now missing term, with additional gauge field $A^D_i$ (D denotes components with Dirichlet boundary conditions). It compensates non-fulfilment of the invariance under such transformations on the end-points of an open string, and the standard gauge field $A^N_a$ (N denotes components with Neumann boundary conditions) compensates non-fulfilment of the gauge invariance. Using a generalized procedure we will perform T-duality of vector fields linear in coordinates. We show that gauge fields $A^N_a$ and $A^D_i$ are T-dual to ${}^\star A_D^a$ and ${}^\star A_N^i$ respectively. We introduce the field strength of T-dual non-geometric theories as derivatives of T-dual gauge fields along both T-dual variable $y_μ$ and its double ${\tilde y}_μ$. This definition allows us to obtain gauge transformation of non-geometric theories which leaves the T-dual field strength invariant. Therefore, we introduce some new features of non-geometric theories where field strength has both antisymmetric and symmetric parts. This allows us to define new kinds of truly non-geometric theories.

hep-th↗
arXiv2017

Fermionic T-duality in fermionic double space

In this article we offer the interpretation of the fermionic T-duality of the type II superstring theory in double space. We generalize the idea of double space doubling the fermionic sector of the superspace. In such doubled space fermionic T-duality is represented as permutation of the fermionic coordinates $θ^α$ and $\barθ^α$ with the corresponding fermionic T-dual ones, $\vartheta_α$ and $\bar\vartheta_α$, respectively. Demanding that T-dual transformation law has the same form as inital one, we obtain the known form of the fermionic T-dual NS-R i R-R background fields. Fermionic T-dual NS-NS background fields are obtained under some assumptions. We conclude that only symmetric part of R-R field strength and symmetric part of its fermionic T-dual contribute to the fermionic T-duality transformation of dilaton field and analyze the dilaton field in fermionic double space. As a model we use the ghost free action of type II superstring in pure spinor formulation in approximation of constant background fields up to the quadratic terms.

hep-th↗
arXiv2015

T-duality as coordinates permutation in double space for weakly curved background

In the paper [1] we showed that in double space, where all initial coordinates $x^μ$ are doubled $x^μ\to y_μ$, the T-duality transformations can be performed by exchanging places of some coordinates $x^a$ and corresponding dual coordinates $y_a$. Here we generalize this result to the case of weakly curved background where in addition to the extended coordinate we will also transform extended argument of background fields with the same operator $\hat {\cal T}^a$. So, in the weakly curved background T-duality leads to the physically equivalent theory and complete set of T-duality transformations form the same group as in the flat background. Therefore, the double space represent all T-dual theories in unified manner.

hep-th↗
arXiv2015

Charge dependent relation between the masses of different generations and Neutrino masses

Despite the enormous achievements, the Standard model of Particle physics can not be consider as complete theory of fundamental interactions. Among other things, it can not describe the gravitational interaction and it depends on 19 parameters. The Standard model includes 12 fermions (matter elementary particles with spin $\frac{1}{2}$) which are divided in three generations, groups with same interactions but different masses. Each generation can be classified into two leptons (with electric charges $Q=-1$, electron-like and $Q=0$, neutrino) and two quarks (with electric charges $Q=-\frac{1}{3}$, down-type and $Q=\frac{2}{3}$, up-type). However, the understanding of the relationship between generations and ratio of masses of different generations are unknown. Here we show that there exists the simple relation between masses of different generations which depend only on the electric charges for $Q=-1,\, \, Q=-\frac{1}{3}$ and $Q=\frac{2}{3}$. It is in pretty good agreement with experimental data. Assuming that the same relation valid for $Q=0$, we are able to calculate neutrino masses. Therefore, our results could pave the way for further investigations beyond Standard model.

hep-ph↗
arXiv2013

Canonical approach to the closed string noncommutativity

We consider the closed string moving in the weakly curved background and its totally T-dualized background. Using T-duality transformation laws, we find the structure of the Poisson brackets in the T-dual space corresponding to the fundamental Poisson brackets in the original theory. From this structure we obtain that the commutative original theory is equivalent to the non-commutative T-dual theory, whose Poisson brackets are proportional to the background fluxes times winding and momenta numbers. The non-commutative theory of the present article is more nongeometrical then T-folds and in the case of three space-time dimensions corresponds to the nongeometric space-time with $R$-flux.

