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Mehmet Ozkan

Publications and source records attributed to Mehmet Ozkan.

At least 19 recordsLinked to original sources
arXiv2026

Chern-Simons-like formulation of 3D MMG-like massive gravity models

We investigate the Chern-Simons-like formulation of 3D MMG-like massive gravity models that are "third-way consistent". Building on previous work on exotic massive gravities, we analyze a class of MMG-like theories characterized by a specific parity structure and an auxiliary field hierarchy. Focusing on the simplest non-trivial case, we solve the full set of field equations, determine the AdS background solutions, compute the central charges of the dual CFT, and perform a linearized analysis to obtain the mass spectrum. Along the chiral line, the linearized mass operator develops a rank-2 Jordan block, signaling logarithmic behavior of massive modes in the dual two-dimensional CFT. At a special degenerate point, this structure is enhanced to a rank-3 Jordan block, giving rise to two logarithmic partners and an ultra-logarithmic sector in the boundary theory.

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arXiv2026

A Twisted Origin for Magnetic Carroll Supersymmetry

Magnetic Carrollian theories provide a natural setting for field theories with nontrivial spatial structure in the Carroll limit and are therefore natural candidates for flat-space holographic duals. Embedding such boundary theories into a top-down framework requires a consistent supersymmetric completion and, in particular, an understanding of the relativistic origin of magnetic Carroll supersymmetry. We show that the relevant magnetic Carroll algebra does not arise from a naive contraction of the standard relativistic supersymmetry algebra, but instead descends from a twisted relativistic parent. As an explicit realization, we construct a three-dimensional ${\mathcal{N}}=2$ magnetic Carroll algebra together with a supersymmetric vector-multiplet action. Unlike the electric case, the resulting structure contains one supercharge that squares to spatial momentum, a mixed anticommutator that yields the Hamiltonian, and a nilpotent second supercharge. We further show that its conformal extension coincides with the global part of a supersymmetric BMS$_4$ algebra. This provides a physical and relativistic origin for a super-BMS$_4$ structure recently identified by complementary algebraic methods, and strengthens the case for magnetic Carroll theories in flat-space holography and supersymmetric asymptotic symmetries.

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arXiv2025

Supersymmetric Carroll Galileons in Three Dimensions

We present the first example of an interacting Carroll supersymmetric field theory with both temporal and spatial derivatives, belonging to the Galileon class, where the non-linear field equation remains second-order in derivative. To achieve this, we introduce two novel tools. First, we demonstrate that the two-dimensional Galilei/Carroll duality can be extended to higher dimensions, and includes the supersymmetry, by expressing the generators in a spinor basis. We then show that Carroll superalgebras are naturally connected to Euclidean, rather than Poincaré, superalgebras. Using the real multiplet of the three-dimensional N $=1$ Euclidean supersymmetry, we construct the scalar multiplet for N $=2$ Carroll supersymmetry and develop a tensor calculus to realize the aforementioned model. These results offer new insights into the structure of genuine higher-dimensional Carroll field theories and Carroll supersymmetry. While these tools are utilized to build a specific model, we anticipate that they possess broader applications in Carrollian physics.

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arXiv2025

On five-dimensional curvature squared supergravity and holography

In this work, we report the recent progress in obtaining new curvature-squared invariants in 5D, N=1 gauged minimal supergravity. We exhibit the structure of various composite multiplets that are pivotal in the construction. We also present the form of the gauged Riemann-squared and Gauss-Bonnet superinvariants in a dilaton-Weyl multiplet. As a first application of the new curvature squared invariants, we compute their corrections to holographic central charges and the Euclidean action of supersymmetric charged rotating black holes, exhibiting exact matching between the gravity and CFT results.

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arXiv2024

Chern-Simons-Like Formulation of Exotic Massive 3D Gravity Models

We investigate the Chern-Simons-like formulation of exotic general massive gravity models within the framework of third-way to three-dimensional gravity. We classify our construction into two main approaches: one using torsional cosmological Einstein and exotic massive gravity equations, and the other a torsion-free approach. The former approach, while mathematically appealing, precludes the construction of critical exotic models where the central charges vanish. In contrast, the latter approach has a wider parameter space and allows for the construction of critical models. An explicit example of an exotic general model is provided to illustrate both methods. Our methodology represents the first step towards establishing the most general Chern-Simons-like formulation of third-way to three-dimensional gravity, which would enable the study of identifying its bulk/boundary unitary sector.

