My academic research focuses on quantum gravity, particularly the study of symmetries in black hole horizons using string theory and supergravity. Below are my peer-reviewed publications, doctoral thesis, and conference presentations.

Open Source Research

Alongside peer-reviewed publications, I maintain open-source symbolic computation tools that extend and verify the results from my doctoral work.

  • py_integrability_sugra

    U. Kayani (Sole Author)  ·  Open Source, 2024–present

    A Python/Cadabra2 symbolic verification engine for Killing Spinor Equation (KSE) integrability in supergravity theories. The core claim: integrability conditions [Da, Db]ε = 0 are automatically satisfied on-shell for the theories listed. A unified 9-step Cadabra2 pipeline, driven by a theories.json schema, verifies each gravitino integrability operator against the field equations.

    Verified theories span the full string/M-theory descent: D=11 M-theory → Type IIA, Heterotic (D=10), D=9 NS-NS, D=6 N=(1,0) (via T4), D=5 minimal & vector (via CY3), D=4 Einstein-Maxwell & minimal gauged. The Lichnerowicz argument guarantees that KSEs together with a subset of field equations imply the full equations of motion — so KSE integrability is a powerful consistency check on the theory.

    GitHub

Research Foundations

My research path spans two interconnected threads: quantum spin systems as a gateway to quantum computing, and symmetry structure of black holes in quantum gravity and string theory — both united by the mathematics of Lie algebras, differential geometry, and integrability. The supergravity work probes the full string/M-theory landscape: D=11 M-theory, Type IIA, massive IIA, Heterotic strings (D=10), and lower-dimensional theories obtained via Calabi-Yau compactifications (D=5) and toroidal reductions (D=9, D=6).

MSci Dissertation: Integrable Quantum Spin Chains

  • Integrable Quantum Spin Chains

    U. Kayani (Sole Author)

    MSci Dissertation, King's College London, 2012  ·  Supervised by Dr. B. Doyon

    Studied the Heisenberg spin chain — a quantum interaction model describing nearest-neighbour spin-½ particles — and the Bethe Ansatz diagonalisation method. These integrable models have direct applications in quantum information processing and quantum computing, providing efficient mechanisms for transferring quantum information. The exponentially-scaling matrix diagonalisation techniques developed here directly underpin modern quantum algorithm design.

Peer-Reviewed Publications

  • Symmetry enhancement of Killing horizons in D = 6 supergravity

    U. Kayani (Sole Author)

    ArXiv Preprint, 2019

    arXiv PDF

  • Symmetry enhancement of extremal horizons in D = 5 supergravity

    U. Kayani (Sole Author)

    Classical and Quantum Gravity, 2018

    DOI Journal

  • Dynamical symmetry enhancement near massive IIA horizons

    J. Gutowski, U. Gran, G. Papadopoulos, U. Kayani

    Classical and Quantum Gravity, 2015

    DOI Journal

  • Dynamical symmetry enhancement near IIA horizons

    J. Gutowski, U. Gran, G. Papadopoulos, U. Kayani

    Journal of High Energy Physics, 2015

    DOI Journal

Doctoral Thesis

  • Dynamical Supersymmetry Enhancement of Black Hole Horizons

    U. Kayani

    PhD Thesis, King's College London, 2019

    KCL Repository arXiv

Conference Presentations

  • Publications in Applied Mathematics

    Mathematics of String Theory (MOST) — King's College London, October 2018

  • Future Research in Mathematical Physics

    2nd South East Mathematical Physics Seminar — King's College London, March 2017

  • Publications in Theoretical Physics

    Localisation and the Gauge/Gravity Duality — King's College London, February 2016

  • Publications in String Theory and Supergravity

    Winter School on Supergravity, Strings, and Gauge Theory — CERN, Switzerland, November 2016

  • Latest Research in Supergravity

    Young Theorists' Forum — Durham University, December 2015, 2016, 2017

Academic Profiles

ORCID Google Scholar arXiv