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Mehmet Ozkan

Publications and source records attributed to Mehmet Ozkan.

35 records · Page 2Linked to original sources
arXiv2019

Three-Dimensional Extended Newtonian (Super)Gravity

We present a three dimensional non-relativistic model of gravity that is invariant under the central extension of the symmetry group that leaves the recently constructed Newtonian gravity action invariant. We show that the model arises from the contraction of a bi-metric model that is the sum of the Einstein gravity in Lorentzian and the Euclidean signatures. We also present the supersymmetric completion of this action which provides one of the very few examples of an action for non-relativistic supergravity.

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arXiv2019

Unitary Extension of Exotic Massive 3D Gravity from Bi-gravity

We obtain a new 3D gravity model from two copies of parity-odd Einstein-Cartan theories. Using Hamiltonian analysis, we demonstrate that the only local degrees of freedom are two massive spin-2 modes. Unitarity of the model in anti-de Sitter and Minkowski backgrounds can be satisfied for vast choices of the parameters without fine-tuning. The recent "exotic massive 3D gravity" model arises as a limiting case of the new model. We also show that there exist trajectories on the parameter space of the new model which cross the boundary between unitary and non-unitary regions. At the crossing point, one massive graviton decouples resulting in a unitary model with just one bulk degree of freedom but two positive central charges at odds with the usual expectation that the critical model has at least one vanishing central charge. Given the fact that a suitable non-relativistic version of bi-gravity has been used as an effective theory for gapped spin-2 fractional quantum Hall states, our model may have interesting applications in condensed matter physics.

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arXiv2019

Curvature squared invariants in six-dimensional ${\cal N} = (1,0)$ supergravity

We describe the supersymmetric completion of several curvature-squared invariants for ${\cal N}=(1,0)$ supergravity in six dimensions. The construction of the invariants is based on a close interplay between superconformal tensor calculus and recently developed superspace techniques to study general off-shell supergravity-matter couplings. In the case of minimal off-shell Poincaré supergravity based on the dilaton-Weyl multiplet coupled to a linear multiplet as a conformal compensator, we describe off-shell supersymmetric completions for all the three possible purely gravitational curvature-squared terms in six dimensions: Riemann, Ricci, and scalar curvature squared. A linear combination of these invariants describes the off-shell completion of the Gauss-Bonnet term, recently presented in arXiv:1706.09330. We study properties of the Einstein-Gauss-Bonnet supergravity, which plays a central role in the effective low-energy description of $α^\prime$-corrected string theory compactified to six dimensions, including a detailed analysis of the spectrum about the ${\rm AdS}_3\times {\rm S}^3$ solution. We also present a novel locally superconformal invariant based on a higher-derivative action for the linear multiplet. This invariant, which includes gravitational curvature-squared terms, can be defined both coupled to the standard-Weyl or dilaton-Weyl multiplet for conformal supergravity. In the first case, we show how the addition of this invariant to the supersymmetric Einstein-Hilbert term leads to a dynamically generated cosmological constant and non-supersymmetric (A)dS$_6$ solutions. In the dilaton-Weyl multiplet, the new off-shell invariant includes Ricci and scalar curvature-squared terms and possesses a nontrivial dependence on the dilaton field.

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arXiv2018

Scale Invariance in Newton-Cartan and Hořava-Lifshitz Gravity

We present a detailed analysis of the construction of $z=2$ and $z\neq2$ scale invariant Hořava-Lifshitz gravity. The construction procedure is based on the realization of Hořava-Lifshitz gravity as the dynamical Newton-Cartan geometry as well as a non-relativistic tensor calculus in the presence of the scale symmetry. An important consequence of this method is that it provides us the necessary mechanism to distinguish the local scale invariance from the local Schrödinger invariance. Based on this result we discuss the $z=2$ scale invariant Hořava-Lifshitz gravity and the symmetry enhancement to the full Schrödinger group.

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arXiv2017

Gauss-Bonnet supergravity in six dimensions

The supersymmetrization of curvature squared terms is important in the study of the low-energy limit of compactified superstrings where a distinguished role is played by the Gauss-Bonnet combination, which is ghost-free. In this letter, we construct its off-shell ${\cal N} = (1, 0)$ supersymmetrization in six dimensions for the first time. By studying this invariant together with the supersymmetric Einstein-Hilbert term we confirm and extend known results of the $α'$-corrected string theory compactified to six dimensions. Finally, we analyze the spectrum about the ${\rm AdS}_3\times{\rm S}^3$ solution.