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arXiv2024

Higher Derivative Supergravities in Diverse Dimensions

We survey on-shell and off-shell higher derivative supergravities in dimensions $1\le D\le 11$. Various approaches to their construction, including the Noether procedure, (harmonic) superspace, superform method, superconformal tensor calculus, $S$-matrix and dimensional reduction, are summarized. Primarily the bosonic parts of the invariants and the supertransformations of the fermionic fields are provided. The process of going on-shell, solutions to the Killing spinor equations, typical supersymmetric solutions, and the role of duality symmetries in the context of $R^4, D^4 R^4$ and $D^6 R^4$ invariants are reviewed.

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arXiv2024

Carrollian Supersymmetry and SYK-like models

This work challenges the conventional notion that in spacetime dimension higher than one, a supersymmetric Lagrangian invariably consists of purely bosonic terms, purely fermionic terms, as well as boson-fermion mixing terms. By recasting a relativistic Lagrangian in terms of its non-relativistic and ultra-relativistic sectors, we reveal that an ultra-relativistic (Carrollian) supersymmetric Lagrangian can exist without a purely bosonic contribution. Based on this result, we demonstrate a link between higher-dimensional Carrollian and (0+1)-dimensional quantum mechanical models, yielding higher-order extensions of supersymmetric SYK models in which purely bosonic higher order terms are absent. Given that supersymmetry plays an essential role in improving the quantum behavior and solubility, our findings may lead to interesting applications in non-AdS holography.

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arXiv2023

All Gauged Curvature Squared Supergravities in Five Dimensions

We present a complete basis to study gauged curvature-squared supergravity in five dimensions. We replace the conventional ungauged Riemann-squared action with a new Log-invariant, offering a comprehensive framework for all gauged curvature-squared supergravities. Our findings address long-standing challenges and have implications for precision tests in the AdS/CFT correspondence.

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arXiv2023

Carrollian Origin of Spacetime Subsystem Symmetry

We propose that models with spacetime dipole symmetry are connected to Lorentz invariant models via the Carrollian limit. In this way, a recently proposed model with spacetime dipole symmetry was readily reproduced together with its conserved charges. We then couple this model to a dynamical Abelian gauge field and Carroll gravity. Our procedure can be applied in arbitrary dimensions and paves the way to construct new models with spacetime dipole symmetry.

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arXiv2022

Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity

We present a method of contraction that can be applied to re-construct the recent extended non-relativistic and ultra-relativistic algebras as well as corresponding action principles. The methodology involves the use of multiple copies of Poincaré algebra. Consequently, the contraction defines non-relativistic or ultra-relativistic limits of multimetric theories of gravity. In particular, we show that the non-relativistic scaling limit of bi-metric gravity corresponds to the recent formulation of an action principle for Newtonian gravity with a constant background mass density.

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arXiv2022

Inverse Resource Rational Based Stochastic Driver Behavior Model

Human drivers have limited and time-varying cognitive resources when making decisions in real-world traffic scenarios, which often leads to unique and stochastic behaviors that can not be explained by perfect rationality assumption, a widely accepted premise in modeling driving behaviors that presume drivers rationally make decisions to maximize their own rewards under all circumstances. To explicitly address this disadvantage, this study presents a novel driver behavior model that aims to capture the resource rationality and stochasticity of the human driver's behaviors in realistic longitudinal driving scenarios. The resource rationality principle can provide a theoretic framework to better understand the human cognition processes by modeling human's internal cognitive mechanisms as utility maximization subject to cognitive resource limitations, which can be represented as finite and time-varying preview horizons in the context of driving. An inverse resource rational-based stochastic inverse reinforcement learning approach (IRR-SIRL) is proposed to learn a distribution of the planning horizon and cost function of the human driver with a given series of human demonstrations. A nonlinear model predictive control (NMPC) with a time-varying horizon approach is used to generate driver-specific trajectories by using the learned distributions of the planning horizon and the cost function of the driver. The simulation experiments are carried out using human demonstrations gathered from the driver-in-the-loop driving simulator. The results reveal that the proposed inverse resource rational-based stochastic driver model can address the resource rationality and stochasticity of human driving behaviors in a variety of realistic longitudinal driving scenarios.

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arXiv2022

Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions

We discuss a general methodology to provide rigid, off-shell matter multiplets and actions for recently constructed non-relativistic superalgebras. The technique is based on the Lie algebra expansion, which, in the context of supersymmetry, has so far been used to obtain non-relativistic on-shell supergravity models. We first explain how the Lie algebra expansion can be implemented to generate off-shell rigid multiplets on a flat background by developing an auxiliary framework where only the lowest order behavior of the spatial and temporal vielbein is relevant. We then provide explicit examples for the field content, the transformation rules as well as action principles for certain multiplets in three and four dimensions.

