Related papers: Flat coordinates for Saito Frobenius manifolds and…
Spin Foam Models (SFMs) are covariant formulations of Loop Quantum Gravity (LQG) in 4 dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries…
In order to produce a low energy effective field theory from a string model, it is necessary to specify a vacuum state. In order that this vacuum be supersymmetric, it is well known that all field expectation values must be along so-called…
We study aspects of superstring vacua of non-compact special holonomy manifolds with conical singularities constructed systematically using soluble N = 1 superconformal field theories (SCFT's). It is known that Einstein homogeneous spaces…
The paper studies three classes of Frobenius manifolds: Quantum Cohomology (topological sigma-models), unfolding spaces of singularities (K. Saito's theory, Landau-Ginzburg models), and the recent Barannikov-Kontsevich construction starting…
We review recent progress in the study of S-folds in light of the gauge/gravity duality and the AdS swampland conjecture. S-folds correspond to non-geometric backgrounds of type IIB supergravity of the form $\,\textrm{AdS}_4 \, \times \,…
Motivated by various possible generalizations of Taubes's \(SW=Gr\) theorem [T] to Floer-theoretic setting, we prove certain variants of Taubes's convergence theorem in \cite{T} (the first part of his proof of \(SW=Gr\)). In place of the…
The base space of a semiuniversal unfolding of a hypersurface singularity carries a rich geometry. By work of K. Saito and M. Saito is can be equipped with the structure of a Frobenius manifold. By work of Cecotti and Vafa it can be…
We initiate the systematic investigation of non-flat resolutions of non-minimal singularities in elliptically fibered Calabi--Yau threefolds. Compactification of M-theory on these geometries provides an alternative approach to studying…
The Frobenius manifold structure on the space of rational functions with multiple simple poles is constructed. In particular, the dependence of the Saito-flat coordinates on the flat coordinates of the intersection form is studied. While…
We show that bi-flat $F$-manifolds can be interpreted as natural geometrical structures encoding the almost duality for Frobenius manifolds without metric. Using this framework, we extend Dubrovin's duality between orbit spaces of Coxeter…
The aim of superstring phenomenology is to develop the tools and methodology needed to confront string theory with experimental data. The first mandatory task is to find string solutions which reproduce the observable data. The subsequent…
The goal of this article is to provide an explicit algorithmic construction of formal $F$-manifold structures, formal Frobenius manifold structures, and higher residue pairings on the primitive middle-dimensional cohomology $\mathbb{H}$ of…
We determine the $d+1$ dimensional topological field theory, which encodes the higher-form symmetries and their 't Hooft anomalies for $d$-dimensional QFTs obtained by compactifying M-theory on a non-compact space $X$. The resulting theory,…
We introduce a class of potential submanifolds in pseudo-Euclidean spaces (each N-dimensional potential submanifold is a special flat torsionless submanifold in a 2N-dimensional pseudo-Euclidean space) and prove that each N-dimensional…
We examine the relation between supersymmetric localization on $\mathbb{S}^4$ and standard QFT results for non-conformal theories in flat space. Specifically, we consider 1/2 BPS circular Wilson loops in four-dimensional SU($N$)…
It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by…
$T\bar{T}$ deformed conformal field theories can be reformulated as worldsheet theories of non-critical strings. We use this correspondence to compute and study the $T\bar{T}$ deformed partition sum of a symmetric product CFT. We find that…
The base space of a semi-universal unfolding of a hypersurface singularity carries a rich geometric structure, which was axiomatized as a CDV-structure by C. Hertling. For any CDV-structure on a Frobenius manifold M, the pull-back of the…
This paper is based on the author's talk at 1997 Taniguchi Symposium ``Integrable Systems and Algebraic Geometry''. We consider an approach to the theory of Frobenius manifolds based on the geometry of flat pencils of contravariant metrics.…
We show that the non-gravitational sectors of certain 6d and 5d supergravity theories can be decomposed into superconformal field theories (SCFTs) which are coupled together by pairwise identifying and gauging mutual global symmetries. In…