Related papers: Old-fashioned dualities revisited
We consider Hilbert's problem of the axioms of Physics at a qualitative or conceptual level. This issue is more pressing than ever as we seek to understand how both General Relativity and quantum theory could emerge from some deeper theory…
These notes are based on lectures presented at the 2001 Les Houches Summerschool ``Unity from Duality: Gravity, Gauge Theory and Strings''
M. Kobayashi introduced a notion of duality of weight systems. We tone this notion slightly down to a notion called coupling. We show that coupling induces a relation between the reduced zeta functions of the monodromy operators of the…
We discuss duality and mirror symmetry phenomena of Landau-Ginzburg orbifolds considering their elliptic genera. Under the duality (or mirror) transform performed by orbifoldizing the Landau-Ginzburg model via some discrete group of the…
A review of the properties of this alternate basis is presented. To appear in the proceedings of the 3rd Workshop on Thermal Field Theory, Banff, August 1993.
In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell's equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of…
The so-called Takahashi's \emph{Inversion Theorem}, the reconstruction of a given spinor based on its bilinear covariants, are re-examined, considering alternative dual structures. In contrast to the classical results, where the Dirac dual…
We begin by presenting a symmetric version of the circle equivariant T-duality result in a joint work of the second author with Siye Wu, thereby generalising the results there. We then initiate the study of twisted equivariant Courant…
Gravity duals for little string theories --- which give rise to four-dimensional theories that undergo permanent confinement in the infrared --- have not been studied in great detail. We address this question in the framework of heterotic…
Generalized dualities had an intriguing incursion into Double Field Theory (DFT) in terms of local $O(d,d)$ transformations. We review this idea and use the higher derivative formulation of DFT to compute the first order corrections to…
Open effective field theories provide a systematic framework for describing systems coupled to an environment, where dissipation, noise, and modified conservation laws naturally arise. Working within the Schwinger-Keldysh formalism, we…
We review some of the recent work on the dynamics of four dimensional, supersymmetric gauge theories. The kinematics are largely determined by holomorphy and the dynamics are governed by duality. The results shed light on the phases of…
We answer to 72 frequently asked questions about theories of multifractional spacetimes. Apart from reviewing and reorganizing what we already know about such theories, we discuss the physical meaning and consequences of the very recent…
We present a technique for deriving certain new natural dualities for any variety of algebras generated by a finite Heyting chain. The dualities we construct are tailored to admit a transparent translation to the more pictorial…
The last two decades have seen the emergence of stunning interconnections among various previously remotely related disciplines such as condensed matter, nuclear physics, gravity and quantum information, fueled both by experimental advances…
CONTENTS: 1 Introduction 2 Analytic Manifolds and Analytic Continuation of Metrics 3 Walker's Spacetimes and their Maximal Extension 4 Global Structure of de Sitter and Reissner-Nordstr\"om-de Sitter Cosmos 4.1 Special Cases 4.2 Collapsing…
We study the dynamics of a large class of N=1 quiver theories, geometrically realized by type IIB D-brane probes wrapping cycles of local Calabi-Yau threefolds. These include N=2 (affine) A-D-E quiver theories deformed by superpotential…
We consider quotients of string and M-theory by discrete subgroups of the U-duality group. This results in what we call O-folds, which are generalisations of orbifolds and orientifolds, and generically involve non-geometric identifications…
We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…
These are the notes of a series of lectures delivered by the author at the Graduate School of Mathematics of the University of Tokyo, during the month of October 2015. They were meant to be as self-contained as possible, taking into account…