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arXiv2017

Broken scale invariance, $α$-attractors and vector impurity

We show that if the $α$-attractor model is realized by the spontaneous breaking of the scale symmetry, then the stability and the dynamics of the vector field that gauges the scale symmetry can severely constrain the $α$-parameter as $5/6 < α< 1$ restricting the inflationary predictions in a very tiny region in the $n_s - r$ plane that are in great agreement with the latest Planck data. Although the different values of $α$ do not make a tangible difference for $n_s$ and $r$, they provide radically different scenarios for the post-inflationary dynamics which determines the standard BBN processes and the large scale isotropy of the universe.

astro-ph.CO↗
arXiv2016

Off-Shell N=2 Linear Multiplets in Five Dimensions

We present a superconformal tensor calculus for an arbitrary number of five dimensional N=2 linear multiplets. We also demonstrate how to construct higher derivative invariants and higher order supersymmetric off-diagonal models. Finally, we show the procedure required for the derivation of the supersymmetric completion of the non-Abelian $F^4$ action.

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arXiv2016

Galileons as the Scalar Analogue of General Relativity

We establish a correspondence between general relativity with diffeomorphism invariance and scalar field theories with Galilean invariance: notions such as the Levi-Civita connection and the Riemann tensor have a Galilean counterpart. This suggests Galilean theories as the unique nontrivial alternative to gauge theories (including general relativity). Moreover, it is shown that the requirement of first-order Palatini formalism uniquely determines the Galileon models with second-order field equations, similar to the Lovelock gravity theories. Possible extensions are discussed.

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arXiv2015

Supersymmetric Backgrounds and Black Holes in ${\cal N}=(1,1)$ Cosmological New Massive Supergravity

Using an off-shell Killing spinor analysis we perform a systematic investigation of the supersymmetric background and black hole solutions of the ${\cal N}=(1,1)$ Cosmological New Massive Gravity model. The solutions with a null Killing vector are the same pp-wave solutions that one finds in the ${\cal N}=1$ model but we find new solutions with a time-like Killing vector that are absent in the ${\cal N}=1$ case. An example of such a solution is a Lifshitz spacetime. We also consider the supersymmetry properties of the so-called rotating hairy BTZ black holes and logarithmic black holes in an $AdS_3$ background. Furthermore, we show that under certain assumptions there is no supersymmetric Lifshitz black hole solution.

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arXiv2015

Planck constraints on inflation in auxiliary vector modified $f(R)$ theories

We show that the universal $α$-attractor models of inflation can be realized by including an auxiliary vector field $A_μ$ for the Starobinsky model with the Lagrangian $f(R)=R+R^2/(6M^2)$. If the same procedure is applied to general modified $f(R)$ theories in which the Ricci scalar $R$ is replaced by $R+A_μ A^μ+β\nabla_μA^μ$ with constant $β$, we obtain the Brans-Dicke theory with a scalar potential and the Brans-Dicke parameter $ω_{\rm BD}=β^2/4$. We also place observational constraints on inflationary models based on auxiliary vector modified $f(R)$ theories from the latest Planck measurements of the Cosmic Microwave Background (CMB) anisotropies in both temperature and polarization. In the modified Starobinsky model, we find that the parameter $β$ is constrained to be $β<25$ (68\,\%\,confidence level) from the bounds of the scalar spectral index and the tensor-to-scalar ratio.

astro-ph.CO↗
arXiv2015

Universality Classes of Scale Invariant Inflation

We investigate the inflationary implications of extensions of Poincare symmetry. The simplest constructions with local scale invariance lead to universal predictions: the spectral index is $n_s = 1-2/N$, in excellent agreement with Planck data, while the tensor-to-scalar ratio is determined by a free parameter to $r = 12 α/ N^2$. For the special value $α=1$ one finds symmetry enhancement to the full conformal group. We show that these findings hold both for two-derivative scalar-tensor theories as well as higher-derivative gravity. Therefore scale invariance underlies a promising set of inflationary models.

