arXiv subjects

Arash Ranjbar

Publications and source records attributed to Arash Ranjbar.

15 recordsLinked to original sources

arXiv2024

Tensor global symmetries and the Stueckelberg mechanism for tensor fields

We investigate the concept of tensor global symmetries, featuring conserved currents of mixed symmetry and higher spin Nambu-Goldstone bosons. We develop a Stueckelberg mechanism for mixed symmetry tensor fields at the linearized level, focusing on the massive graviton, the massive $(2,1)$ Curtright field and the massive $(2,2)$ field. Counting degrees of freedom, we identify the set of fields that necessarily appear in the gauge invariant Stueckelberg action in each case. These fields transform under shift symmetries and they are a vector and a scalar in the first case, a graviton, a Kalb-Ramond field and a vector in the second case and a Curtright field and a graviton in the third case. The analysis results in gauge invariant and fully conserved currents of mixed symmetry for the corresponding gauge theories, which are linked to their tensor global symmetries and they can be minimally coupled to suitable background fields. Viewing the graviton and the Kalb-Ramond field as Nambu-Goldstone bosons for constant symmetric and antisymmetric shift symmetries, we use a nonminimal coupling to uncover a 't Hooft anomaly in linearized gravity.

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arXiv2023

Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited

We reconsider the Hamiltonian reduction of the action for three dimensional AdS supergravity and $W_3$ higher spin AdS gravity in the Chern-Simons formulation under asymptotically anti-de Sitter boundary conditions. We show that the reduction gives two copies of chiral bosons on the boundary. In particular, we take into account the holonomy of the Chern-Simons connection which manifests itself as zero mode of the momentum of the boundary chiral boson. We provide an equivalent formulation of the boundary action which we claim to be the geometric action on symplectic leaves of a (super-)Virasoro or a higher spin $W_N$ Poisson manifold in the case of supergravity or higher spin gravity respectively, where the intersection of leaves (given in terms of leaves representatives) can be identified as the bulk holonomy. This concludes the extension to non-linear algebras where the notion of coadjoint representation is not well-defined. The boundary Hamiltonian depends on a choice of boundary conditions and is equivalent to the Schwarzian action for corresponding Brown-Henneaux boundary conditions. We make this connection explicit in the extended supersymmetric case. Moreover, we discuss the geometric action in the case of $W_3$ AdS$_3$ gravity in both $\mathfrak{sl}(3)$ highest weight representations based on principal and diagonal $\mathfrak{sl}(2)$ embeddings.

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arXiv2022

Duality, generalized global symmetries and jet space isometries

We revisit universal features of duality in linear and nonlinear relativistic scalar and Abelian 1-form theories with single or multiple fields, which exhibit ordinary or generalized global symmetries. We show that such global symmetries can be interpreted as generalized Killing isometries on a suitable, possibly graded, target space of fields or its jet space when the theory contains higher derivatives. This is realized via a generalized sigma model perspective motivated from the fact that higher spin particles can be Nambu-Goldstone bosons of spontaneously broken generalized global symmetries. We work out in detail the 2D examples of a compact scalar and the massless Heisenberg pion fireball model and the 4D examples of Maxwell, Born-Infeld and ModMax electrodynamics. In all cases we identify the 't Hooft anomaly that obstructs the simultaneous gauging of both global symmetries and confirm the anomaly matching under duality. These results readily generalize to higher gauge theories for p-forms. For multifield theories we discuss the transformation of couplings under duality as two sets of Buscher rules for even or odd differential forms.

