arXiv subjects

Mustafa Mullahasanoglu

Publications and source records attributed to Mustafa Mullahasanoglu.

15 recordsLinked to original sources

arXiv2026

Arithmetic selection rules in dispersionless Hamiltonian systems

In this work, we derive selection rules imposed by Liouville integrability conditions for monomial charge densities with arbitrary powers. For a certain monomial Hamiltonian system, the selection rules reduce to a negative Pell equation, and its solutions generate an infinite set of integrals of motion that are mutually in involution. Furthermore, we study the correspondence between combinatorial polynomial sequences and Liouville integrable Hamiltonian field theories in 1+1 dimensions. We show that the Motzkin system coincides with the dispersionless limit of the Levi system, while the binomial system is equivalent to the dispersionless derivative nonlinear Schr\"odinger equation. Additionally, we show that the binomial Hamiltonian model admits a reduction to the inviscid Burgers equation and its higher-order charges generate generalized Burgers-type conservation laws.

nlin.SI↗

arXiv2026

On conformal symmetry in large-$N$ quiver mechanics

The microscopic description of extremal supersymmetric black holes in AdS$_2$/CFT$_1$ holography has remained elusive despite recent progress in the statistical description of near-extremal black hole physics. In this work we revisit Denef's quiver mechanics description of D-brane bound states in the Coulomb branch, which displays an emergent conformal symmetry in the AdS$_2$ scaling limit. This conformal symmetry is however broken by superpotential corrections near the locus where the Coulomb and Higgs branches meet, and its significance has so far remained unclear. In order to to clarify this issue, we derive and interpret a fixed-point formula for the superconformal quiver index using localization techniques. Focusing on cyclic abelian quivers, we show that, in a certain large-$N$ limit (with the rank $N$ of the quiver gauge group), the fixed points are located in the regime where the conformal description is reliable. In this limit, our expression for the superconformal index precisely captures a contribution to the microscopic scaling BPS index derived by Beaujard, Mondal and Pioline, which was hitherto not visible on the Coulomb branch. Our results are hoped to provide a step towards a stringy realization of AdS$_2$/CFT$_1$ duality.

hep-th↗

arXiv2025

From dual gauge theories to dual spin models

This brief review surveys recent progress driven by the gauge/Yang-Baxter equation (YBE) correspondence. This connection has proven to be a powerful tool for discovering novel integrable lattice spin models in statistical mechanics by exploiting dualities in supersymmetric gauge theories. In recent years, research has demonstrated the use of dual gauge theories to construct new lattice spin models that are dual to Ising-like models.

hep-th↗

arXiv2025

Bailey chain approach to 2d $\mathcal{N}=(0,2)$ dualities

We study a two-dimensional $\mathcal{N}=(0,2)$ supersymmetric duality and construct novel Bailey pairs for the associated elliptic genera. This framework provides a systematic method to establish the equivalence of the elliptic genera of quiver gauge theories generated via iterative applications of the seed duality.

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

Ordinary limits of the hyperbolic hypergeometric integral identities

The computation of the partition function of supersymmetric gauge theories on compact manifolds can be reduced to matrix integrals by using the supersymmetric localization technique. Such matrix integrals in the case of three-dimensional supersymmetric gauge theories on lens space can be expressed in terms of hyperbolic hypergeometric integrals. By studying partition functions of supersymmetric dual theories, one can obtain new complicated identities for this type of special function. We derive new ordinary hypergeometric identities from the reduction of certain hyperbolic hypergeometric integral identities obtained via supersymmetric infrared dualities.

hep-th↗

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↗

arXiv2023

The star-square relation and the generalized star-triangle relation from 3d supersymmetric dualities I

We study duality transformations of the star-square relation and the generalized star-triangle relation for Ising-like integrable lattice spin models. The integrable models are obtained via gauge/YBE correspondence which connects the supersymmetric gauge theories and lattice spin models of statistical mechanics. By the use of integral identities coming from the duality of three-dimensional supersymmetric gauge theories, we construct hyperbolic, lens hyperbolic, trigonometric, and rational solutions to the duality transformations. These duality transformations allow us to construct spin lattice models with four-spin (the star-square relation) and three-spin (the generalized star-triangle relation) interactions.

hep-th↗

arXiv2023

Liouville integrable binomial Hamiltonian system

In this study we work on a novel Hamiltonian system which is Liouville integrable. In the integrable Hamiltonian model, conserved currents can be represented as Binomial polynomials in which each order corresponds to the integral of motion of the system. From a mathematical point of view, the equations of motion can be written as integrable second-order nonlinear partial differential equations in 1 + 1 dimensions.

nlin.SI↗

arXiv2022

On Bailey pairs for $\mathcal N=2$ supersymmetric gauge theories on $S_b^3/\mathbb{Z}_r$

We study Bailey pairs construction for hyperbolic hypergeometric integral identities acquired via the duality of lens partitions functions for the three-dimensional $\mathcal N=2$ supersymmetric gauge theories on $S_b^3/\mathbb{Z}_r$. The novel Bailey pairs are constructed for the star-triangle relation, the star-star relation and the pentagon identity. The first two of them are integrability conditions for the Ising-type integrable lattice models. The last one corresponds to the representation of the basic $2-3$ Pachner move for triangulated 3-manifolds.

hep-th↗

arXiv2021

Lens Partition Functions and Integrability Properties

We study lens partitions functions for the three-dimensional $ N=2$ supersymmetric gauge theories on $S_b^3/Zr$. We consider an equality as a new hyperbolic hypergeometric solution to the star-star relation via the gauge/YBE correspondence. The correspondence allows the construction of integrable lattice spin models of statistical mechanics by the use of integral identities. Additionally, we obtain new hyperbolic hypergeometric integral identities of gauge theories.

hep-th↗

arXiv2021

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↗

arXiv2020

Lens partition function, pentagon identity and star-triangle relation

We study the three-dimensional lens partition function for $\mathcal N=2$ supersymmetric gauge dual theories on $S^3/\mathbb{Z}_r$ by using the gauge/YBE correspondence. 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 hypergeometric functions. We obtain such an integral identity which can be written as the star-triangle relation for Ising type integrable models and as the integral pentagon identity. The latter represents the basic 2-3 Pachner move for triangulated 3-manifolds. A special case of our integral identity can be used for proving orthogonality and completeness relation of the Clebsch-Gordan coefficients for the self-dual continuous series of $U_q(osp(1|2))$.

hep-th↗