Related papers: Invariant quasimorphisms and generalized mixed Bav…
Toric Duality arises as an ambiguity in computing the quiver gauge theory living on a D3-brane which probes a toric singularity. It is reviewed how, in simple cases Toric Duality is Seiberg Duality. The set of all Seiberg Dualities on a…
In string theory it is known that abelian isometries in the sigma model lead to target space duality. We generalize this duality to backgrounds with non--abelian isometries. The procedure we follow consists of gauging the isometries of the…
We extend the techniques of double field theory to more general gravity theories and U-duality symmetries, having in mind applications to the complete D=11 supergravity. In this paper we work out a (3+3)-dimensional `U-duality…
Solutions to scalar theories with derivative self-couplings often have regions where non-linearities are important. Given a classical source, there is usually a region, demarcated by the Vainshtein radius, inside of which the classical…
We give a new geometric proof of a theorem of Heuer showing that, in the presence of letter-quasimorphisms (which are analogues of real-valued quasimorphisms with image in free groups), and in particular in RAAGs, there is a sharp lower…
Non-Abelian duality transformations built on non-semi-simple isometry groups are analysed. We first give the conditions under which the original non-linear sigma model and its non-Abelian dual are equivalent. The existence of an invariant…
In the paper we introduce a notion of the Bruck-Reilly $\lambda$-polycyclic extension of a monoid $S$ with a homomorphism $\theta$ which is an analogue of the Bruck-Reilly extension of a monoid $S$. We describe idempotens of the semigroup…
We study the action of the $SL(2;R)$ group on the noncommutative DBI Lagrangian. The symmetry conditions of this theory under the above group will be obtained. These conditions determine the extra U(1) gauge field. By introducing some…
We introduce the notion of an invariantly universal pair (S,E) where S is an analytic quasi-order and E \subseteq S is an analytic equivalence relation. This means that for any analytic quasi-order R there is a Borel set B invariant under E…
The theory of quasirandomness has greatly expanded from its inaugural graph theoretical setting to several different combinatorial objects such as hypergraphs, tournaments, permutations, etc. However, these quasirandomness variants have…
We analyse the global (rigid) symmetries that are realised on the bosonic fields of the various supergravity actions obtained from eleven-dimensional supergravity by toroidal compactification followed by the dualisation of some subset of…
We study 4d superconformal indices for a large class of N=1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T^2. An exchange of loops, which we call a…
Dualities between quantum field theories have proven to be a powerful tool in various areas of physics. In this paper, we introduce a new perspective for obtaining strong coupling expansions based on a well-known technique -- the…
A differential calculus of the first order over multi-braided quantum groups is developed. In analogy with the standard theory, left/right-covariant and bicovariant differential structures are introduced and investigated. Furthermore,…
Duality is one of the oldest known symmetries of Maxwell equations. In recent years the significance of duality symmetry has been recognized in superstrings and high energy physics and there has been a renewed interest on the question of…
Division algebras have demonstrated their utility in studying non-associative algebras and their connection to the Standard Model through complex Clifford algebras. This article focuses on exploring the connection between these complex…
We prove a higher-dimensional Chevalley restriction theorem for orthogonal groups, which was conjectured by Chen and Ng\^{o} for reductive groups. In characteristic $p>2$, we also prove a weaker statement. In characteristic $0$, the theorem…
Gauge theories in four dimensions can exhibit interesting low energy phenomena, such as infrared enhancements of global symmetry. We explore a class of 4d N=1 gauge theories arising from a construction that is motivated by duality walls in…
The notion of quadratic self-duality for coalgebras is developed with applications to algebraic structures which arise naturally in algebraic topology, related to the universal Steenrod algebra via an appropriate form of duality. This…
We examine from an invariant theory viewpoint the monoid algebras for two monoids having large symmetry groups. The first monoid is the free left-regular band on $n$ letters, defined on the set of all injective words, that is, the words…