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We study a generalization of higher gauge theory which makes use of generalized geometry and seems to be closely related to double field theory. The local kinematical data of this theory is captured by morphisms of graded manifolds between…
We study the twisted version of the supersymmetric $G/T=SU(n)/U(1)^{\otimes(n-1)} gauged Wess-Zumino-Witten model. By studying its fixed points under BRST transformation this model is shown to be reduced to a simple topological field…
We study Minkowski supersymmetric flux vacua of type II string theory. Based on the work by M. Grana, R. Minasian, M. Petrini and A. Tomasiello, we briefly explain how to reformulate things in terms of Generalized Complex Geometry, which…
Given a two-dimensional quantum lattice model with an abelian gauge theory interpretation, we investigate a duality operation that amounts to gauging its invertible 1-form symmetry, followed by gauging the resulting 0-form symmetry in a…
We construct two-parameter families of integrable $\lambda$-deformations of two-dimensional field theories. These interpolate between a CFT (a WZW/gauged WZW model) and the non-Abelian T-dual of a principal chiral model on a group/symmetric…
We review and pursue further the study of constrained realisations of affine Gaudin models, which form a large class of two-dimensional integrable field theories with gauge symmetries. In particular, we develop a systematic gauging…
We explore various aspects of 2-form topological gauge theories in (3+1)d. These theories can be constructed as sigma models with target space the second classifying space $B^2G$ of the symmetry group $G$, and they are classified by…
Following recent advances in the local theory of current-algebraic orbifolds, we study various geometric properties of the general WZW orbifold, the general coset orbifold and a large class of (non-linear) sigma model orbifolds. Phase-space…
We note that two formulations of dual gonihedric Ising models in 3d, one based on using Wegner's general framework for duality to construct a dual Hamiltonian for codimension one surfaces, the other on constructing a dual Hamiltonian for…
In this paper we identify the problem of equivariant vortex counting in a $(2,2)$ supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov-Witten invariants of the GIT quotient target…
We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $GL(n)/K$ where $K$ is an orthogonal or symplectic group. In…
It is known that connected translation invariant $n$-dimensional noncommutative differentials $d x^i$ on the algebra $k[x^1,\cdots,x^n]$ of polynomials in $n$-variables over a field $k$ are classified by commutative algebras $V$ on the…
We introduce Orbifold Reduction, a new method for generating $2d$ $(0,2)$ gauge theories associated to D1-branes probing singular toric Calabi-Yau 4-folds starting from $4d$ $\mathcal{N}=1$ gauge theories on D3-branes probing toric…
We discuss observables of an equivariant extension of the A-model in the framework of the AKSZ construction. We introduce the A-model observables, a class of observables that are homotopically equivalent to the canonical AKSZ observables…
${\bf Z}_2\times {\bf Z}_2$ Coxeter orbifolds are constructed with the property that some twisted sectors have fixed planes for which the six-torus can not be decomposed into a direct sum ${\bf T}^2\bigoplus{\bf T}^4 $ with the fixed plane…
We sketch a procedure to capture general non-invertible symmetries of a d-dimensional quantum field theory in the data of a higher-category, which captures the local properties of topological defects associated to the symmetries. We also…
We show how the theory of $\mathbb{Z}_2^n$ -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such…
We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group $G$ associated to outer automorphisms of $G$, and their corresponding defects. We show that the gauge theory partition function with defects can be…
We discuss Z_2 \times Z_2 orientifolds where the orbifold twists are accompanied by shifts on momentum or winding lattice states. The models contain variable numbers of D5 branes, whose massless (and, at times, even massive) modes have…
In this paper, we study the all genus Gromov-Witten theory for any GKM orbifold $X$. We generalize the Givental formula which is studied in the smooth case in \cite{Giv2} \cite{Giv3} \cite{Giv4} to the orbifold case. Specifically, we…