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arXiv2015

Massive N=2 Supergravity in Three Dimensions

There exists two distinct off-shell ${\mathcal{N}}=2$ supergravities in three dimensions. They are also referred to as ${\mathcal{N}}=(1,1)$ and ${\mathcal{N}}=(2,0)$ supergravities, and they arise from the coupling of the Weyl multiplet to a compensating scalar or vector multiplet, respectively, followed by fixing of conformal symmetries. The ${\mathcal{N}} =(p,q)$ terminology refers to the underlying anti-de Sitter superalgebras $OSp(2,p) \oplus OSp(2,q)$ with $R$-symmetry group $SO(p) \times SO(q)$. We construct off-shell invariants of these theories up to fourth order in derivatives. As an application of these results, we determine the special combinations of the ${\mathcal{N}}=(1,1)$ invariants that admit anti-de Sitter vacuum solution about which there is a ghost-free massive spin-2 multiplet of propagating modes. We also show that the ${\mathcal{N}}=(2,0)$ invariants do not allow such possibility.

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arXiv2014

$R^n$ Extension of Starobinsky Model in Old Minimal Supergravity

We provide a succinct way to construct the supersymmetric completion of $R^n$ $(n\ge3)$ in components using superconformal formulation of old minimal supergravity. As a consequence, we obtain the polynomial $f(R)$ supergravity extending the supersymmetric Starobinsky model to any higher power of $R$. The supersymmetric vacua in polynomial $f(R)$ supergravity are studied. We also present the $R^n$ extended Minimal Volkov-Akulov-Starobinsky Model.

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arXiv2014

3D Born-Infeld Gravity and Supersymmetry

We construct the most general parity-even higher-derivative N=1 off-shell supergravity model in three dimensions with a maximum of six derivatives. Excluding terms quadratic in the curvature tensor with two explicit derivatives and requiring the absence of ghosts in a linearized approximation around an AdS_3 background, we find that there is a unique supersymmetric invariant which we call supersymmetric `cubic extended' New Massive Gravity. The purely gravitational part of this invariant is in agreement with an earlier analysis based upon the holographic c-theorem and coincides with an expansion of Born-Infeld gravity to the required order. Our results lead us to propose an expression for the bosonic part of off-shell N=1 Born-Infeld supergravity in three dimensions that is free of ghosts. We show that different truncations of a perturbative expansion of this expression gives rise to the bosonic part of (i) Einstein supergravity; (ii) supersymmetric New Massive Gravity and (iii) supersymmetric `cubic extended' New Massive Gravity.

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arXiv2013

All Off-Shell R^2 Invariants in Five Dimensional N=2 Supergravity

We construct supersymmetric completions of various curvature squared terms in five dimensional supergravity with eight supercharges. Adopting the dilaton Weyl multiplet, we obtain the minimal off-shell supersymmetric Ricci scalar squared as well as all vector multiplets coupled curvature squared invariants. Since the minimal off-shell supersymmetric Riemann tensor squared and Gauss-Bonnet combination in the dilaton Weyl multiplet have been obtained before, both the minimal off-shell and the vector multiplets coupled curvature squared invariants in the dilation Weyl multiplet are complete. We also constructed an off-shell Ricci scalar squared invariant utilizing the standard Weyl multiplet. The supersymmetric Ricci scalar squared in the standard Weyl multiplet is coupled to n number of vector multiplets by construction, and it deforms the very special geometry. We found that in the supersymmetric AdS_5 vacuum, the very special geometry defined on the moduli space is modified in a simple way. Finally, we study the magnetic string and electric black hole solutions in the presence of supersymmetric Ricci scalar squared.

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arXiv2013

An off-shell formulation for internally gauged D=5, N=2 supergravity from superconformal methods

We use the superconformal method to construct a new formulation for pure off-shell D=5, N=2 Poincaré supergravity and present its internal gauging. The main difference between the traditional formulation and our new formulation is the choice of the Dilaton Weyl Multiplet as the background Weyl Multiplet and the choice of a Linear compensating Multiplet. We do not introduce an external vector multiplet to gauge the theory, but instead use the internal vector of the Dilaton Weyl Multiplet. We show that the corresponding on-shell theory is Einstein-Maxwell supergravity. We believe that this gauging method can be applied in more complicated scenarios such as the inclusion of off-shell higher derivative invariants.

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