arXiv subjects

Luke Martin

Publications and source records attributed to Luke Martin.

6 recordsLinked to original sources

arXiv2026

Einstein-aether Elliptic Charges and the First Law of Asymptotically AdS Black Holes

We investigate the thermodynamic role of asymptotic aether alignment for universal horizons in Einstein-aether theory. In the static, spherically symmetric, asymptotically AdS sector with $c_{14}=0$, the known first law for universal horizons contains an additional term whenever the aether is misaligned with the timelike Killing vector at infinity. While this term has recently been interpreted in Ho\v{r}ava--Lifshitz gravity as the contribution of an elliptic charge associated with khronon reparameterizations, no corresponding explanation was available in Einstein-aether theory. We show that, in the same sector, Einstein-aether theory possesses a previously unidentified symmetry of the reduced action, generated by infinitesimal transformations of the form $\delta u^a=f a^a$, where $a^a$ is the aether acceleration and $f$ obeys an elliptic constraint. We derive the associated current and charge, and show that the aligned limit is naturally interpreted as the ensemble in which this aether-charge contribution vanishes. This provides the Einstein-aether counterpart of the elliptic-charge mechanism in Ho\v{r}ava--Lifshitz gravity and clarifies the thermodynamic significance of asymptotic aether alignment.

gr-qc↗

arXiv2024

Mixed Gauge-Global Symmetries, Elliptic Modes, and Black Hole Thermodynamics in Ho\v{r}ava-Lifshitz Gravity

In Ho\v{r}ava-Lifshitz gravity, a putative consistent theory of quantum gravity for which there is evidence for both black hole thermodynamics and a holographic construction, spacetime is endowed with a preferred dynamical spacelike foliation. The theory has a leaf reparameterization symmetry that is neither global nor local gauge, hyperbolic and elliptic equations of motion, a lack of splittability, and universal horizon black hole solutions. The reparameterization symmetry is ``mixed'': it is a local symmetry in one coordinate yet global on each leaf. More broadly it is an example of both unfree and projectable gauge symmetries. The mixed symmetry and associated charge has not yet been accounted for in calculations of universal horizon thermodynamics in Ho\v{r}ava-Lifshitz gravity. This has led to problems, in particular the failure of the first law in a class of asymptotically AdS solutions where the normal to the leaves of the foliation is not aligned with the time translation Killing vector at infinity. We show how the dynamics of the charge corresponding to this symmetry coupled with the other features above resolves this issue. We then briefly comment how this mixed symmetry, the corresponding charge, and the elliptic equations of motion also conspire to evade recent holographic arguments for only local gauge fields in consistent theories of quantum gravity due to the lack of splittability of the elliptic equation and associated mode.

hep-th↗

arXiv2023

SASS: Data and Methods for Subject Aware Sentence Simplification

Sentence simplification tends to focus on the generic simplification of sentences by making them more readable and easier to understand. This paper provides a dataset aimed at training models that perform subject aware sentence simplifications rather than simplifying sentences as a whole. We also test models on that dataset which are inspired by model architecture used in abstractive summarization. We hand generated portions of the data and augment the dataset by further manipulating those hand written simplifications. Our results show that data-augmentation, data-masking, and model architecture choices used in summarization provide a solid baseline for comparison on subject aware simplification.

cs.CL↗

arXiv2023

On the Characterization of Sporadic Simple Groups by Codegrees

Let $G$ be a finite group and $\mathrm{Irr}(G)$ the set of all irreducible complex characters of $G$. Define the codegree of $\chi \in \mathrm{Irr}(G)$ as $\mathrm{cod}(\chi):=\frac{|G:\mathrm{ker}(\chi) |}{\chi(1)}$ and denote by $\mathrm{cod}(G):=\{\mathrm{cod}(\chi)|\chi\in \mathrm{Irr}(G)\}$ the codegree set of $G$. Let $H$ be one of the $26$ sporadic simple groups. In this paper, we show that $H$ is determined up to isomorphism by cod$(H)$.

math.GR↗

arXiv2023

On the Characterization of Alternating Groups by Codegrees

Let $G$ be a finite group and $\mathrm{Irr}(G)$ the set of all irreducible complex characters of $G$. Define the codegree of $\chi \in \mathrm{Irr}(G)$ as $\mathrm{cod}(\chi):=\frac{|G:\mathrm{ker}(\chi) |}{\chi(1)}$ and denote by $\mathrm{cod}(G):=\{\mathrm{cod}(\chi) \mid \chi\in \mathrm{Irr}(G)\}$ the codegree set of $G$. Let $\mathrm{A}_n$ be an alternating group of degree $n \ge 5$. In this paper, we show that $\mathrm{A}_n$ is determined up to isomorphism by $\mathrm{cod}(\mathrm{A}_n)$.

math.GR↗

arXiv2022

Classifying Solvable Primitive Permutation Groups of Low Rank

Suppose that $G$ is a finite, transitive, solvable permutation group acting on a set $S$ with $n$ elements. Let $G_0$ be the stabilizer of a point $\alpha \in \Omega$. Define the rank of a permutation group, denoted $r(G),$ as the number of distinct orbits of $G_0$ in $S$ (including the trivial orbit $\{\alpha\}$). Huppert \cite{Huppert} and Foulser \cite{Foulser} classified all finite, solvable, permutation groups of rank two and three respectively, and Foulser restricted the rank four groups to a small list of possibilities. This paper completes the classification of all groups of rank less than $5$ by explicitly confirming these past results and computationally constructing the groups of rank $4$.

math.GR↗