A bstract We propose a systematic approach to computing the BPS spectrum of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge descriptions or geometric descriptions, based on Nakajima-Yoshioka’s blowup equations. provide significant generalization equation terms both properly quantized magnetic fluxes $$ \hat{\mathrm{\mathbb{C}}} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>ℂ</mml:mi> <mml:mo>̂</mml:mo> </mml:mover>...

A bstract We propose two novel methods for computing the superconformal index of 5d field theories that cannot be described by conventional Lagrangian descriptions under mass deformations. The first approach involves use Higgs branch flows from UV theories, guided transitions in 5-brane webs Type IIB string theory. second method employs relationship between O7 + -plane and − with eight D7-branes, which applies to particular non-Lagrangian realized brane configurations involving an -plane. As...

A bstract We explore BPS strings in supergravity theories six-dimensions and related Swampland Conjectures. first propose a general modular ansatz for bootstrapping elliptic genera of 2d worldvolume on the 6d theories. By employing mirror symmetry F-theory examples, we explicitly compute validate our ansatz. extend this approach to investigate their spectrum non-geometric which have no known constructions, confirm conjectures, including Weak Gravity Conjecture, Distance Emergent String...

Superconductors with the A15 structure are prototypical type-II s-wave superconductors which have generated considerable interest in early superconducting material history. However, topological nature of electronic remains unnoticed so far. Here, using first-principles band calculations based on density functional theory, we show that (Ta$_3$Sb, Ta$_3$Sn, and Ta$_3$Pb) nontrivial topology bulk structures, leading to formation surface states near Fermi energy. Due superconductivity, proximity...

A bstract We propose blowup equations for 6d little string theories which generalize Nakajima-Yoshioka’s the 4d/5d instanton partition functions on Omega background. find that unlike standard SQFTs, we need to sum over auxiliary magnetic fluxes blown-up ℙ 1 a non-dynamical 2-form gauge field plays role in canceling mixed anomalies of symmetries. demonstrate with explicit examples equations, when combined modular properties, can be solved order determine elliptic genera strings.

A bstract We compute the partition function for 6d $$ \mathcal{N} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math> = 1 SO(2 N ) gauge theories compactified on a circle with ℤ 2 outer automorphism twist. perform computation based 5-brane webs two O5-planes using topological vertex O5-planes. As representative examples, we consider SO(8) and SU(3) confirm that these functions obtained from indeed agree elliptic genus computations.

A bstract We generalize Nakajima-Yoshioka’s blowup formula to calculate the partition functions counting spectrum of bound states half-BPS Wilson loop operators in 5d (and 6d) supersymmetric field theories. The function presence a operator on Ω-background is factorized when put $$ \hat{\mathbb{C}} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>ℂ</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> </mml:math> 2 into two under localization. This structure provides set...

Using the first-principles method based on density functional theory, we investigate electronic, mechanical, phononic, superconducting, and topological properties of A15 superconductor Ti3Sb with/without inclusion spin–orbit coupling (SOC). We find that calculated elastic constants satisfy Born stability criteria ductile nature Ti3Sb. The result phonon calculations reveals Pm3¯n structure is dynamically stable. Sb atoms are dominated in low-frequency region due to mass difference between Ti...

Intriguing topological phases may appear in both insulating and semimetallic states. Topological insulators exhibit topologically nontrivial band inversion, while Dirac/Weyl semimetals show ``relativistic'' linear crossings. Here, we report an unusual state of ${\mathrm{Pt}}_{3}\mathrm{Sn}$, where the two features simultaneously. Based on first-principles calculations, that ${\mathrm{Pt}}_{3}\mathrm{Sn}$ is a three-dimensional weak semimetal with inversion between valence conduction bands,...

We propose two novel methods for computing the superconformal index of 5d field theories that cannot be described by conventional Lagrangian descriptions under mass deformations. The first approach involves use Higgs branch flows from UV theories, guided transitions in 5-brane webs Type IIB string theory. second method employs relationship between O$7^+$-plane and O$7^-$-plane with eight D7-branes, which applies to particular non-Lagrangian realized brane configurations involving an...

We explore BPS strings in supergravity theories six-dimensions and related Swampland Conjectures. first propose a general modular ansatz for bootstrapping elliptic genera of 2d worldvolume on the 6d theories. By employing mirror symmetry F-theory examples, we explicitly compute validate our ansatz. extend this approach to investigate their spectrum non-geometric which have no known constructions, confirm conjectures, including Weak Gravity Conjecture, Distance Emergent String Conjecture....

It is shown that a two-dimensional topological insulator can be realized and the band topology (equivalently, edge states) may further controlled by charge doping in an ultrathin SnTe film with defect superstructure. Based on first-principles density functional theory (DFT), we predict Sn-Te bilayer, if exfoliated from three-dimensional bulk (1 1 1) direction, has trivial its pristine form, but made topologically nontrivial introducing appropriate array of defects. The emergence state...

The main results of this paper are to prove bounds for ergodic averages nilflows on general higher step nilmanifolds. Under Diophantine condition the frequency a toral projection flow, we that almost all orbits become equidistributed at polynomial speed. We analyze exponent with speed decay which is determined by number steps and structure nilpotent Lie algebras. result follows from technique over controlling scaling operators in irreducible representations measure estimation close return orbit

We propose blowup equations for 6d little string theories which generalize Nakajima-Yoshioka's the 4d/5d instanton partition functions on Omega background. find that unlike standard SQFTs, we need to sum over auxiliary magnetic fluxes blown-up $ \mathbb{P}^1$ a non-dynamical 2-form gauge field plays role in canceling mixed anomalies of symmetries. demonstrate with explicit examples equations, when combined modular properties, can be solved order determine elliptic genera strings.

Continuing the research initiated in \cite{Fr-Ki2}, we study existence of solutions and their regularity for cohomological equations $X u=f$ locally Hamiltonian flows (determined by vector field $X$) on a compact surface $M$ genus $g\geq 1$. We move beyond case studied so far Forni \cite{Fo1,Fo3}, when flow is minimal over entire function $f$ satisfies some Sobolev conditions. deal with restricted to any its component smooth whenever Full Filtration Diophantine Condition (FFDC) (this full...

We introduce anisotropic Banach spaces on Heisenberg nilmanifolds and study the resonance spectrum associated to partially hyperbolic automorphisms. In this work we describe an alternative proof of which takes advantage geometric-style norms.

The main result of this paper is a construction finitely additive measures for higher rank abelian actions on Heisenberg nilmanifolds. Under full measure set Diophantine conditions the generators action, we construct \emph{Bufetov functionals} rectangles $(2g+1)$-dimensional manifolds. We prove that deviation ergodic integral described by asymptotic Bufetov functionals sufficiently smooth function. As corollary, distribution normalized integrals which have variance 1, converges along certain...

We consider smooth locally Hamiltonian flows on compact surfaces of genus $g\geq 2$ to prove their deviation Birkhoff integrals for observables. Our work generalizes results Forni and Bufetov which the existence spectrum observables whose jets vanish at sufficiently high order around fixed points flow. They showed that ergodic can display a power behaviours with exactly $g$ positive exponents related Lyapunov cocycle so-called Kontsevich-Zorich, renormalization over Teichm\"uller flow...