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arXiv2020

Duality and higher Buscher rules in p-form gauge theory and linearized gravity

We perform an in-depth analysis of the transformation rules under duality for couplings of theories containing multiple scalars, $p$-form gauge fields, linearized gravitons or $(p,1)$ mixed symmetry tensors. Following a similar reasoning to the derivation of the Buscher rules for string background fields under T-duality, we show that the couplings for all classes of aforementioned multi-field theories transform according to one of two sets of duality rules. These sets comprise the ordinary Buscher rules and their higher counterpart; this is a generic feature of multi-field theories in spacetime dimensions where the field strength and its dual are of the same degree. Our analysis takes into account topological theta terms and generalized $B$-fields, whose behavior under duality is carefully tracked. For a 1-form or a graviton in 4D, this reduces to the inversion of the complexified coupling or generalized metric under electric/magnetic duality. Moreover, we write down an action for linearized gravity in the presence of $θ$-term from which we obtain previously suggested on-shell duality and double duality relations. This also provides an explanation for the origin of theta in the gravitational duality relations as a specific additional sector of the linearized gravity action.

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arXiv2020

Asymptotic dynamics of AdS$_3$ gravity with two asymptotic regions

The asymptotic dynamics of AdS$_3$ gravity with two asymptotically anti-de Sitter regions is investigated, paying due attention to the zero modes, i.e., holonomies along non-contractible circles and their canonically conjugates. This situation covers the eternal black hole solution. We derive how the holonomies around the non-contractible circles couple the fields on the two different boundaries and show that their canonically conjugate variables, needed for a consistent dynamical description of the holonomies, can be related to Wilson lines joining the boundaries. The action reduces to the sum of four free chiral actions, one for each boundary and each chirality, with additional non-trivial couplings to the zero modes which are explicitly written. While the Gauss decomposition of the $SL(2,\mathbb{R})$ group elements is useful in order to treat hyperbolic holonomies, the Iwasawa decomposition turns out to be more convenient in order to deal with elliptic and parabolic holonomies. The connection with the geometric action is also made explicit. Although our paper deals with the specific example of two asymptotically anti-de Sitter regions, most of our global considerations on holonomies and radial Wilson lines qualitatively apply whenever there are multiple boundaries, independently of the form that the boundary conditions explicitly take there.

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arXiv2019

Flat $\mathfrak{so}(p,q)$-Connections for Manifolds of Non-Euclidean Signature

The well-known fact that $S^1$, $S^3$ and $S^7$ are parallelizable manifolds admitting flat connections is revisited. The role of torsion in the construction of those flat connections is made explicit, and the possibilities allowed by different metric signatures are examined. A necessary condition for parallelizability in an open region is that the torsion tensor must be covariantly constant. This property can be used to obtain a relation between a torsion-free and flat connections. Our treatment covers Riemannian and pseudo-Riemannian (non-Euclidean signature) hyperbolic manifolds of dimensions three and seven. Apart from the spherical cases mentioned above, the explicit flat $\mathfrak{so}(p,q)$ connections with $p+q=3,7$ are constructed for the coset manifolds $SO(p,q+1)/SO(p,q)$ or $SO(p+1,q)/SO(p,q)$.

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arXiv2018

String Dualities and Gaugings of Supergravity

This thesis is devoted to various questions connected with duality. It is composed of two parts. The first part discusses some aspects of timelike T-duality. We explore the possibility of compactification of supergravity theories with various signatures (low energy limit of $M$-theories which are dual under timelike T-dualities) on parallelizable internal seven dimensional (pseudo-)spheres. We show that, beside the standard theory, only one of the dual theories known as $M'$-theory can admit such a solution. The effective four dimensional theory is non-supersymmetric and due to the presence of torsion the symmetry of seven dimensional (pseudo-)sphere breaks down to $Spin(3,4)$. In the second part, in an attempt to have a systematic discussion of gaugings in supergravity, we show the isomorphism between the space of local deformations of the appropriate zero coupling limit of the embedding tensor Lagrangian and that of the second-order scalar-vector Lagrangian, describing the bosonic sector of supergravity ignoring gravity, in a chosen duality frame determined by embedding tensors. We analyze the BV-BRST deformation of a class of scalar-vector coupled Lagrangians, which contains supergravity Lagrangians as examples, and find a set of constraints that guarantee the consistency of the deformations of the Lagrangians. We show in principle that for a large class of theories considered in this thesis, the only deformations are those of the Yang-Mills type associated with a subgroup of the rigid symmetries.