hep-th↗
arXiv2011

Fermionic T-duality and momenta noncommutativity

In this article we establish the relationship between fermionic T-duality and momenta noncommuativity. This is extension of known relation between bosonic T-duality and coordinate noncommutativity. The case of open string propagating in background of the type IIB superstring theory has been considered. We perform T-duality with respect to the fermionic variables instead to the bosonic ones. We also choose Dirichlet boundary conditions at the string endpoints, which lead to the momenta noncommutativity, instead Neumann ones which lead to the coordinates noncommutativity. Finally, we establish the main result of the article that momenta noncommutativity parameters are just fermionic T-dual fields.

hep-th↗
arXiv2010

$D5$-brane type I superstring background fields in terms of type IIB ones by canonical method and T-duality approach

We consider type IIB superstring theory with embedded $D5$-brane and choose boundary conditions which preserve half of the initial supersymmetry. In the canonical approach that we use, boundary conditions are treated as canonical constraints. The effective theory, obtained from the initial one on the solution of boundary conditions, has the form of the type I superstring theory with embedded $D5$-brane. We obtain the expressions for $D5$-brane background fields of type I theory in terms of the $D5$-brane background fields of type IIB theory. We show that beside known $Ω$ even fields, they contain squares of $Ω$ odd ones, where $Ω$ is world-sheet parity transformation, $Ω:σ\to -σ$. We relate result of this paper and the results of [1] using T-dualities along four directions orthogonal to $D5$-brane.

hep-th↗
arXiv2005

CT-duality as a local property of the world-sheet

In the present article, we study the local features of the world-sheet in the case when probe bosonic string moves in antisymmetric background field. We generalize the geometry of surfaces embedded in space-time to the case when the torsion is present. We define the mean extrinsic curvature for spaces with Minkowski signature and introduce the concept of mean torsion. Its orthogonal projection defines the dual mean extrinsic curvature. In this language, the field equation is just the equality of mean extrinsic curvature and extrinsic mean torsion, which we call CT-duality. To the world-sheet described by this relation we will refer as CT-dual surface.

hep-th↗
arXiv2004

Dilaton field induces commutative Dp-brane coordinate

It is well known that space-time coordinates and corresponding Dp-brane world-volume become non-commutative, if open string ends on Dp-brane with Neveu-Schwarz background field $B_{μν}$. In this paper we extend these considerations including the dilaton field $Φ$, linear in coordinates $x^μ$. In that case the conformal part of the world-sheet metric appears as new non-commutative variable and the coordinate in direction orthogonal to the hyper plane $Φ= const$, becomes commutative.

hep-th↗
arXiv2003

Bosonic string theory in background fields by canonical methods

We investigate classical dynamics of the bosonic string in the background metric, antisymmetric and dilaton fields. We use canonical methods to find Hamiltonian in terms of energy-momentum tensor components. The later are secondary constraints of the theory. Due to the presence of the dilaton field the Virasoro generators have nonlinear realization. We find that, in the curve space-time, opposite chirality currents do not commute. As a consequence of the two-dimensional general covariance, the energy-momentum tensor components satisfy two Virasoro algebras, even in the curve space-time. We obtain new gauge symmetry which acts on both world-sheet and space-time variables, and includes world-sheet Weyl transformation. We emphasize that background antisymmetric and dilaton fields are the origin of space-time torsion and space-time nonmetricity, respectively.

hep-th↗
arXiv2003

Torsion and nonmetricity in the stringy geometry

In the present article, we study the space-time geometry felt by probe bosonic string moving in antisymmetric and dilaton background fields. This space-time geometry we shall call the stringy geometry. In particular, the presence of the antisymmetric field leads to the space-time torsion, and the presence of the dilaton field leads to the space-time nonmetricity. We generalize the geometry of surfaces embedded in space-time to the case when torsion and nonmetricity are present. We define the mean extrinsic curvature for Minkowski signature and introduce the concept of mean torsion. Its orthogonal projection defines the dual mean extrinsic curvature. In this language, one field equation is just the equality of mean extrinsic curvature and dual mean extrinsic curvature, which we call self-duality relation. In the torsion and nonmetricity free case, the world-sheet is a minimal surface, specified by the requirement that mean extrinsic curvature vanishes. Generally, it is stringy self-dual (anti self-dual) surface. In the presence of the dilaton field, which breaks conformal invariance, the conformal factor which connects intrinsic and induced metrics, is determined as a function of the dilaton field itself. We also derive the integration measure for the space-time with stringy nonmetricity.

hep-th↗