Research
Research
Research
Research
9,551+ open-access research outputs.
We develop the ODE/IM correspondence for the higher-order Mathieu equation arising from the quantum Seiberg-Witten curve of the pure $SU(r+1)$ ${\cal N}=2$ supersymmetric Yang-Mills theory. From the s…
We compute exact finite-rank BPS generating functions for the fermionic matrix model with single-trace supercharge $Q_p=\operatorname{tr}(\Psi^p)$ at $(p,N)=(5,3),(5,4),(5,5),(7,4)$, together with par…
We investigate the resilience of spinon quasiparticles in the $J_1$-$J_2$ zig-zag spin chain ($J_2>0$) from the viewpoint of momentum-space entanglement. For small $J_2$, we show that deconfined spino…
We study moduli spaces of logarithmic stable maps to proper toric surfaces with prescribed tangency conditions to the toric boundary. Fixing a surface, we define a chamber decomposition on the space o…
One of the most important applications of topological recursion concerns spectral curves for which the functions $(x,y)$ defining the spectral curve are allowed to have logarithmic singularities. This…
In the previous paper, the author showed that for a smooth family $X \to \mathbb{X} \to B$ of a homotopy $K3$ surface, the obstruction for the tangent bundle along the fibers $T_B \mathbb{X}$ to have …
Stephen Wolfram proclaimed in his 2003 seminal work "A New Kind Of Science" that simple recursive programs in the form of Cellular Automata (CA) are a promising approach to replace currently used math…
We prove that given two compact oriented $3$-manifolds $N$ and $M,$ with $M$ satisfying only a mild hypothesis, there is a hyperbolic $3$-manifold $N'$ arbitrarily ``closely related'' to $N,$ and such…
There are 7,407 languages in the world. But, what about the languages that are not there in the world? Are humans so narrow minded that we don't care about the languages aliens communicate in? Aliens …
Large families of confining holographic QFTs, described by Einstein-Dilaton gravity, are considered on constant-curvature manifolds in the presence of a $\theta$-angle. The space of ground states of s…
We compute the Floer homology and Seiberg-Witten Floer homotopy type of Seifert rational homology $3$-spheres which fiber over $\mathbb{RP}^2$. We show that they are all $L$-spaces and their Floer hom…
We demonstrate that simple feed-forward neural networks (NNs) can accurately compute correlation functions of conformal field theories (CFTs) on a line. Strikingly, by optimising a NN solely on crossi…
In this review branes of string theory are described from three different perspectives: as endpoints of open string, as supergravity backgrounds with BPS properties, as dynamical objects with gauge in…
Let $\Bbbk$ be an algebraically closed field of characteristic $p>3$, and let $W$ denote the $p$-dimensional Witt algebra, the first example of a non-classical simple Lie algebra. For a non-negative i…
Inspired by the Ozsv\'ath-Szab\'o mixed invariant in ordinary Heegaard Floer theory, we define a mixed invariant $\Phi_{X, \mathfrak{s}}^{I}$ for closed, spin four-manifolds $(X, \mathfrak{s})$ using …
In this work, we describe local and 2-local $\frac12$-derivations of infinite-dimensional Lie algebras. We prove that all local and 2-local $\frac12$-derivations of the Witt algebra as well as of the …
We calculate the Witt ring of the real sphere.…
T. Saito introduced FW-derivations and the modules of FW-differentials. He gave a regularity criterion in terms of the modules of FW-differentials. In this paper, we introduce logarithmic analogues of…
We present a review of supersymmetry, supergravity, and the non-perturbative dynamics of gauge theories, tracing a path from the supersymmetry algebra to moduli stabilisation and de~Sitter vacua in st…
Non-commutative electrodynamics obtained through the Seiberg-Witten map ceases to have equivalent action-level and equation-level realizations once fixed external currents are introduced, and in the a…
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