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arXiv2022

The Holographic c-theorem and Infinite-dimensional Lie Algebras

We discuss a non-dynamical theory of gravity in three-dimensions which is based on an infinite-dimensional Lie algebra that is closely related to an infinite-dimensional extended AdS algebra. We find an intriguing connection between on the one hand higher-derivative gravity theories that are consistent with the holographic c-theorem and on the other hand truncations of this infinite-dimensional Lie algebra that violate the Lie algebra structure. We show that in three dimensions different truncations reproduce, up to terms that do not contribute to the c-theorem, Chern-Simons-like gravity models describing extended 3D massive gravity theories. Performing the same procedure with similar truncations in dimensions larger than or equal to four reproduces higher derivative gravity models that are known in the literature to be consistent with the c-theorem but do not have an obvious connection to massive gravity like in three dimensions.

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arXiv2021

Personalized Adaptive Cruise Control and Impacts on Mixed Traffic

This paper presents a personalized adaptive cruise control (PACC) design that can learn driver behavior and adaptively control the semi-autonomous vehicle (SAV) in the car-following scenario, and investigates its impacts on mixed traffic. In mixed traffic where the SAV and human-driven vehicles share the road, the SAV's driver can choose a PACC tuning that better fits the driver's preferred driving behaviors. The individual driver's preferences are learned through the inverse reinforcement learning (IRL) approach by recovering a unique cost function from the driver's demonstrated driving data that best explains the observed driving style. The proposed PACC design plans the motion of the SAV by minimizing the learned unique cost function considering the short preview information of the preceding human-driven vehicle. The results reveal that the learned driver model can identify and replicate the personalized driving behaviors accurately and consistently when following the preceding vehicle in a variety of traffic conditions. Furthermore, we investigated the impacts of the PACC with different drivers on mixed traffic by considering time headway, gap distance, and fuel economy assessments. A statistical investigation shows that the impacts of the PACC on mixed traffic vary among tested drivers due to their intrinsic driving preferences.

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arXiv2020

Off-Shell ${\mathcal N}=(1,0)$ Linear Multiplets in Six Dimensions

We provide a tensor calculus for $n$-number of ${\mathcal N}=(1,0)$ linear multiplets in six dimensions. The coupling of linear multiplets is encoded in a function ${\mathcal F}_{IJ}$ that is subject to certain constraints. We provide various rigid and local supersymmetric models depending on the choice of the function ${\mathcal F}_{IJ}$ and provide an interesting off-diagonal superinvariant, which leads to an $R^2$ supergravity upon elimination of auxiliary fields.

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arXiv2020

Three-Dimensional Higher-Order Schrödinger Algebras and Lie Algebra Expansions

We provide a Lie algebra expansion procedure to construct three-dimensional higher-order Schrödinger algebras which relies on a particular subalgebra of the four-dimensional relativistic conformal algebra. In particular, we reproduce the extended Schrödinger algebra and provide a new higher-order Schrödinger algebra. The structure of this new algebra leads to a discussion on the uniqueness of the higher-order non-relativistic algebras. Especially, we show that the recent d-dimensional symmetry algebra of an action principle for Newtonian gravity is not uniquely defined but can accommodate three discrete parameters. For a particular choice of these parameters, the Bargmann algebra becomes a subalgebra of that extended algebra which allows one to introduce a mass current in a Bargmann-invariant sense to the extended theory.

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arXiv2020

Superconformal generalizations of auxiliary vector modified polynomial f(R) theories

We present the supersymmetric completion of the auxiliary vector modified polynomial $f(R)$ theories in their dual scalar-tensor theory formulation that interpolate between the auxiliary vector modified polynomial $f(R)$ theories and chaotic inflation with the power-law potential $V(ϕ) \propto ϕ^p$. The supersymmetrization is achieved in two steps: First, we introduce a superconformal theory for three chiral multiplets by choosing a conformal Kähler potential and a conformal superpotential. In the second step, we use one of the chiral multiplets to compensate for the superconformal symmetries and achieve the Kähler potential and the superpotential while the other two are used to realize inflation with a stable inflationary trajectory. The stability of the inflationary trajectory requires certain deformations to the Kähler potential which we discuss their compatibility against the inflationary observables from the latest Planck data.

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