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arXiv2018

Deformations of vector-scalar models

Abelian vector fields non-minimally coupled to uncharged scalar fields arise in many contexts. We investigate here through algebraic methods their consistent deformations ("gaugings"), i.e., the deformations that preserve the number (but not necessarily the form or the algebra) of the gauge symmetries. Infinitesimal consistent deformations are given by the BRST cohomology classes at ghost number zero. We parametrize explicitly these classes in terms of various types of global symmetries and corresponding Noether currents through the characteristic cohomology related to antifields and equations of motion. The analysis applies to all ghost numbers and not just ghost number zero. We also provide a systematic discussion of the linear and quadratic constraints on these parameters that follow from higher-order consistency. Our work is relevant to the gaugings of extended supergravities.

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arXiv2017

A note on "gaugings" in four spacetime dimensions and electric-magnetic duality

The variety of consistent "gauging" deformations of supergravity theories in four dimensions depends on the choice of Lagrangian formulation. One important goal is to get the most general deformations without making hidden assumptions. Ignoring supersymmetry we consider in this paper $n_v$ abelian vector potentials in four spacetime dimensions with non-minimal kinetic coupling to $n_s$ uncharged (possibly nonlinear) scalar fields. As in the case of extended supergravities, one model may possess different formulations related by $Sp(2n_v,\mathbb{R})$. The symplectic group mixes its electric and magnetic potentials. The model admits a global duality symmetry subgroup $G$ which acts also on the scalars. We recall first how the general second order Lagrangian, its local deformations and those of its abelian gauge group will depend on the choice of $2n_v$ directions (choice of "Darboux frame"). We start from a general frame defined by the symplectic transformation relating it to a fixed"reference" one. Combinations of symplectic matrix coefficients appear then as constant parameters in the second order Lagrangians. Another gauging method uses an "embedding tensor" that characterizes the realization of the gauge group via the global duality group. It involves additional 2-form gauge fields. A suitable zero charge limit of this realization has abelian gauge group and the "gauging" can be viewed as a consistent deformation of that limit. We show that the two methods applied to the corresponding ungauged models have equivalent local deformations -- and more generally, have isomorphic local BRST cohomology at all ghost numbers. We finally consider manifestly duality invariant first order actions with abelian gauge group. We point out that obstructions to non-abelian deformations of the Yang-Mills type exhibited in a previous work remain present when couplings to scalar fields are included.

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arXiv2017

Timelike duality, $M'$-theory and an exotic form of the Englert solution

Through timelike dualities, one can generate exotic versions of $M$-theory with different spacetime signatures. These are the $M^*$-theory with signature $(9,2,-)$, the $M'$-theory, with signature $(6,5,+)$ and the theories with reversed signatures $(1,10, -)$, $(2,9, +)$ and $(5,6, -)$. In $(s,t, \pm)$, $s$ is the number of space directions, $t$ the number of time directions, and $\pm$ refers to the sign of the kinetic term of the $3$ form. The only irreducible pseudo-riemannian manifolds admitting absolute parallelism are, besides Lie groups, the seven-sphere $S^7 \equiv SO(8)/SO(7)$ and its pseudo-riemannian version $S^{3,4} \equiv SO(4,4)/SO(3,4)$. [There is also the complexification $SO(8,\mathbb{C})/SO(7, \mathbb{C})$, but it is of dimension too high for our considerations.] The seven-sphere $S^7\equiv S^{7,0}$ has been found to play an important role in $11$-dimensional supergravity, both through the Freund-Rubin solution and the Englert solution that uses its remarkable parallelizability to turn on non trivial internal fluxes. The spacetime manifold is in both cases $AdS_4 \times S^7$. We show that $S^{3,4}$ enjoys a similar role in $M'$-theory and construct the exotic form $AdS_4 \times S^{3,4}$ of the Englert solution, with non zero internal fluxes turned on. There is no analogous solution in $M^*$-theory.

