Related papers: D-particle Field Category

Let $\g_1$ and $\g_2$ be two dg Lie algebras, then it is well-known that the $L_\infty$ morphisms from $\g_1$ to $\g_2$ are in 1-1 correspondence to the solutions of the Maurer-Cartan equation in some dg Lie algebra $\Bbbk(\g_1,\g_2)$. Then…

In this paper, we establish a theorem that proves a condition when an inclusion morphism between simplicial sets becomes a weak homotopy equivalence. Additionally, we present two applications of this result. The first application…

We argue that quantum Liouville field theory supplemented with a suitable source term is the effective theory which describes the short-range correlations of the gluon saturation momentum in the two-dimensional impact-parameter space, at…

Inspired by the low wave-length limit of topological M-theory, which re-constructs the theory of $3+1$D gravity in the self-dual variables' formulation, and by the realization that in Loop Quantum Gravity the holonomy of a flat connection…

The dissipative Hofstadter model, which describes a particle in 2-D subject to a periodic potential, uniform magnetic field, and dissipation, is also related to open string boundary states. This model exhibits an SL(2,Z) duality symmetry…

Quantum coherence stemming from the superposition behaviour of a particle beyond the classical realm, serves as one of the most fundamental features in quantum mechanics. The wave-particle duality phenomenon, which shares the same origin,…

Let $D$ be a large category which is cocomplete. We construct a model structure (in the sense of Quillen) on the category of small functors from $D$ to simplicial sets. As an application we construct homotopy localization functors on the…

The partition function of $D_{N+1}$ topological string, the coupled system of topological gravity and $D_{N+1}$ topological minimal matter , is proposed in the framework of KP hierarchy. It is specified by the elements of $GL(\infty)$ which…

We consider the D2-brane probe action in the gravity background dual to N coincident Dp-branes by treating the separation between the D2- and Dp-branes as a nondynamical parameter for $p=2,4,6$. The gauge coupling, the core size of a…

Let A be a dg category, F:A->A a dg functor inducing an equivalence of categories in degree-zero cohomology, and A/F the associated dg orbit category. For every A1-homotopy invariant (e.g. homotopy K-theory, K-theory with coefficients,…

We give rigorous foundations for parametrized homotopy theory in this monograph. After preliminaries on point-set topology, base change functors, and proper actions of non-compact Lie groups, we develop the homotopy theory of equivariant…

We make explicit some conditions on a semi-abelian category D such that, for any abelian group A in D and any object Y in D, the cohomology group homomorphisms with coefficients in A, induced by the inclusion of the abelian objects of D at…

We introduce and study a notion of duality for two classes of optimization problems commonly occurring in probability theory. That is, on an abstract measurable space $(\Omega,\mathcal{F})$, we consider pairs $(E,\mathcal{G})$ where $E$ is…

We develop a new perspective on the discretization of the phase space structure of gravity in 2+1 dimensions as a piecewise-flat geometry in 2 spatial dimensions. Starting from a subdivision of the continuum geometric and phase space…

The first part of the series formulates the Einstein-Cartan theory in the covariant hamiltonian framework. The first section revises the general multisymplectic approach and introduces the notion of the d-jet bundles. Since the whole…

We perform an in-depth analysis of the transformation rules under duality for couplings of theories containing multiple scalars, $p$-form gauge fields, linearized gravitons or $(p,1)$ mixed symmetry tensors. Following a similar reasoning to…

We classify possible `self-duality' equations for p-form gauge fields in space-time dimension up to D=16, generalizing the pioneering work of Corrigan et al. (1982) on Yang-Mills fields (p=1) for D from 5 to 8. We impose two crucial…

We suggest that the physically irrelevant choice of a representative worldline of a relativistic spinning particle should correspond to a gauge symmetry in an action approach. Using a canonical formalism in special relativity, we identify a…

The notion of conformal algebras was introduced by Victor G. Kac using the axiomatic description of the operator product expansion of chiral fields in conformal field theory. The structure theory, representations and cohomology of Lie and…

Let $R$ be a commutative ring with unit. We consider the homotopy theory of the category of spectral sequences of $R$-modules with the class of weak equivalences given by those morphisms inducing a quasi-isomorphism at a certain fixed page.…