arXiv subjects

Kuba Krawczyk

Publications and source records attributed to Kuba Krawczyk.

3 recordsLinked to original sources

arXiv2026

Black Holes, the Bethe Ansatz, and Elliptic Calogero--Moser Systems

We define a map from solutions of the Bethe Ansatz equations (BAEs) of four-dimensional $\mathcal{N}=4$ super-Yang--Mills with arbitrary semisimple gauge algebra $\mathfrak{g}$ to extrema and poles of the potential of the untwisted elliptic Calogero--Moser system of type $\mathfrak{g}$. We conjecture the map to be a bijection on the preimage of the Calogero--Moser extrema, and show that it intertwines the symmetries of the two systems, both the gauge ones (torus, Weyl and center invariance) and a $\mathrm{PSL}(2,\mathbb{Z})$ action, so that solutions on both sides organize into orbits, each BAE orbit mapping onto a single orbit of Calogero--Moser extrema or poles. That the system produced is the untwisted one has a consequence: the conjectured correspondence between BAE solutions and vacua of the $\mathcal{N}=1^\ast$ deformation of $\mathcal{N}=4$ on $\mathbb{R}^{3,1}$, which are extrema of the twisted system, cannot extend to non-simply-laced $\mathfrak{g}$. It also fails within the simply-laced cases, though not for $\mathfrak{su}(N)$: we exhibit an $\mathfrak{so}(8)$ solution that flows to a pole of the Calogero--Moser potential rather than to an extremum, and so has no $\mathcal{N}=1^\ast$ counterpart. We illustrate the map in detail for every rank-two $\mathfrak{g}$, classical and exceptional alike, and use these cases as evidence for the conjecture.

hep-th↗

arXiv2026

The $\mathcal{N}=4$ Bethe Ansatz beyond $\mathrm{SU}(N)$

We solve the Bethe Ansatz equations (BAEs) to evaluate the superconformal index of four-dimensional $\mathcal{N}=4$ super-Yang--Mills with rank-two gauge algebra, at equal angular momentum fugacities $p=q$. The solutions for $A_2$ are known, and those for $D_2\cong A_1\oplus A_1$ follow readily from the (equally known) $A_1$ ones. The first genuinely new case is $B_2\cong C_2$, for which we obtain the complete solution set in closed form; for the exceptional case $G_2$ our results are numerical, with a single fully rational solution obtained in closed form. To the best of our knowledge, this is the first time any solution, analytic or numerical, has been found in non-$A$-type gauge algebra (for $\mathcal{N}=4$ or any other $\mathcal{N}=1$ theory). Along the way we uncover several phenomena absent in type $A$: isolated Weyl-fixed solutions contributing nontrivially to the index; isolated solutions in which at most half of the holonomies have rational coefficients (in contrast with the $A$-type fully rational Hong--Liu family); and solutions whose $|\omega|\to0$ limit (with $p=q=:e^{2\pi i\omega}$) evades assumptions standardly made in the Cardy-like limit literature, landing on saddles that the usual analysis does not capture, for all types $BC\!D$. We also clarify the Bethe origin of the finite logarithmic correction to the Cardy expansion: it arises from the orbit size of a BAE solution under the gauge symmetries of the equations, rather than from the one-form center symmetry of the theory, to which the index is insensitive.

hep-th↗

arXiv2024

Tulczyjew triple on the Atiyah algebroid with connection

The Tulczyjew triple on a principal bundle with connection is constructed in a convenient trivialisation. A reduction by the structure group is performed leading to the triple on the trivialised Atiyah algebroid and a presentation of this algebroid via a double vector bundle morphism. The dynamics of physical systems with configuration manifolds having the structure of a principal bundle with connection or the Atiyah algebroid is discussed and applied to the example of an axially symmetric body confined to a sphere.

math-ph↗