arXiv research

Introduces a new geometric framework for non-perturbative BV-theory.

Perturbative string amplitudes are correctly derived from the string geometry theory, which is one of the candidates of a non-perturbative formulation of string theory. In order to derive non-perturbative effects rather easily, we formulate topological string geometry theory. We derive the perturbative partition functi…

Study of harmonic maps and instantons in 4D.

New non-perturbative counterexamples to Min-Oo's Conjecture are created.

New method proves instability of naked singularity and censors it.

Formally equates two quantization methods and constructs non-commutative algebras.

We propose a conjecture to compute the all-order asymptotic expansion of the colored Jones polynomial of the complement of a hyperbolic knot, J_N(q = exp(2u/N)) when N goes to infinity. Our conjecture claims that the asymptotic expansion of the colored Jones polynomial is a the formal wave function of an integrable sys…

This paper analyzes $Δ_a$ invariants in non-perturbative complex Chern-Simons theory.

We consider Chern-Simons theory with complex gauge group and present a complete non-perturbative evaluation of the path integral (the partition function and certain expectation values of Wilson loops) on Seifert fibred 3-Manifolds. We use the method of Abelianisation. In certain cases the path integral can be seen to f…

ContrastiveVI+ models CRISPR screens with noisy guide efficiency.

String geometry theory uniquely determines classical action with T-symmetry.

Study non-perturbative quantum geometry of string theories using finite difference equations and resurgence analysis.

Lectures detail field theory dynamics and exact WKB analysis.

We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces in a target manifold. Based on the string geometry, we define Einstein-Hilbert ac…

We consider the non-perturbative superpotential for a class of four-dimensional $\mathcal N=1$ vacua obtained from M-theory on seven-manifolds with holonomy $G_2$. The class of $G_2$-holonomy manifolds we consider are so-called twisted connected sum (TCS) constructions, which have the topology of a K3-fibration over $S…

Novel mathematical approach using resurgent analysis reveals new structures in complex Chern-Simons theory.

Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in F-theory, as the corresponding branch of the moduli space does not exist in the theory. Accordingly, even non-abelian gauge theories have not been fully understood in global F-theory compactifications. We present a systematic disc…

Mathematical structures link Gromov-Witten to Donaldson-Thomas invariants.

In this paper we prescribe a fourth order conformal invariant on the standard $n-$sphere, with $n\geq5$, and study the related fourth order elliptic equation. We first find some existence results in the perturbative case. After some blow up analysis we build a homotopy to pass from the perturbative case to the non-pert…

Identifies all perturbative vacua in bosonic string theory.

Alternative finance models from physics for non-equilibrium systems.

Derives path-integrals for superstrings on curved backgrounds using string geometry theory.

New method extends knot theory to non-bipartite knots, revealing PDs.

Derives path integrals for perturbative strings on various backgrounds.

Quantum Kerr learning shows enhancements in convergence and generalization for kernel-based methods.

Study of rotating gravastars with de Sitter interiors and Kerr exteriors.

We propose a non-perturbative formulation of the Atiyah-Patodi-Singer(APS) index in lattice gauge theory, in which the index is given by the $η$ invariant of the domain-wall Dirac operator. Our definition of the index is always an integer with a finite lattice spacing. To verify this proposal, using the eigenmode set o…

We show that the four derivative terms in the effective action of three-dimensional N=8 Yang-Mills theory are determined by supersymmetry. These terms receive both perturbative and non-perturbative corrections. Using our technique for constraining the effective action, we are able to determine the exact form of the eig…

Identifies most probable flows for Kunita SDEs in fluid dynamics.

Study on 4D Einstein manifolds with Kähler conformal geometry.

Lectures on deep learning properties in infinite and large-width networks.

We use the twistorial construction of D-instantons in Calabi-Yau compactifications of type II string theory to compute an explicit expression for the metric on the hypermultiplet moduli space affected by these non-perturbative corrections. In this way we obtain an exact quaternion-Kahler metric which is a non-trivial d…

The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the market stochastic dynamics, allowing us to write and formally solve the generaliz…

Precise scientific analysis in collider-based particle physics is possible because of complex simulations that connect fundamental theories to observable quantities. The significant computational cost of these programs limits the scope, precision, and accuracy of Standard Model measurements and searches for new phenome…

Constructs geodesics near intersection points of Lagrangian submanifolds.

The paper explores how fields in higher dimensions are quantized.

Formalizes quantum path integrals using groupoids and differential forms.

Using probabilistic methods, we first define Liouville quantum field theory on Riemann surfaces of genus $\mathbf{g}\geq 2$ and show that it is a conformal field theory. We use the partition function of Liouville quantum field theory to give a mathematical sense to Polyakov's partition function of noncritical bosonic s…

We identify a large class R of three-dimensional N=2 superconformal field theories. This class includes the effective theories T_M of M5-branes wrapped on 3-manifolds M, discussed in previous work by the authors, and more generally comprises theories that admit a UV description as abelian Chern-Simons-matter theories w…

We consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel …

Study wave functions in complex Chern-Simons theory, finding integrality and rational points.

New insights connect strong coupling SYM amplitudes to hyperkähler geometry.

We use the 3d-3d correspondence together with the DGG construction of theories $T_n[M]$ labelled by 3-manifolds M to define a non-perturbative state-integral model for SL(n,C) Chern-Simons theory at any level k, based on ideal triangulations. The resulting partition functions generalize a widely studied k=1 state-integ…

Extract anomalies from 5D SCFTs using extra-dimensional η-invariants.

Study of IR phases in 3D class R theories linked to non-hyperbolic 3-manifolds.

Many four-dimensional supersymmetric compactifications of F-theory contain gauge groups that cannot be spontaneously broken through geometric deformations. These "non-Higgsable clusters" include realizations of $SU(3)$, $SU(2)$, and $SU(3) \times SU(2)$, but no $SU(n)$ gauge groups or factors with $n> 3$. We study poss…

Paper proves existence of anisotropic dynamical horizons in gravitational collapse.

Complex Chern-Simons theory reveals peacock patterns in perturbative series.