arXiv subjects

Aytül Filiz

Publications and source records attributed to Aytül Filiz.

10 recordsLinked to original sources

arXiv2026

Holonomies and Boundary Symmetries in Discrete BF Formulation of Jackiw-Teitelboim Gravity

We develop a fully discrete and non-perturbative realization of two--dimensional Jackiw--Teitelboim (JT) gravity as an $\mathrm{sl}(2,\mathbb{R})$ BF theory. Using group--valued holonomies and Lie-algebra--valued dilatons, the bulk theory is shown to be purely topological, with all physical information encoded at the boundary. We analyze admissible discrete boundary conditions and derive the corresponding asymptotic symmetry algebras directly at the lattice level, including an affine Kac--Moody symmetry and its Brown--Henneaux reduction to a Virasoro algebra, together with the associated Virasoro--dilaton structure. A precise operator product expansion\,(OPE) dictionary is established by taking the controlled continuum limit of the discrete Poisson brackets. Beyond asymptotic symmetries, we provide an effective boundary description and a representation-theoretic quantization organized by monodromy sectors. Within this discrete framework, black hole entropy follows from gauge--invariant holonomy data and is expressed in terms of the dilaton Casimir, reproducing the Bekenstein--Hawking result within a framework that does not require an explicit Schwarzian action.

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arXiv2026

Generalized Schwarzian Dynamics from a Bulk-First BF Perspective

We investigate the emergence of generalized Schwarzian dynamics from a bulk-first BF perspective. Starting from two-dimensional BF gravity, we analyze the associated boundary phase space and its Drinfeld-Sokolov reductions. For the sl(2,R) theory, we recover the ordinary Schwarzian action as the reduced boundary dynamics arising from a particular sector of the BF asymptotic phase space. We then extend this construction to sl(3,R), where the reduced dynamics is governed by the second and third Wilczynski invariants, providing a natural higher-rank generalization of the Schwarzian derivative. In this framework, generalized Schwarzian dynamics emerges directly from flat BF connections and their companion forms rather than being introduced as an independent boundary theory. We further relate the resulting projective invariants to Casimir charges, monodromy data, and generalized Schwarzian thermodynamics, including monodromy spectra and semiclassical thermodynamics. In particular, constant projective invariants determine the corresponding Casimir sectors and monodromy data, which in turn organize the thermodynamic structure of the theory. Our results provide a unified bulk-first description of Schwarzian and generalized Schwarzian dynamics and reveal a direct link between BF gravity, asymptotic symmetry reductions, projective geometry, and boundary thermodynamics.

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arXiv2026

Holonomies and Boundary Symmetries in the Discrete BF Formulation of Carroll Dilaton Gravity

We construct a discrete realization of two-dimensional Carroll dilaton gravity based on a BF-type gauge structure with holonomy variables on lattice links. The bulk theory remains topological, while the physical dynamics is encoded in boundary degrees of freedom. Imposing admissible boundary conditions, we derive the asymptotic symmetry structure directly at the lattice level. The least restrictive conditions yield an affine extension of the Carroll algebra, while additional constraints reduce the symmetry to a conformal sector governed by a discrete Virasoro-type algebra. In the continuum limit, the lattice symmetry structure reproduces the expected affine Carroll algebra together with its conformal reduction. The construction therefore provides the ultra-relativistic counterpart of discrete Jackiw-Teitelboim(JT) gravity.

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arXiv2026

Holonomies and Boundary Symmetries in the Discrete Warped Chern-Simons Gravity

We investigate a discrete warped Chern-Simons description of three-dimensional warped gravity based on boundary holonomies and monodromy sectors. Starting from the lower-spin SL(2, R) + U(1) gauge structure associated with warped AdS(3) holography and warped conformal field theories (WCFTs), we construct a discrete boundary framework in which ordered products of link holonomies replace continuous gauge connections along noncontractible cycles. In this setting, boundary monodromies become the primary gauge-invariant observables characterizing the physical sectors of the theory. We show that the hyperbolic, eliliptic, and parabolic sectors naturally arise from the conjugacy classes of the discrete SL(2, R) monodromy, while the additional U(1) holonomy supplies the warped contribution to the boundary charges. Using these monodromy invariants, we derive a discrete entropy relation entirely from boundary holonomy data without relying on a smooth geometric thermal background. The resulting entropy reproduces the characteristic warped black-hole and WCFT structure in the continuum limit. We further demonstrate that the continuum warped holonomy conditions are recovered from the large-lattice limit of the ordered boundary products, establishing a direct correspondence between discrete monodromies and continuous Wilson loops. Our analysis suggests that warped gravitational thermodynamics may be understood from a fundamentally holonomy-based perspective in which boundary monodromy sectors provide an alternative organizational description of the physical states within the discrete warped framework. Keywords: warped Chern-Simons theory, boundary monodromies, holonomy sectors, Wilson loops, warped thermodynamics.

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arXiv2026

$\mathcal{N}=1$ Jackiw -Teitelboim supergravity beyond the Schwarzian regime

We investigate the asymptotic symmetry structure of two--dimensional dilaton gravity in its $\mathcal{N}=1$ supersymmetric extension based on the $\mathfrak{osp}(1|2)$ Lie superalgebra. Within the BF theoretical framework, we analyze affine and superconformal boundary conditions and systematically derive the corresponding asymptotic symmetry algebra(ASA). While the bosonic theory reproduces the Virasoro algebra and its affine enhancement, the supersymmetric extension yields a classical $\mathcal{N}=1$ superconformal algebra whose realization is dynamically restricted by the dilaton supermultiplet. We show that the boundary behavior of the dilaton induces a controlled dynamical reduction of the full affine $\mathfrak{osp}(1|2)_k$ symmetry to its $\tt{O}\tt{S}p(1|2)$ stabilizer subalgebra, while simultaneously generating an abelian ideal composed of mutually commuting modes. This establishes a coherent interplay between asymptotic symmetry breaking and symmetry extension in low--dimensional supergravity.Our construction generalizes previous analyses of $\mathfrak{sl}(2,\mathbb{R})$ dilaton gravity to the supersymmetric setting and provides a consistent bulk--based framework for investigating boundary dynamics beyond the Schwarzian regime.

