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Erdal Catak

Publications and source records attributed to Erdal Catak.

6 recordsLinked to original sources
arXiv2025

More solutions to the decoration transformation

In this work, we investigate new solutions to the decoration transformation in terms of various special functions, including the hyperbolic gamma function, the basic hypergeometric function, and the Euler gamma function. These solutions to the symmetry transformation are important to decorate Ising-like integrable lattice spin models obtained via the gauge/YBE correspondence. The integral identities represented as the solution of the decoration transformation are derived from the three-dimensional partition functions and superconformal index for the dual supersymmetric gauge theories.

hep-th↗
arXiv2025

Flipping relation as a reduced star-star relation

In this paper, we consider the lens hyperbolic gamma solution to the star-star relation and the flipping relation from three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories on $S^3_b/\mathbb{Z}_r$. We explore that a certain limit of the star-star relation yields the latter symmetry transformation, which exchanges the edge interactions of two outer spins with a centrally sited spin. Furthermore, we obtain more solutions to the flipping relation in terms of the hyperbolic gamma, basic hypergeometric, and the Euler gamma functions.

hep-th↗
arXiv2025

Displacement Memory Effect from Supersymmetry

We explain the recent results on the displacement memory effect (DME) of plane gravitational waves using supersymmetric quantum mechanics. This novel approach stems from that both the geodesic and the Schr\"odinger equations are Sturm-Liouville boundary value problems. Supersymmetry provides a unified framework for the P\"oschl-Teller and the Scarf profiles and yields the critical values of the associated wave amplitudes for DME in a natural way. Within our framework, we obtain a compact formula for DME in terms of the asymptotic values of the superpotential and the geodesics. In addition, this new technique enables us to build plane and gravitational waves with 2-transverse directions using superpartner potentials. Lastly, we study DME within a singular wave profile inspired by supersymmetric quantum mechanics, which demonstrates the broader applicability of our method.

gr-qc↗
arXiv2024

Decorating the gauge/YBE correspondence

In this paper, we aim to study the three-dimensional $\mathcal N=2$ supersymmetric dual gauge theories on $S_b^3/\mathbb{Z}_r$ in the context of the gauge/YBE correspondence. We consider hyperbolic hypergeometric integral identities acquired via the equality of supersymmetric lens partition functions as solutions to the decoration transformation and the flipping relation in statistical mechanics. The solutions of those transformations aim at investigating various decorated lattice models possessing the Boltzmann weights of integrable Ising-like models obtained via the gauge/YBE correspondence. We also constructed The Bailey pairs for the decoration transformation and the flipping relation.

hep-th↗
arXiv2022

Hyperbolic and trigonometric hypergeometric solutions to the star-star equation

We construct the hyperbolic and trigonometric solutions to the star-star relation via the gauge/YBE correspondence by using the three-dimensional lens partition function and superconformal index for a certain N=2 supersymmetric gauge dual theories. This correspondence relates supersymmetric gauge theories to exactly solvable models of statistical mechanics. The equality of partition functions for the three-dimensional supersymmetric dual theories can be written as an integral identity for hyperbolic and basic hypergeometric functions.

hep-th↗