arXiv subjects

Usman Kayani

Publications and source records attributed to Usman Kayani.

3 recordsLinked to original sources

arXiv2026

The warp factor of supersymmetric $D=11$ near-horizon geometries: single-point rigidity, the $Spin(7)$ perfect square, and global constraints

On a compact connected section ${\cal S}$ of a supersymmetric $M$-horizon the Killing-spinor bilinears give a pointwise identity relating the warp factor $\Delta$, the rotation one-form $h$ and the two spinor norms, with nothing assumed about the norm of the Killing spinor. We derive three consequences of that unreduced identity. First, a single-point rigidity theorem: if $\Delta$ and $h$ vanish at one point of the section, then the flux vanishes identically, ${\cal S}$ is Ricci-flat and the horizon is $\mathbb{R}^{1,1}\times{\cal S}$. A single point replaces the usual global spinorial hypothesis. Second, the ${\rm Spin}(7)$ decomposition of the flux fixes $h$ algebraically and exhibits the invariant flux content of the scalar square $\Delta=4\Phi^2$ known in an adapted gauge, $\Delta=\frac{1}{108}\|w_{\bf 7}\pm\sigma({\cal Y}_{\bf 7})\|^2$. Only the two ${\bf 7}$-summands $w_{\bf 7}$, ${\cal Y}_{\bf 7}$ reach the warp factor, and the square is degenerate rather than definite: it vanishes on the linear subspace $w_{\bf 7}=\mp\sigma({\cal Y}_{\bf 7})$ rather than at the origin, so positivity of $\Delta$ yields no case list. Third, the two combine into a pointwise budget: the single constant of supersymmetry is shared between the deviation from staticity and the ${\rm Spin}(7)$ mismatch of the flux, each bounded by that constant. The same identities characterise the constancy hypothesis, equivalent to $V=-fh$ for the bilinear one-form $V$, which fails on the static branch of known warped $AdS_2$ solutions; they fix a weighted integral of the warp factor; and they reduce the Komar angular momentum of the horizon to a positive bilinear integral. Two no-go statements, for hidden symmetries built from the Killing spinor and for a second isometry from its bilinears, are stated with their hypotheses.

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arXiv2026

A second rotational Killing field on gauged $D=5$ vector-multiplet horizons, and a no-go for varying-moduli black rings

We study supersymmetric near-horizon geometries of gauged $D=5$ supergravity coupled to vector multiplets, on the branch where the canonical rotational Killing vector $\tilde V$ of the cross-section ${\cal S}$ is non-vanishing. No rotational symmetry is assumed, and nothing about the set where the frame built from the Killing spinors degenerates. On a compact connected ${\cal S}$ without boundary a second rotational Killing field, independent of $\tilde V$, always exists and is an isometry of all of ${\cal S}$. Where the moduli vary it is $$ U_i=\parallel\eta_-\parallel^2\big(\alpha Z_i-\epsilon_{ijk}Z^ju^k\big) , \qquad u_i=\Phi P_i-h_i , $$ a polynomial in the horizon data, hence smooth everywhere; where the moduli are constant the horizon is locally homogeneous. The only further hypothesis for these results is that the superpotential $\Phi=\chi V_IX^I$ is nowhere zero --- weaker than the non-negativity of the scalar potential assumed in the earlier literature. The two sub-branches are separated by $K=Q_{IJ}C^IC^J$, which vanishes exactly in the minimal theory: $K\equiv0$ recovers the result of Grover, Gutowski, Papadopoulos and Sabra, while elsewhere $K>0$ and $\alpha$ is either identically zero or nowhere zero. Each of $K\equiv0$, $P\equiv0$ and $P\not\equiv0$ occurs on compact ${\cal S}$. Constant moduli return the local geometries of Kunduri and Lucietti as a conclusion, not an ansatz. Varying moduli with $\alpha\not\equiv0$ give a cohomogeneity-one $T^2$ action whose orbit space is a closed interval, so ${\cal S}$ is $S^3$, a lens space or $S^1\times S^2$; the last is excluded by two global first integrals, a new one, $\alpha\parallel\eta_-\parallel^4$, and the constant spinor norm already known. A varying-moduli supersymmetric $AdS_5$ black ring therefore cannot exist with $\alpha\not\equiv0$; the $S^1\times S^2$ window survives only at constant moduli or at $\alpha\equiv0$.

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arXiv2020

Dynamical supersymmetry enhancement of black hole horizons

This thesis is devoted to the study of dynamical symmetry enhancement of black hole horizons in string theory. In particular, we consider supersymmetric horizons in the low energy limit of string theory known as supergravity and we prove the $\textit{horizon conjecture}$ for a number of supergravity theories. We first give important examples of symmetry enhancement in $D=4$ and the mathematical preliminaries required for the analysis. Type IIA supergravity is the low energy limit of $D=10$ IIA string theory, but also the dimensional reduction of $D=11$ supergravity which itself the low energy limit of M-theory. We prove that Killing horizons in IIA supergravity with compact spatial sections preserve an even number of supersymmetries. By analyzing the global properties of the Killing spinors, we prove that the near-horizon geometries undergo a supersymmetry enhancement. This follows from a set of generalized Lichnerowicz-type theorems we establish, together with an index theory argument. We also show that the symmetry algebra of horizons with non-trivial fluxes includes an $\mathfrak{sl}(2, \mathbb{R})$ subalgebra. As an intermediate step in the proof, we also demonstrate new Lichnerowicz type theorems for spin bundle connections whose holonomy is contained in a general linear group. We prove the same result for Roman's Massive IIA supergravity. We also consider the near-horizon geometry of supersymmetric extremal black holes in un-gauged and gauged 5-dimensional supergravity, coupled to abelian vector multiplets. We consider important examples in $D=5$ such as the BMPV and supersymmetric black ring solution, and investigate the near-horizon geometry to show the enhancement of the symmetry algebra of the Killing vectors. We repeat a similar analysis as above to prove the horizon conjecture. We also investigate the conditions on the geometry of the spatial horizon section $\cal{S}$.

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