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arXiv2016

Conformal field theories from deformations of theories with $W_n$ symmetry

We construct a set of non-rational conformal field theories that consist of deformations of Toda field theory for sl(n). Besides conformal invariance, the theories still enjoy a remnant infinite-dimensional affine symmetry. The case n=3 is used to illustrate this phenomenon, together with further deformations that yield enhanced Kac-Moody symmetry algebras. For generic n we compute N-point correlation functions on the Riemann sphere and show that these can be expressed in terms of sl(n) Toda field theory correlation functions.

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arXiv2015

Screening Stringy Horizons

It has been argued recently that string theory effects qualitatively modify the effective black hole geometry experienced by modes with radial momentum of order $1/\sqrt{α'}$. At tree level, these $α'$-effects can be explicitly worked out in two-dimensional string theory, and have a natural explanation in the T-dual description as coming from the integration of the zero-mode of the linear dilaton, what yields a contribution that affects the scattering phase-shift in a peculiar manner. It has also been argued that the phase-shift modification has its origin in a region of the moduli space that does not belong to the exterior black hole geometry, leading to the conclusion that at high energy the physics of the problem is better described by the dual model. Here, we elaborate on this argument. We consider the contribution of worldsheet instantons in the 2D Euclidean black hole sigma-model and study its influence on the phase-shift at high energy.

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arXiv2015

Trapped surfaces and nature of singularities in Lyra's geometry

Motivated by the geometrical interpretation of Brans-Dicke (BD) scalar field which may also act as a torsion potential in Lyra geometry, we study the effects of spacetime torsion on the dynamics of a collapsing massive star. Taking the interior spacetime as the FLRW metric and the matter content as spherically symmetric, homogeneous perfect fluid with the equation of state (EoS) $p=wρ$, we show that the collapse ends in a spacetime singularity which is of the strong curvature type in the sense of Tipler. Whether the trapped surfaces form during the dynamical evolution of the collapse depends on the torsion parameter, related to the BD coupling parameter, and the EoS subject to the conditions on physical reasonableness of the collapse configuration. Hence, the space of torsion and EoS parameters is divided into two portions, one for which the collapse process leads to the formation of apparent horizon and the other for which the apparent horizon is failed to form in the interior region. The nature of the singularity is examined from the exterior perspective, by searching for the existence of radial null geodesics reaching the faraway observers. Moreover, it is found that the effects of a dynamical torsion can be transferred to the outside region of the collapsing star, making the exterior region dynamic.

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arXiv2014

Einstein-Cartan gravitational collapse of a homogeneous Weyssenhoff fluid

We consider the gravitational collapse of a spherically symmetric homogeneous matter distribution consisting of a Weyssenhoff fluid in the presence of a negative cosmological constant. Our aim is to investigate the effects of torsion and spin averaged terms on the final outcome of the collapse. For a specific interior spacetime setup, namely the homogeneous and isotropic FLRW metric, we obtain two classes of solutions to the field equations where depending on the relation between spin source parameters, $(i)$ the collapse procedure culminates in a spacetime singularity or $(ii)$ it is replaced by a non-singular bounce. We show that, under certain conditions, for a specific subset of the former solutions, the formation of trapped surfaces is prevented and thus the resulted singularity could be naked. The curvature singularity that forms could be gravitationally strong in the sense of Tipler. Our numerical analysis for the latter solutions shows that the collapsing dynamical process experiences four phases, so that two of which occur at the pre-bounce and the other two at post-bounce regimes. We further observe that there can be found a minimum radius for the apparent horizon curve, such that the main outcome of which is that there exists an upper bound for the size of the collapsing body, below which no horizon forms throughout the whole scenario.

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arXiv2012

Asymptotically Lifshitz Brane-World Black Holes

We study the gravity dual of a Lifshitz field theory in the context of a RSII brane-world scenario, taking into account the effects of the extra dimension through the contribution of the electric part of the Weyl tensor. We study the thermodynamical behavior of such asymptotically Lifshitz black holes. It is shown that the entropy imposes the critical exponent $z$ to be bounded from above. This maximum value of $z$ corresponds to a positive infinite entropy as long as the temperature is kept positive. The stability and phase transition for different spatial topologies are also discussed.

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