Related papers: Quantum ${D_4}$ Drinfeld-Sokolov hierarchy and qua…

It is shown how a chiral Wess-Zumino-Witten theory with globally defined vertex operators and a one-to-one correspondence between fields and states can be constructed. The Hilbert space of this theory is the direct sum of tensor products of…

Double Field Theory (DFT) is an attempt to make the O(d,d) T-duality symmetry of string theory manifest, already before reducing on a d-torus. It is known that supergravity can be formulated in an O(D,D) covariant way, and remarkably this…

We continue our program initiated in [arXiv:0912.4261] to consider supersymmetric surface operators in a topologically-twisted N=2 pure SU(2) gauge theory, and apply them to the study of four-manifolds and related invariants. Elegant…

We prove a version of de Rham and Hyodo-Kato flip-flopping for dual towers of rigid analytic spaces including those coming from dual basic local Shimura varieties. The main tool are comparison theorems expressing the two cohomologies as…

Given a closed symplectic manifold $X$, we construct Gromov-Witten-type invariants valued both in (complex) $K$-theory and in any complex-oriented cohomology theory $\mathbb{K}$ which is $K_p(n)$-local for some Morava $K$-theory $K_p(n)$.…

We develop the deformation theory of cohomological field theories (CohFTs), which is done as a special case of a general deformation theory of morphisms of modular operads. This leads us to introduce two new natural extensions of the notion…

The complexified ${\Bbb Z}/2$-graded $C^\infty$-Algebraic Geometry aspect of a superspace(-time) $\widehat{X}$ in Sec.\,1 of D(14.1) (arXiv:1808.05011 [math.DG]) together with the Spin-Statistics Theorem in Quantum Field Theory, which…

By constructing new quasimap compactifications of Hurwitz spaces of degrees 4 and 5, we establish a new connection between arithmetic statistics, quantum algebra, and geometry and answer a question of Ellenberg-Tran-Westerland and…

We take the first steps in a systematic study of Group Field Theory renormalization, focusing on the Boulatov model for 3D quantum gravity. We define an algorithm for constructing the 2D triangulations that characterize the boundary of the…

After global completion of higher gauge fields (as appearing in higher-dimensional supergravity) by proper flux quantization in extraordinary nonabelian cohomology, the (non-perturbative, renormalized) topological quantum observables and…

Circuit complexity for two-dimensional topological quantum field theories (2D TQFT) was defined by Couch, Fan, and Shashi in [12]. In this paper, we study complexity for the 2D TQFT given by quantum cohomology of compact symplectic…

This article presents a formula for products of Schubert classes in the quantum cohomology ring of the Grassmannian. We introduce a generalization of Schur symmetric polynomials for shapes that are naturally embedded in a torus. Then we…

We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4 d=3 supersymmetric gauge theory…

We study the issue of diffeomorphism symmetry in group field theories (GFT), using the recently introduced noncommutative metric representation. In the colored Boulatov model for 3d gravity, we identify a field (quantum) symmetry which ties…

We provide descriptions of the derived categories of degree $d$ hypersurface fibrations which generalize a result of Kuznetsov for quadric fibrations and give a relative version of a well-known theorem of Orlov. Using a local generator and…

In this paper we prove the following results: Given the Drinfeld double $\mathcal{A}^{ext}_{Q}$ of the localised preprojective $K$-theoretic Hall algebra $\mathcal{A}^{+}_{Q}$ of quiver type $Q$ with the Cartan elements, there is a…

Recall that Tamarkin's construction arXiv:math/9803025, arXiv:math/0003052 gives us a map from the set of Drinfeld associators to the set of homotopy classes of L-infinity quasi-isomorphisms for Hochschild cochains of a polynomial algebra.…

Double Field Theory suggests that people can view the whole massless NS-NS sector as the gravitational unity. The $O(D,D)$ covariance and the doubled diffeomorphisms determine precisely how the Standard Model as well as a relativistic point…

A topological quantum field theory is introduced which reproduces the Seiberg-Witten invariants of four-manifolds. Dimensional reduction of this topological field theory leads to a new one in three dimensions. Its partition function yields…

To describe quantal collective phenomena, it is useful to requantize the time-dependent mean-field dynamics. We study the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory for the two-level pairing Hamiltonian, and compare results of…