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arXiv2025

On the Explicit Asymptotic Symmetry Breaking of sl(3,R) Jackiw-Teitelboim Gravity

This study investigates the asymptotic symmetry algebras (ASA) of Jackiw-Teitelboim (JT) gravity within the framework of sl(3,R) symmetry. By explicitly constructing this algebra, we explore how the presence of the dilaton field influences the structure of asymptotic symmetries and symmetry breaking mechanisms at the AdS(2) boundary. For the sl(3,R) model, the dilaton field preserves a subset of the complete W(3)-symmetry, restricting the algebra to sl(3,R). These results provide deeper insights into the role of dilaton dynamics in holographic dualities, with implications for the thermodynamics and geometry of AdS(2). The findings pave the way for systematically exploring extended gauge symmetries in two-dimensional gravity and their relevance to higher-rank Lie algebras.

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arXiv2025

On the $\mathcal{N}=3$ and $\mathcal{N}=4$ superconformal holographic dictionary

This study presents comprehensive examples of $\mathfrak{osp}(\mathcal{N}|2)$ Chern$\,-\,$Simons supergravity on $AdS_3$ for $\mathcal{N}>2$. These formulations, which include the most general boundary conditions, represent extensions of previously discovered works $(\textit{Ozer and Filiz$,$Eur Phys J C 82(5):472, 2022})$ for $\mathcal{N}<3$. In our work, we show that under the loosest set of boundary conditions, the asymptotic symmetry algebras consist of two copies of the $\mathfrak{osp}(3|2)_k$ and $\mathfrak{osp}(4|2)_k$ algebras. We subsequently restrict the gauge fields upon the boundary conditions to achieve supersymmetric extensions of the Brown$\,-\,$Henneaux boundary conditions. Based on these results, we finally find that the asymptotic symmetry algebras are two copies of the $\mathcal{N}=3$ and $\mathcal{N}=4$ superconformal algebras for $\mathcal{N}=(3,3)$ and $\mathcal{N}=(4,4)$ extended higher$\,-\,$spin supergravity theory in $AdS_3$.

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arXiv2021

$\mathcal{N} = (2,2)$ extended $\mathfrak{sl}(3|2)$ Chern-Simons $AdS_3$ supergravity with new boundaries

We present the first example of $\mathcal{N}=(2,2)$ formulation for the extended higher-spin $AdS_3$ supergravity with the most general boundary conditions as an extension of the $\mathcal{N} =\,(1,1)$ work, discovered recently by us [1]. Using the method proposed by Grumiller and Riegler, we construct a consistent class of the most general boundary conditions to extend it. An important consequence of our method is that, for the loosest set of boundary conditions it ensures that their asymptotic symmetry algebras consist of two copies of the $\mathfrak{sl}(3|2)_k$. Moreover, we enjoin some certain restrictions on the gauge fields for the most general boundary conditions, leading to the supersymmetric extensions of the Brown and Henneaux boundary conditions. Based on these results, we finally find out that the asymptotic symmetry algebras are two copies of the super $\mathcal{W}_3$ algebra for $\mathcal{N} = (2,2)$ extended higher-spin supergravity theory in $AdS_3$.

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arXiv2020

Exploring new Boundary Conditions for $\mathcal{N}=(1,1)$ Extended Higher Spin $AdS_3$ Supergravity

In this paper, we present a candidate for $\mathcal{N}=(1,1)$ extended higher - spin $AdS_3$ supergravity with the most general boundary conditions discussed by Grumiller and Riegler recently. We show that the asymptotic symmetry algebra consists of two copies of the $\mathfrak{osp}(3|2)_k$ affine algebra in the presence of the most general boundary conditions.Furthermore, we impose some certain restrictions on gauge fields on the most general boundary conditions and that leads us to the supersymmetric extension of the Brown - Henneaux boundary conditions. We eventually see that the asymptotic symmetry algebra reduces to two copies of the $\mathcal{SW}(\frac{3}{2},2)$ algebra for $\mathcal{N}=(1,1)$ extended higher - spin supergravity.

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arXiv2018

On the Explicit Asymptotic $\mathcal{W}_5$ Symmetry of 3D Chern-Simons Higher Spin $AdS_3$ Gravity

In this paper, we explicitly construct an asymptotic $\mathcal{W}_5$ symmetry algebra of the three-dimensional anti-de Sitter $(AdS_3)$ higher spin gravity. We use an $\mathfrak{sl}(5,R) \oplus \mathfrak{sl}(5,R)$ Lie algebra valued Chern-Simons gauge theory with a negative cosmological constant and its asymptotic symmetry algebra is explicitly calculated as two copies of the classical $\mathcal{W}_5$ algebra with central charge c. Our results can be interpreted as a spin $5$ extension of $AdS_3$ gravity and a proof of how the higher spin Ward identities and as well as the asymptotic $\mathcal{W}_5$ symmetry algebra are derived from the higher spin bulk field equations of motion. This higher spin asymptotic $\mathcal{W}_5$ symmetry algebra contains a finite number of conformal primary spin s: $s\,=\,2,\,3,\,4,\,5.$ We also indicated how to introduce chemical potentials and holonomy conditions associated with these higher spin charges in $AdS_3$ higher spin gravity in a manner that it preserves the asymptotic symmetry algebra.

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